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math_qa__TZ2xBDTkDxGzNlng
in a group of 86 students , each student is registered for at least one of 3 classes – history , math and english . 20 - 8 students are registered for history , 20 - 3 students are registered for math , and forty - 4 students are registered for english . if only 3 students are registered for all 3 classes , how many students are registered for exactly two classes ? Choose the correct answer. A) 3 B) 10 C) 9 D) 8 E) 7
<gadget id="calculator">20 + 3</gadget> <output>23</output> <gadget id="calculator">20 + 8</gadget> <output>28</output> <gadget id="calculator">23 + 28</gadget> <output>51</output> <gadget id="calculator">4 * 10</gadget> <output>40</output> <gadget id="calculator">40 + 4</gadget> <output>44</output> <gadget id="calculator">51 + 44</gadget> <output>95</output> <gadget id="calculator">3 * 3</gadget> <output>9</output> <gadget id="calculator">95 - 9</gadget> <output>86</output> <gadget id="calculator">86 - 3</gadget> <output>83</output> <gadget id="calculator">86 - 83</gadget> <output>3</output> <result>A</result>
A
3
in a group of 86 students , each student is registered for at least one of 3 classes – history , math and english . 20 - 8 students are registered for history , 20 - 3 students are registered for math , and forty - 4 students are registered for english . if only 3 students are registered for all 3 classes , how many students are registered for exactly two classes ?
{ "A": "3", "B": "10", "C": "9", "D": "8", "E": "7" }
subtract(subtract(add(add(add(20, 3), add(20, 8)), add(multiply(4, const_10), 4)), multiply(3, 3)), subtract(86, 3))
add(n1,n2)|add(n2,n3)|multiply(n6,const_10)|multiply(n1,n1)|subtract(n0,n1)|add(#0,#1)|add(n6,#2)|add(#5,#6)|subtract(#7,#3)|subtract(#8,#4)
a u b u c = a + b + c - ab - bc - ac + abc 86 = 28 + 23 + 44 - ab - bc - ac + 3 = > ab + bc + ac = 12 exactly two classes = ab + bc + ac - 3 abc = 12 - 3 * 3 = 3 hence a
general
math_qa__8UL0dF2Maa1v09At
A man can row his boat with the stream at 24 km/h and against the stream in 10 km/h. The man's rate is? Choose the correct choice from the following options: A) 1 kmph B) 6 kmph C) 7 kmph D) 4 kmph E) 9 kmph
<gadget id="calculator">24 - 10</gadget> <output>14</output> <gadget id="calculator">14 / 2</gadget> <output>7</output> <result>C</result>
C
7
A man can row his boat with the stream at 24 km/h and against the stream in 10 km/h. The man's rate is?
{ "A": "1 kmph", "B": "6 kmph", "C": "7 kmph", "D": "4 kmph", "E": "9 kmph" }
divide(subtract(24, 10), const_2)
subtract(n0,n1)|divide(#0,const_2)|
"explanation : ds = 24 us = 10 s = ? s = ( 24 - 10 ) / 2 = 7 kmph answer : c"
gain
math_qa__rQhKYfyIGSoyLQEB
There were totally 100 men.82 are married.75 have T.V, 85 have radio,70 have A.C. How many men have T.V, radio, A.C and also married? Choose the correct choice from the following answers: A) 11 B) 12 C) 13 D) 14 E) 15
<gadget id="calculator">100 - 82</gadget> <output>18</output> <gadget id="calculator">100 - 75</gadget> <output>25</output> <gadget id="calculator">18 + 25</gadget> <output>43</output> <gadget id="calculator">100 - 85</gadget> <output>15</output> <gadget id="calculator">43 + 15</gadget> <output>58</output> <gadget id="calculator">100 - 70</gadget> <output>30</output> <gadget id="calculator">58 + 30</gadget> <output>88</output> <gadget id="calculator">100 - 88</gadget> <output>12</output> <result>B</result>
B
12
There were totally 100 men.82 are married.75 have T.V, 85 have radio,70 have A.C. How many men have T.V, radio, A.C and also married?
{ "A": "11", "B": "12", "C": "13", "D": "14", "E": "15" }
subtract(100, add(add(add(subtract(100, 82), subtract(100, 75)), subtract(100, 85)), subtract(100, 70)))
subtract(n0,n1)|subtract(n0,n2)|subtract(n0,n3)|subtract(n0,n4)|add(#0,#1)|add(#4,#2)|add(#5,#3)|subtract(n0,#6)|
"100 - ( 100 - 82 ) - ( 100 - 75 ) - ( 100 - 85 ) - ( 100 - 70 ) = 100 - 18 - 25 - 15 - 30 = 100 - 88 = 12 answer : b"
general
math_qa__4v8IbAXYDZ033XTV
The roof of an apartment building is rectangular and its length is 4 times longer than its width. If the area of the roof is 900 feet squared, what is the difference between the length and the width of the roof? Choose the correct answer A) 38 . B) 40 . C) 42 . D) 44 . E) 45 .
<gadget id="calculator">900 / 4</gadget> <output>225</output> <gadget id="calculator">225 ** (1/2)</gadget> <output>15</output> <gadget id="calculator">15 * 4</gadget> <output>60</output> <gadget id="calculator">60 - 15</gadget> <output>45</output> <result>E</result>
E
45
The roof of an apartment building is rectangular and its length is 4 times longer than its width. If the area of the roof is 900 feet squared, what is the difference between the length and the width of the roof?
{ "A": "38 .", "B": "40 .", "C": "42 .", "D": "44 .", "E": "45 ." }
subtract(multiply(sqrt(divide(900, 4)), const_4), sqrt(divide(900, 4)))
divide(n1,n0)|sqrt(#0)|multiply(#1,const_4)|subtract(#2,#1)
let the width = x x * 4 x = 900 x ^ 2 = 225 x = 15 length = 4 * 15 = 60 difference = 60 - 15 = 45 e is the answer
geometry
math_qa__NuCjl3rujS3g7Unx
Sachin is younger than Rahul by 18 years. If the ratio of their ages is 7:9, find the age of Sachin Pick one. A) 24.5 B) 63 C) 65 D) 36 E) 24.19
<gadget id="calculator">9 - 7</gadget> <output>2</output> <gadget id="calculator">18 / 2</gadget> <output>9</output> <gadget id="calculator">9 * 7</gadget> <output>63</output> <result>B</result>
B
63
Sachin is younger than Rahul by 18 years. If the ratio of their ages is 7:9, find the age of Sachin
{ "A": "24.5", "B": "63", "C": "65", "D": "36", "E": "24.19" }
multiply(divide(18, subtract(9, 7)), 7)
subtract(n2,n1)|divide(n0,#0)|multiply(n1,#1)|
"explanation : if rahul age is x , then sachin age is x - 18 , so , 9 x - 162 = 7 x 2 x = 162 x = 81 so sachin age is 81 - 18 = 63 answer : b ) 63"
other
math_qa__Sak9wd0rATzS4dEL
Average monthly income of a family of 4 earning members was Rs. 735. One of the earning members died and therefore, the average income came down to Rs 590. The income of the deceased was? Select the correct option: A) rs . 692.80 B) rs . 820 C) rs . 1170 D) rs . 1385 E) none
<gadget id="calculator">735 * 4</gadget> <output>2_940</output> <gadget id="calculator">4 - 1</gadget> <output>3</output> <gadget id="calculator">590 * 3</gadget> <output>1_770</output> <gadget id="calculator">2_940 - 1_770</gadget> <output>1_170</output> <result>C</result>
C
1,170
Average monthly income of a family of 4 earning members was Rs. 735. One of the earning members died and therefore, the average income came down to Rs 590. The income of the deceased was?
{ "A": "rs . 692.80", "B": "rs . 820", "C": "rs . 1170", "D": "rs . 1385", "E": "none" }
subtract(multiply(735, 4), multiply(590, subtract(4, const_1)))
multiply(n0,n1)|subtract(n0,const_1)|multiply(n2,#1)|subtract(#0,#2)|
"answer income of the deceased = total income of 4 members - total income of remaining 3 members . = 735 x 4 - 590 x 3 rs . = 1170 rs . correct option : c"
general
math_qa__cwv6zLwyL3dwuFIR
Peter invested a certain sum of money in a simple interest bond whose value grew to $100 at the end of 2 years and further to $200 at the end of another 4 years. What was the rate of interest in which he invested his sum? Select A) 50 % B) 25 % C) 10 % D) 30 % E) 18 %
<gadget id="calculator">200 - 100</gadget> <output>100</output> <gadget id="calculator">100 / 4</gadget> <output>25</output> <gadget id="calculator">25 * 2</gadget> <output>50</output> <gadget id="calculator">100 - 50</gadget> <output>50</output> <gadget id="calculator">25 / 50</gadget> <output>1/2 = around 0.5</output> <gadget id="calculator">(1/2) * 100</gadget> <output>50</output> <result>A</result>
A
50
Peter invested a certain sum of money in a simple interest bond whose value grew to $100 at the end of 2 years and further to $200 at the end of another 4 years. What was the rate of interest in which he invested his sum?
{ "A": "50 %", "B": "25 %", "C": "10 %", "D": "30 %", "E": "18 %" }
multiply(divide(divide(subtract(200, 100), 4), subtract(100, multiply(divide(subtract(200, 100), 4), 2))), const_100)
subtract(n2,n0)|divide(#0,n3)|multiply(n1,#1)|subtract(n0,#2)|divide(#1,#3)|multiply(#4,const_100)|
"explanatory answer initial amount invested = $ x amount at the end of year 2 = $ 100 amount at the end of year 6 ( another 4 years ) = $ 200 therefore , the interest earned for the 4 year period between the 2 rd year and 6 th year = $ 200 - $ 100 = $ 100 as the simple interest earned for a period of 4 years is $ 100 , interest earned per year = $ 25 . therefore , interest earned for 2 years = 2 * 25 = $ 50 . hence , initial amount invested x = amount after 2 years - interest for 2 years = 100 - 50 = $ 50 . rate of interest = ( interest per year / principal ) * 100 = 25 / 50 * 100 = 50 % correct choice is a"
gain
math_qa__LIDEcCOSIt4me7aH
Two Nascar stock cars take off from the starting line at the exact same time, heading in opposite directions. The Budweiser Car travels at 145 miles per hour, while the Stella Artois car travels at 150 miles per hour. At this rate, and ignoring other variable, how long will the cars have to drive in order to be 500 miles, in total, from each other? Choices A) 1.5 hours B) 1.27 hours C) 1.73 hours D) 2 hours E) 1.69 hours
<gadget id="calculator">145 + 150</gadget> <output>295</output> <gadget id="calculator">500 / 295</gadget> <output>100/59 = around 1.694915</output> <result>E</result>
E
1.69
Two Nascar stock cars take off from the starting line at the exact same time, heading in opposite directions. The Budweiser Car travels at 145 miles per hour, while the Stella Artois car travels at 150 miles per hour. At this rate, and ignoring other variable, how long will the cars have to drive in order to be 500 miles, in total, from each other?
{ "A": "1.5 hours", "B": "1.27 hours", "C": "1.73 hours", "D": "2 hours", "E": "1.69 hours" }
divide(500, add(145, 150))
add(n0,n1)|divide(n2,#0)
the cars travel ( 145 + 150 = 295 ) miles in one hour . 500 miles / 295 miles / hour = 1.69 hours answer is e
general
math_qa__e63Cr1oD1zoHHy6y
At a loading dock, each worker on the night crew loaded 3/4 as many boxes as each worker on the day crew. If the night crew has 2/3 as many workers as the day crew, what fraction of all the boxes loaded by the two crews did the day crew load? Choose the correct choice from the following choices: A) 1 / 2 B) 2 / 3 C) 3 / 5 D) 4 / 5 E) 5 / 8
<gadget id="calculator">3 * 4</gadget> <output>12</output> <gadget id="calculator">3 * 2</gadget> <output>6</output> <gadget id="calculator">12 + 6</gadget> <output>18</output> <gadget id="calculator">12 / 18</gadget> <output>2/3 = around 0.666667</output> <result>B</result>
B
0.666667
At a loading dock, each worker on the night crew loaded 3/4 as many boxes as each worker on the day crew. If the night crew has 2/3 as many workers as the day crew, what fraction of all the boxes loaded by the two crews did the day crew load?
{ "A": "1 / 2", "B": "2 / 3", "C": "3 / 5", "D": "4 / 5", "E": "5 / 8" }
divide(multiply(3, 4), add(multiply(3, 4), multiply(3, 2)))
multiply(n1,n3)|multiply(n0,n2)|add(#0,#1)|divide(#0,#2)|
"let x be the number of workers on the day crew . let y be the number of boxes loaded by each member of the day crew . then the number of boxes loaded by the day crew is xy . the number of boxes loaded by the night crew is ( 2 x / 3 ) ( 3 y / 4 ) = xy / 2 the total number of boxes is xy + xy / 2 = 3 xy / 2 the fraction loaded by the day crew is xy / ( 3 xy / 2 ) = 2 / 3 the answer is b ."
physics
math_qa__eihjkzQqSEmLyVws
Find the average of all numbers between 6 and 36 which are divisible by 7 Choose the correct choice from the following: A) 20 B) 15 C) 25 D) 30 E) 35
<gadget id="calculator">7 * 3</gadget> <output>21</output> <gadget id="calculator">7 * 2</gadget> <output>14</output> <gadget id="calculator">7 + 14</gadget> <output>21</output> <gadget id="calculator">21 + 21</gadget> <output>42</output> <gadget id="calculator">7 * 4</gadget> <output>28</output> <gadget id="calculator">42 + 28</gadget> <output>70</output> <gadget id="calculator">4 + 1</gadget> <output>5</output> <gadget id="calculator">5 * 7</gadget> <output>35</output> <gadget id="calculator">70 + 35</gadget> <output>105</output> <gadget id="calculator">105 / 7</gadget> <output>15</output> <result>B</result>
B
15
Find the average of all numbers between 6 and 36 which are divisible by 7
{ "A": "20", "B": "15", "C": "25", "D": "30", "E": "35" }
divide(add(add(add(multiply(7, const_3), add(7, multiply(7, const_2))), multiply(7, const_4)), multiply(add(const_4, const_1), 7)), 7)
add(const_1,const_4)|multiply(n2,const_2)|multiply(n2,const_3)|multiply(n2,const_4)|add(n2,#1)|multiply(n2,#0)|add(#4,#2)|add(#6,#3)|add(#7,#5)|divide(#8,n2)
explanation : average = ( 7 + 14 + 21 + 28 + 35 ) / 7 = 105 / 7 = 15 option b
general
math_qa__3Aitg2NmT15ASaFb
In how many ways 3 boys and 3 girls can be seated in a row so that they are alternate. Choose the correct choice from the following options: A) 144 B) 288 C) 36 D) 256 E) none
<gadget id="calculator">factorial(3)</gadget> <output>6</output> <gadget id="calculator">6 * 6</gadget> <output>36</output> <result>C</result>
C
36
In how many ways 3 boys and 3 girls can be seated in a row so that they are alternate.
{ "A": "144", "B": "288", "C": "36", "D": "256", "E": "none" }
multiply(factorial(3), factorial(3))
factorial(n0)|factorial(n1)|multiply(#0,#1)|
"solution : let the arrangement be , b g b g b g b 34 boys can be seated in 3 ! ways . girl can be seated in 3 ! ways . required number of ways , = 3 ! * 3 ! = 36 . answer : option c"
probability
math_qa__sdE2mAnOq3hj25UQ
A straight line in the xy- plane has slope 4 . On this line the x-coordinate of the point is 50 and y-coordinate is 300 then what is the y intercept of the plane? Choose the correct choice: A) 150 B) 110 C) 100 D) 200 E) 50
<gadget id="calculator">50 * 4</gadget> <output>200</output> <gadget id="calculator">300 - 200</gadget> <output>100</output> <result>C</result>
C
100
A straight line in the xy- plane has slope 4 . On this line the x-coordinate of the point is 50 and y-coordinate is 300 then what is the y intercept of the plane?
{ "A": "150", "B": "110", "C": "100", "D": "200", "E": "50" }
subtract(300, multiply(50, 4))
multiply(n0,n1)|subtract(n2,#0)
eq of line = y = mx + c m = 4 x = 50 y = 50 * 4 + c , substitute y by 300 as given in question . 300 = 200 + c , c = 100 correct option is c
general
math_qa__kllj8BvopflxqBak
What two-digit number is less than the sum of the square of its digits by 13 and exceeds their doubled product by 5? Choose the correct choice from the following choices: A) 95 B) 99 C) 26 D) 73 E) none of the above
<gadget id="calculator">13 - 5</gadget> <output>8</output> <gadget id="calculator">8 + 1</gadget> <output>9</output> <gadget id="calculator">10 * 9</gadget> <output>90</output> <gadget id="calculator">90 + 5</gadget> <output>95</output> <result>B</result>
B
99
What two-digit number is less than the sum of the square of its digits by 13 and exceeds their doubled product by 5?
{ "A": "95", "B": "99", "C": "26", "D": "73", "E": "none of the above" }
add(multiply(const_10, add(subtract(13, 5), const_1)), 5)
subtract(n0,n1)|add(#0,const_1)|multiply(#1,const_10)|add(n1,#2)
let the digits be x and y . the number would be 10 x + y . we are given that 2 xy + 5 = 10 x + y = x ^ 2 y ^ 2 - 13 thus 2 xy + 5 = x ^ 2 + y ^ 2 - 13 x ^ 2 + y ^ 2 - 2 xy = 16 ( x - y ) ^ 2 = 16 ( x - y ) = 4 or - 4 substituting the values of ( x - y ) in the equation 2 xy + 5 = 10 x + y x comes out to be 1 or 9 . . . thus the two numbers can be 15 or 99 thus the answer is b
general
math_qa__AD92qSFN3we5KaeY
The surface area of a sphere is 4πR2, where R is the radius of the sphere. If the area of the base of a hemisphere is 3, what is the surface area Q of that hemisphere? Choose the correct choice from the following answers: A) 6 / π B) 9 / π C) 6 D) 9 E) 12
<gadget id="calculator">4 * pi</gadget> <output>4*pi = around 12.566371</output> <gadget id="calculator">3 / pi</gadget> <output>3/pi = around 0.95493</output> <gadget id="calculator">(4*pi) * (3/pi)</gadget> <output>12</output> <gadget id="calculator">12 / 2</gadget> <output>6</output> <gadget id="calculator">pi * (3/pi)</gadget> <output>3</output> <gadget id="calculator">6 + 3</gadget> <output>9</output> <result>D</result>
D
9
The surface area of a sphere is 4πR2, where R is the radius of the sphere. If the area of the base of a hemisphere is 3, what is the surface area Q of that hemisphere?
{ "A": "6 / π", "B": "9 / π", "C": "6", "D": "9", "E": "12" }
add(divide(multiply(multiply(4, const_pi), divide(3, const_pi)), 2), multiply(const_pi, divide(3, const_pi)))
divide(n2,const_pi)|multiply(n0,const_pi)|multiply(#0,#1)|multiply(#0,const_pi)|divide(#2,n1)|add(#4,#3)|
"given area of the base of a hemisphere is 3 = pi * r ^ 2 thus r = sqrt ( 3 / pi ) . surface area of whole sphere = 4 * pi * r ^ 2 . = 4 * pi * 3 / pi = 12 . since the hemisphere is half of a sphere the surface area of the hemisphere = 12 / 2 = 6 ( curved part , not including the flat rounded base ) . but the total surface area = 6 + area of the base of a hemisphere . = 6 + 3 = 9 . answer is d ! !"
geometry
math_qa__vgJ7o18gtxg4Zq6r
A river 3m deep and 36 m wide is flowing at the rate of 2 kmph the amount of water that runs into the sea per minute is? Select the correct option A) 4500 B) 2678 C) 3600 D) 3400 E) 2500
<gadget id="calculator">3 * 36</gadget> <output>108</output> <gadget id="calculator">2 * 1_000</gadget> <output>2_000</output> <gadget id="calculator">108 * 2_000</gadget> <output>216_000</output> <gadget id="calculator">1 * 60</gadget> <output>60</output> <gadget id="calculator">216_000 / 60</gadget> <output>3_600</output> <result>C</result>
C
3,600
A river 3m deep and 36 m wide is flowing at the rate of 2 kmph the amount of water that runs into the sea per minute is?
{ "A": "4500", "B": "2678", "C": "3600", "D": "3400", "E": "2500" }
divide(multiply(multiply(3, 36), multiply(2, const_1000)), multiply(const_1, const_60))
multiply(n0,n1)|multiply(n2,const_1000)|multiply(const_1,const_60)|multiply(#0,#1)|divide(#3,#2)|
"( 2000 * 3 * 36 ) / 60 = 3600 m 3 answer : c"
physics
math_qa__3XTIDzJ7DlXBqJBK
A train traveling at 100 kmph overtakes a motorbike traveling at 64 kmph in 20 seconds. What is the length of the train in meters? Choose the correct answer: A) 400 meters B) 1111 meters C) 1777 meters D) 200 meters E) none of these
<gadget id="calculator">100 - 64</gadget> <output>36</output> <gadget id="calculator">10 / 36</gadget> <output>5/18 = around 0.277778</output> <gadget id="calculator">36 * (5/18)</gadget> <output>10</output> <gadget id="calculator">10 * 20</gadget> <output>200</output> <result>D</result>
D
200
A train traveling at 100 kmph overtakes a motorbike traveling at 64 kmph in 20 seconds. What is the length of the train in meters?
{ "A": "400 meters", "B": "1111 meters", "C": "1777 meters", "D": "200 meters", "E": "none of these" }
multiply(multiply(subtract(100, 64), const_0_2778), 20)
subtract(n0,n1)|multiply(#0,const_0_2778)|multiply(n2,#1)|
"train overtakes a bike means that we are talking about total length of the train . ( train ' s head is close to bike when it started and its tail crosses the bike when it overtakes the bike ) relative speed = 100 - 64 = 36 km / h = 36000 m / h time = 20 seconds distance = speed * time 36000 * 20 / 3600 = 200 meters . d is the answer ."
physics
math_qa__qbYbSQhoEYP17Lwf
How many seconds will a 900 m long train take to cross a man walking with a speed of 3 km/hr in the direction of the moving train if the speed of the train is 63 km/hr? Choose the correct choice from the following answers. A) 23 sec B) 30 sec C) 49 sec D) 54 sec E) 59 sec
<gadget id="calculator">63 - 3</gadget> <output>60</output> <gadget id="calculator">10 / 36</gadget> <output>5/18 = around 0.277778</output> <gadget id="calculator">60 * (5/18)</gadget> <output>50/3 = around 16.666667</output> <gadget id="calculator">900 / (50/3)</gadget> <output>54</output> <result>D</result>
D
54
How many seconds will a 900 m long train take to cross a man walking with a speed of 3 km/hr in the direction of the moving train if the speed of the train is 63 km/hr?
{ "A": "23 sec", "B": "30 sec", "C": "49 sec", "D": "54 sec", "E": "59 sec" }
divide(900, multiply(subtract(63, 3), const_0_2778))
subtract(n2,n1)|multiply(#0,const_0_2778)|divide(n0,#1)|
"speed of train relative to man = 63 - 3 = 60 km / hr . = 60 * 5 / 18 = 50 / 3 m / sec . time taken to pass the man = 900 * 3 / 50 = 54 sec . answer : d"
physics
math_qa__fQMosUYhsedu3vNy
Two airplanes take off from one airfield at noon. One flies due east at 201 miles per hour while the other flies directly northeast at 283 miles per hour. Approximately how many miles apart are the airplanes at 2 p.m.? Pick. A) 166 B) 332 C) 400 D) 402 E) 566
<gadget id="calculator">283 * 2</gadget> <output>566</output> <gadget id="calculator">566 ** 2</gadget> <output>320_356</output> <gadget id="calculator">201 * 2</gadget> <output>402</output> <gadget id="calculator">402 ** 2</gadget> <output>161_604</output> <gadget id="calculator">320_356 - 161_604</gadget> <output>158_752</output> <gadget id="calculator">158_752 ** (1/2)</gadget> <output>44*sqrt(82) = around 398.436946</output> <result>D</result>
D
402
Two airplanes take off from one airfield at noon. One flies due east at 201 miles per hour while the other flies directly northeast at 283 miles per hour. Approximately how many miles apart are the airplanes at 2 p.m.?
{ "A": "166", "B": "332", "C": "400", "D": "402", "E": "566" }
sqrt(subtract(power(multiply(283, 2), 2), power(multiply(201, 2), 2)))
multiply(n1,n2)|multiply(n0,n2)|power(#0,n2)|power(#1,n2)|subtract(#2,#3)|sqrt(#4)|
"d in two hours : the plane flying east will be 402 miles away from airport . the other plane will be 566 miles away from airport . 566 / 402 = ~ 1.4 = ~ sqrt ( 2 ) this means that planes formed a right isocheles triangle = > sides of such triangles relate as 1 : 1 : sqrt ( 2 ) = > the planes are 402 miles apart . d"
physics
math_qa__tI2DpY307hrDsHjc
The ratio 4:20 expressed as percent equals to Choose the correct answer. A) 20 % B) 25 % C) 55 % D) 65 % E) none of above
<gadget id="calculator">4 / 20</gadget> <output>1/5 = around 0.2</output> <gadget id="calculator">(1/5) * 100</gadget> <output>20</output> <result>A</result>
A
20
The ratio 4:20 expressed as percent equals to
{ "A": "20 %", "B": "25 %", "C": "55 %", "D": "65 %", "E": "none of above" }
multiply(divide(4, 20), const_100)
divide(n0,n1)|multiply(#0,const_100)
explanation : actually it means 4 is what percent of 20 , which can be calculated as , ( 4 / 20 ) * 100 = 4 * 5 = 20 answer : option a
general
math_qa__LYTmemsNudD59YB1
jack takes a loan of $ 120000 with 12 % annual interest : the interest is paid once , at the end of the year . jill takes a loan of $ 120000 with 12 % annual interest , compounding monthly at the end of each month . at the end of one full year , compared to jack ' s loan interest , approximately how much more does jill have to repay ? Select: A) zero B) $ 81.90 C) $ 8190.03 D) $ 819.00 E) $ 8.19
<gadget id="calculator">12 * 100</gadget> <output>1_200</output> <gadget id="calculator">12 / 1_200</gadget> <output>1/100 = around 0.01</output> <gadget id="calculator">1 + (1/100)</gadget> <output>101/100 = around 1.01</output> <gadget id="calculator">(101/100) ** 12</gadget> <output>1_126_825_030_131_969_720_661_201/1_000_000_000_000_000_000_000_000 = around 1.126825</output> <gadget id="calculator">120_000 * (1_126_825_030_131_969_720_661_201/1_000_000_000_000_000_000_000_000)</gadget> <output>3_380_475_090_395_909_161_983_603/25_000_000_000_000_000_000 = around 135_219.003616</output> <gadget id="calculator">(3_380_475_090_395_909_161_983_603/25_000_000_000_000_000_000) - 120_000</gadget> <output>380_475_090_395_909_161_983_603/25_000_000_000_000_000_000 = around 15_219.003616</output> <gadget id="calculator">120_000 * 12</gadget> <output>1_440_000</output> <gadget id="calculator">1_440_000 / 100</gadget> <output>14_400</output> <gadget id="calculator">(380_475_090_395_909_161_983_603/25_000_000_000_000_000_000) - 14_400</gadget> <output>20_475_090_395_909_161_983_603/25_000_000_000_000_000_000 = around 819.003616</output> <result>D</result>
D
819
jack takes a loan of $ 120000 with 12 % annual interest : the interest is paid once , at the end of the year . jill takes a loan of $ 120000 with 12 % annual interest , compounding monthly at the end of each month . at the end of one full year , compared to jack ' s loan interest , approximately how much more does jill have to repay ?
{ "A": "zero", "B": "$ 81.90", "C": "$ 8190.03", "D": "$ 819.00", "E": "$ 8.19" }
subtract(subtract(multiply(120000, power(add(const_1, divide(12, multiply(12, const_100))), 12)), 120000), divide(multiply(120000, 12), const_100))
multiply(n1,const_100)|multiply(n0,n1)|divide(n1,#0)|divide(#1,const_100)|add(#2,const_1)|power(#4,n1)|multiply(n0,#5)|subtract(#6,n0)|subtract(#7,#3)
jack ' s interest = $ 120,000 * 0.12 = $ 14400 or $ 1,200 each month . jills ’ s interest , 12 % / 12 = 1 % each month : for the 1 st month = $ 120,000 * 0.01 = $ 1,200 ; for the 2 nd month = $ 1,200 + 1 % of 1,200 = $ 1,212 , so we would have interest earned on interest ( very small amount ) ; for the 3 rd month = $ 1,212 + 1 % of 1,212 = ~ $ 1,224 ; for the 4 th month = $ 1,224 + 1 % of 1,224 = ~ $ 1,236 ; . . . for the 12 th month = $ 1,320 + 1 % of 1,320 = ~ $ 1,332 . the difference between jack ' s interest and jill ’ s interest = ~ ( 12 + 24 + . . . + 132 ) = $ 792 . answer : d .
general
math_qa__NKiCExRgaby9OjBk
The area of one square is x^2 + 8x + 16 and the area of another square is 4x^2 − 12x + 9. If the sum of the perimeters of both squares is 32, what is the value of x? Choose the correct choice: A) 0 B) 2 C) 2.5 D) 7 / 3 E) 10
<gadget id="calculator">8 / 2</gadget> <output>4</output> <gadget id="calculator">4 * 4</gadget> <output>16</output> <gadget id="calculator">16 - 12</gadget> <output>4</output> <gadget id="calculator">32 - 4</gadget> <output>28</output> <gadget id="calculator">28 / 12</gadget> <output>7/3 = around 2.333333</output> <result>D</result>
D
2.333333
The area of one square is x^2 + 8x + 16 and the area of another square is 4x^2 − 12x + 9. If the sum of the perimeters of both squares is 32, what is the value of x?
{ "A": "0", "B": "2", "C": "2.5", "D": "7 / 3", "E": "10" }
divide(subtract(32, subtract(multiply(4, divide(8, 2)), 12)), 12)
divide(n1,n0)|multiply(#0,n3)|subtract(#1,n5)|subtract(n7,#2)|divide(#3,n5)|
"spotting the pattern of equations both are in form of ( x + c ) ^ 2 so a 1 = ( x + 4 ) ^ 2 a 2 = ( 2 x - 3 ) ^ 2 l 1 = x + 5 l 2 = 2 x - 3 p 1 = 4 ( x + 4 ) p 2 = 4 ( 2 x - 3 ) p 1 + p 2 = 32 4 ( x + 4 ) + 4 ( 2 x - 3 ) = 32 . . . . . . . . . . . . . . > x = 7 / 3 answer : d"
general
math_qa__AuUzr2GQLtqhS8SF
Evaluate 45 / .05 Choose the correct option: A) 700 B) 900 C) 705 D) none of these E) 506
<gadget id="calculator">5 / 45</gadget> <output>1/9 = around 0.111111</output> <gadget id="calculator">100 / (1/9)</gadget> <output>900</output> <result>B</result>
B
900
Evaluate 45 / .05
{ "A": "700", "B": "900", "C": "705", "D": "none of these", "E": "506" }
divide(const_100.0, divide(05, 45))
divide(n1,const_100)|divide(n0,#0)|
"explanation : 45 / . 05 = 4500 / 5 = 900 option b"
general
math_qa__oKioaliubIBQoUFS
How many 3-digit even numbers are possible such that if one of the digits is 5, the next/succeeding digit to it should be 1? Choose the correct choice from the following: A) 5 B) 305 C) 365 D) 405 E) 495
<gadget id="calculator">3 + 1</gadget> <output>4</output> <gadget id="calculator">4 + 1</gadget> <output>5</output> <result>A</result>
A
5
How many 3-digit even numbers are possible such that if one of the digits is 5, the next/succeeding digit to it should be 1?
{ "A": "5", "B": "305", "C": "365", "D": "405", "E": "495" }
add(add(3, 1), 1)
add(n0,n2)|add(n2,#0)
510 , 512 , 514 , 516 , and 518 , so total 5 . hence option a .
general
math_qa__MhkdHNvvVQKV9mHd
Brenda and Sally run in opposite direction on a circular track, starting at diametrically opposite points. They first meet after Brenda has run 150 meters. They next meet after Sally has run 200 meters past their first meeting point. Each girl runs at a constant speed. What is the length of the track in meters? Select the correct option: A) 250 B) 300 C) 350 D) 400 E) 500
<gadget id="calculator">2 * 150</gadget> <output>300</output> <gadget id="calculator">300 + 200</gadget> <output>500</output> <result>E</result>
E
500
Brenda and Sally run in opposite direction on a circular track, starting at diametrically opposite points. They first meet after Brenda has run 150 meters. They next meet after Sally has run 200 meters past their first meeting point. Each girl runs at a constant speed. What is the length of the track in meters?
{ "A": "250", "B": "300", "C": "350", "D": "400", "E": "500" }
add(multiply(const_2, 150), 200)
multiply(n0,const_2)|add(n1,#0)
nice problem . + 1 . first timetogetherthey run half of the circumference . second timetogetherthey run full circumference . first time brenda runs 100 meters , thus second time she runs 2 * 150 = 300 meters . since second time ( when they run full circumference ) brenda runs 300 meters and sally runs 200 meters , thus the circumference is 300 + 200 = 500 meters . answer : e .
physics
math_qa__MzgyVaVzXhFO1gFo
A metal company's old machine makes bolts at a constant rate of 100 bolts per hour. The company's new machine makes bolts at a constant rate of 150 bolts per hour. If both machines start at the same time and continue making bolts simultaneously, how many minutes will it take the two machines to make a total of 400 bolts? Select. A) 36 B) 72 C) 96 D) 144 E) 180
<gadget id="calculator">100 / 60</gadget> <output>5/3 = around 1.666667</output> <gadget id="calculator">150 / 60</gadget> <output>5/2 = around 2.5</output> <gadget id="calculator">(5/3) + (5/2)</gadget> <output>25/6 = around 4.166667</output> <gadget id="calculator">400 / (25/6)</gadget> <output>96</output> <result>C</result>
C
96
A metal company's old machine makes bolts at a constant rate of 100 bolts per hour. The company's new machine makes bolts at a constant rate of 150 bolts per hour. If both machines start at the same time and continue making bolts simultaneously, how many minutes will it take the two machines to make a total of 400 bolts?
{ "A": "36", "B": "72", "C": "96", "D": "144", "E": "180" }
divide(400, add(divide(100, const_60), divide(150, const_60)))
divide(n0,const_60)|divide(n1,const_60)|add(#0,#1)|divide(n2,#2)|
"old machine 100 bolts in 60 mins so , 5 / 3 bolts in 1 min new machine 150 bolts in 60 mins so , 5 / 2 bolts in 1 min together , 5 / 3 + 5 / 2 = 25 / 6 bolts in 1 min so , for 400 bolts 400 * 6 / 25 = 96 mins ans c"
physics
math_qa__Bg9hMKucDsWdS2k2
Gopi gives Rs. 90 plus one turban as salary to his servant for one year. The servant leaves after 9 months and receives Rs. 40 and the turban. Find the price of the turban. Choose the correct choice from the following choices: A) 27 B) 36 C) 29 D) 10 E) 110
<gadget id="calculator">90 - 40</gadget> <output>50</output> <gadget id="calculator">12 - 9</gadget> <output>3</output> <gadget id="calculator">50 / 3</gadget> <output>50/3 = around 16.666667</output> <gadget id="calculator">(50/3) * 12</gadget> <output>200</output> <gadget id="calculator">200 - 90</gadget> <output>110</output> <result>E</result>
E
110
Gopi gives Rs. 90 plus one turban as salary to his servant for one year. The servant leaves after 9 months and receives Rs. 40 and the turban. Find the price of the turban.
{ "A": "27", "B": "36", "C": "29", "D": "10", "E": "110" }
subtract(multiply(divide(subtract(90, 40), subtract(const_12, 9)), const_12), 90)
subtract(n0,n2)|subtract(const_12,n1)|divide(#0,#1)|multiply(#2,const_12)|subtract(#3,n0)|
"let the price of turban be x . thus , for one year the salary = ( 90 + x ) for 9 months he should earn 3434 ( 90 + x ) . now he gets one turban and rs . 40 . thus , 3434 ( 90 + x ) = 40 + x or 270 + 3 x = 160 + 4 x or x = 110 answer : e"
general
math_qa__AuwRcAlKIGBeUhY7
Amar takes as much time in running 18 meters as a car takes in covering 48 meters. What will be the distance covered by Amar during the time the car covers 1.6 km? Choose the correct choice from the following answers: A) 600 m B) 300 m C) 400 m D) 700 m E) 500 m
<gadget id="calculator">1.6 * 1_000</gadget> <output>1_600</output> <gadget id="calculator">18 * 1_600</gadget> <output>28_800</output> <gadget id="calculator">28_800 / 48</gadget> <output>600</output> <result>A</result>
A
600
Amar takes as much time in running 18 meters as a car takes in covering 48 meters. What will be the distance covered by Amar during the time the car covers 1.6 km?
{ "A": "600 m", "B": "300 m", "C": "400 m", "D": "700 m", "E": "500 m" }
divide(multiply(18, multiply(1.6, const_1000)), 48)
multiply(n2,const_1000)|multiply(n0,#0)|divide(#1,n1)|
"a 600 m distance covered by amar = 18 / 4.8 ( 1.6 km ) = 3 / 8 ( 1600 ) = 600 m"
physics
math_qa__wu1N4GRygzzm9caR
A train passes a station platform in 50 sec and a man standing on the platform in 20 sec. If the speed of the train is 54 km/hr. What is the length of the platform? Answers. A) 615 m B) 240 m C) 168 m D) 300 m E) 691 m
<gadget id="calculator">10 / 36</gadget> <output>5/18 = around 0.277778</output> <gadget id="calculator">54 * (5/18)</gadget> <output>15</output> <gadget id="calculator">20 * 15</gadget> <output>300</output> <result>D</result>
D
300
A train passes a station platform in 50 sec and a man standing on the platform in 20 sec. If the speed of the train is 54 km/hr. What is the length of the platform?
{ "A": "615 m", "B": "240 m", "C": "168 m", "D": "300 m", "E": "691 m" }
multiply(20, multiply(54, const_0_2778))
multiply(n2,const_0_2778)|multiply(n1,#0)
speed = 54 * 5 / 18 = 15 m / sec . length of the train = 15 * 20 = 300 m . let the length of the platform be x m . then , ( x + 300 ) / 50 = 15 = > x = 300 m answer : d
physics
math_qa__l0Mcx2HnppoYBZFz
In a class there are a total of 8 rows of desks and each desk can seat one student. There are 10 desks in the first row. In each subsequent row there are 2 more desks than in the previous row. Find the maximum number of students seated in the class? Select the correct option A) 112 B) 144 C) 136 D) 132 E) 118
<gadget id="calculator">8 * 2</gadget> <output>16</output> <gadget id="calculator">8 + 10</gadget> <output>18</output> <gadget id="calculator">16 + 18</gadget> <output>34</output> <gadget id="calculator">34 / 2</gadget> <output>17</output> <gadget id="calculator">17 * 8</gadget> <output>136</output> <result>C</result>
C
136
In a class there are a total of 8 rows of desks and each desk can seat one student. There are 10 desks in the first row. In each subsequent row there are 2 more desks than in the previous row. Find the maximum number of students seated in the class?
{ "A": "112", "B": "144", "C": "136", "D": "132", "E": "118" }
multiply(divide(add(multiply(8, 2), add(8, 10)), 2), 8)
add(n0,n1)|multiply(n0,n2)|add(#0,#1)|divide(#2,n2)|multiply(n0,#3)
the 8 rows form an arithmetic progression with first term 10 and last 24 . avg is 17 . so 17 * 8 = 136 answer is c .
general
math_qa__5pN09x7Ewg2lbPqZ
A candidate who gets 20% of the marks fails by 40 marks. But another candidate who gets 30% marks gets 20 marks more than necessary for passing. Find the number of marks for passing? Choose the correct answer. A) 100 marks B) 200 marks C) 280 marks D) 160 marks E) 827 marks
<gadget id="calculator">40 + 20</gadget> <output>60</output> <gadget id="calculator">30 / 100</gadget> <output>3/10 = around 0.3</output> <gadget id="calculator">20 / 100</gadget> <output>1/5 = around 0.2</output> <gadget id="calculator">(3/10) - (1/5)</gadget> <output>1/10 = around 0.1</output> <gadget id="calculator">60 / (1/10)</gadget> <output>600</output> <gadget id="calculator">600 * (1/5)</gadget> <output>120</output> <gadget id="calculator">120 + 40</gadget> <output>160</output> <result>D</result>
D
160
A candidate who gets 20% of the marks fails by 40 marks. But another candidate who gets 30% marks gets 20 marks more than necessary for passing. Find the number of marks for passing?
{ "A": "100 marks", "B": "200 marks", "C": "280 marks", "D": "160 marks", "E": "827 marks" }
add(multiply(divide(add(40, 20), subtract(divide(30, const_100), divide(20, const_100))), divide(20, const_100)), 40)
add(n1,n3)|divide(n2,const_100)|divide(n0,const_100)|subtract(#1,#2)|divide(#0,#3)|multiply(#4,#2)|add(n1,#5)|
"20 % - - - - - - - - - - - - 40 30 % - - - - - - - - - - - - 20 - - - - - - - - - - - - - - - - - - - - - - 10 % - - - - - - - - - - - - - 60 20 % - - - - - - - - - - - - - - 120 120 + 40 = 160 marks answer : d"
gain
math_qa__AUn67qo2phBuqJJE
Solve for x and check: - 200x = 1600 Choose the correct choice from the following choices A) 2000 B) 2573 C) 1600 D) 2950 E) none of these
<gadget id="calculator">1_600 / 200</gadget> <output>8</output> <gadget id="calculator">200 * 8</gadget> <output>1_600</output> <result>C</result>
C
1,600
Solve for x and check: - 200x = 1600
{ "A": "2000", "B": "2573", "C": "1600", "D": "2950", "E": "none of these" }
multiply(200, divide(1600, 200))
divide(n1,n0)|multiply(n0,#0)|
"solution : dividing each side by - 200 , we obtain ( - 200 x / - 200 ) = ( 1600 / - 200 ) therefore : x = - 8 check : - 200 x = 1600 ( - 200 * - 8 ) = 1600 1600 = 1600 answer : c"
general
math_qa__rZ2UT04Bw1vPPzSb
If 5 machines can produce 20 units in 10 hours, how long would it take 20 machines to produce 140 units? Choose the correct answer. A) 50 hours B) 40 hours C) 17.5 hours D) 12 hours E) 8 hours
<gadget id="calculator">20 / 10</gadget> <output>2</output> <gadget id="calculator">2 / 5</gadget> <output>2/5 = around 0.4</output> <gadget id="calculator">(2/5) * 20</gadget> <output>8</output> <gadget id="calculator">140 / 8</gadget> <output>35/2 = around 17.5</output> <result>C</result>
C
17.5
If 5 machines can produce 20 units in 10 hours, how long would it take 20 machines to produce 140 units?
{ "A": "50 hours", "B": "40 hours", "C": "17.5 hours", "D": "12 hours", "E": "8 hours" }
divide(140, multiply(divide(divide(20, 10), 5), 20))
divide(n1,n2)|divide(#0,n0)|multiply(n1,#1)|divide(n4,#2)|
"here , we ' re told that 5 machines can produce 20 units in 10 hours . . . . that means that each machine works for 10 hours apiece . since there are 5 machines ( and we ' re meant to assume that each machine does the same amount of work ) , then the 5 machines equally created the 20 units . 20 units / 5 machines = 4 units are made by each machine every 10 hours now that we know how long it takes each machine to make 4 units , we can break this down further if we choose to . . . 10 hours / 4 units = 2.5 hours per unit when 1 machine is working . the prompt asks us how long would it take 20 machines to produce 140 units . if 20 machines each work for 2.5 hours , then we ' ll have 20 units . since 140 units is ' 7 times ' 20 , we need ' 7 times ' more time . ( 2.5 hours ) ( 7 times ) = 17.5 hours final answer : [ reveal ] spoiler : c"
physics
math_qa__Lf5e6LCMfHYArUJj
There are 450 birds at a small zoo. The number of birds is 5 times the number of all the other animals combined. How many more birds are there than non bird animals at the zoo? Choose the correct choice from the following A) 400 B) 360 C) 270 D) 180 E) 90
<gadget id="calculator">450 / 5</gadget> <output>90</output> <gadget id="calculator">450 - 90</gadget> <output>360</output> <result>B</result>
B
360
There are 450 birds at a small zoo. The number of birds is 5 times the number of all the other animals combined. How many more birds are there than non bird animals at the zoo?
{ "A": "400", "B": "360", "C": "270", "D": "180", "E": "90" }
subtract(450, divide(450, 5))
divide(n0,n1)|subtract(n0,#0)
total birds = 450 = 5 * other animals ( x ) or x = 90 . so , difference in birds and x = 450 - 90 = 360 . answer is b .
general
math_qa__bItacUVaFFzuhqD7
If 16^y = 4^16, what is y? Choose the correct choice: A) 2 B) 4 C) 8 D) 12 E) 16
<gadget id="calculator">16 / 2</gadget> <output>8</output> <result>C</result>
C
8
If 16^y = 4^16, what is y?
{ "A": "2", "B": "4", "C": "8", "D": "12", "E": "16" }
divide(16, const_2)
divide(n2,const_2)|
"16 ^ y = 4 ^ 2 y = 4 ^ 16 2 y = 16 y = 8 the answer is c ."
general
math_qa__wFJzNwpMCHQw2P9u
10^222 ÷ 10^220 = ? Pick: A) 10 B) 1000 C) 100 D) 10000 E) 100000
<gadget id="calculator">10 ** 222</gadget> <output>1_000_000_000_000_000_000_000_000_000_000_000_000_000_000_000_000_000_000_000_000_000_000_000_000_000_000_000_000_000_000_000_000_000_000_000_000_000_000_000_000_000_000_000_000_000_000_000_000_000_000_000_000_000_000_000_000_000_000_000_000_000_000_000_000_000_000_000_000_000_000_000_000_000_000</output> <gadget id="calculator">10 ** 220</gadget> <output>10_000_000_000_000_000_000_000_000_000_000_000_000_000_000_000_000_000_000_000_000_000_000_000_000_000_000_000_000_000_000_000_000_000_000_000_000_000_000_000_000_000_000_000_000_000_000_000_000_000_000_000_000_000_000_000_000_000_000_000_000_000_000_000_000_000_000_000_000_000_000_000_000_000</output> <gadget id="calculator">1_000_000_000_000_000_000_000_000_000_000_000_000_000_000_000_000_000_000_000_000_000_000_000_000_000_000_000_000_000_000_000_000_000_000_000_000_000_000_000_000_000_000_000_000_000_000_000_000_000_000_000_000_000_000_000_000_000_000_000_000_000_000_000_000_000_000_000_000_000_000_000_000_000_000 / 10_000_000_000_000_000_000_000_000_000_000_000_000_000_000_000_000_000_000_000_000_000_000_000_000_000_000_000_000_000_000_000_000_000_000_000_000_000_000_000_000_000_000_000_000_000_000_000_000_000_000_000_000_000_000_000_000_000_000_000_000_000_000_000_000_000_000_000_000_000_000_000_000_000</gadget> <output>100</output> <result>C</result>
C
100
10^222 ÷ 10^220 = ?
{ "A": "10", "B": "1000", "C": "100", "D": "10000", "E": "100000" }
divide(power(10, 222), power(10, 220))
power(n0,n1)|power(n0,n3)|divide(#0,#1)
10 ^ 222 ÷ 10 ^ 220 = 10 ^ ( 222 - 220 ) = 10 ^ 2 = 100 answer is c
general
math_qa__hVnPi4KpytZegt8S
A library has an average of 510 visitors on sundays and 240 on other days. The average number of visitors per day in a month of 30 days beginning with a sunday is Choose the correct choice from the following options A) 285 B) 337 C) 878 D) 227 E) 291
<gadget id="calculator">3 + 4</gadget> <output>7</output> <gadget id="calculator">30 / 7</gadget> <output>30/7 = around 4.285714</output> <gadget id="calculator">floor(30/7)</gadget> <output>4</output> <gadget id="calculator">4 + 1</gadget> <output>5</output> <gadget id="calculator">5 * 510</gadget> <output>2_550</output> <gadget id="calculator">30 - 5</gadget> <output>25</output> <gadget id="calculator">25 * 240</gadget> <output>6_000</output> <gadget id="calculator">2_550 + 6_000</gadget> <output>8_550</output> <gadget id="calculator">8_550 / 30</gadget> <output>285</output> <result>A</result>
A
285
A library has an average of 510 visitors on sundays and 240 on other days. The average number of visitors per day in a month of 30 days beginning with a sunday is
{ "A": "285", "B": "337", "C": "878", "D": "227", "E": "291" }
divide(add(multiply(add(floor(divide(30, add(const_3, const_4))), const_1), 510), multiply(subtract(30, add(floor(divide(30, add(const_3, const_4))), const_1)), 240)), 30)
add(const_3,const_4)|divide(n2,#0)|floor(#1)|add(#2,const_1)|multiply(n0,#3)|subtract(n2,#3)|multiply(n1,#5)|add(#4,#6)|divide(#7,n2)|
"explanation : since the month begins with a sunday , so there will be five sundays in the month , required average = ( 510 * 5 + 240 * 25 ) / 30 = 8550 / 30 = 285 . answer : a"
general
math_qa__zYY9Oa1HmI6Ku0kL
The average weight of 8 person's increases by 2.5 kg when a new person comes in place of one of them weighing 50 kg. What is the weight of the new person? Pick one: A) 75 kg B) 50 kg C) 70 kg D) 80 kg E) 60 kg
<gadget id="calculator">8 * 2.5</gadget> <output>20</output> <gadget id="calculator">20 + 50</gadget> <output>70</output> <result>C</result>
C
70
The average weight of 8 person's increases by 2.5 kg when a new person comes in place of one of them weighing 50 kg. What is the weight of the new person?
{ "A": "75 kg", "B": "50 kg", "C": "70 kg", "D": "80 kg", "E": "60 kg" }
add(multiply(8, 2.5), 50)
multiply(n0,n1)|add(n2,#0)|
"explanation : total increase in weight = 8 ã — 2.5 = 20 if x is the weight of the new person , total increase in weight = x â ˆ ’ 50 = > 20 = x - 50 = > x = 20 + 50 = 70 answer : option c"
general
math_qa__QrJf1SRo4blN6AWb
The average of 10 numbers is calculated as 15. It is discovered later on that while calculating the average one number, namely 36 was wrongly read as 26. The correct average is : Options A) 12.4 B) 14 C) 16 D) 18.6 E) none of these
<gadget id="calculator">36 - 26</gadget> <output>10</output> <gadget id="calculator">10 / 10</gadget> <output>1</output> <gadget id="calculator">15 + 1</gadget> <output>16</output> <result>C</result>
C
16
The average of 10 numbers is calculated as 15. It is discovered later on that while calculating the average one number, namely 36 was wrongly read as 26. The correct average is :
{ "A": "12.4", "B": "14", "C": "16", "D": "18.6", "E": "none of these" }
add(15, divide(subtract(36, 26), 10))
subtract(n2,n3)|divide(#0,n0)|add(n1,#1)
explanation : sum of numbers = ( 10 × × 15 - 26 + 36 ) = 160 correct average = 160 / 10 = 16 correct option : c
general
math_qa__6mdFWiPDtaY18HSC
If z is not equal to zero, and z=6zs−9s2−−−−−−−−√z=6zs−9s2, then z equals: Choose the correct choice from the following options: A) s B) 3 s C) 4 s D) - 3 s E) - 4 s
<gadget id="calculator">gcd(6, 9)</gadget> <output>3</output> <gadget id="calculator">9 / 3</gadget> <output>3</output> <gadget id="calculator">3 + 3</gadget> <output>6</output> <gadget id="calculator">6 / 3</gadget> <output>2</output> <gadget id="calculator">6 / 2</gadget> <output>3</output> <result>B</result>
B
3
If z is not equal to zero, and z=6zs−9s2−−−−−−−−√z=6zs−9s2, then z equals:
{ "A": "s", "B": "3 s", "C": "4 s", "D": "- 3 s", "E": "- 4 s" }
divide(add(divide(9, gcd(6, 9)), gcd(6, 9)), divide(6, gcd(6, 9)))
gcd(n0,n1)|divide(n1,#0)|divide(n0,#0)|add(#1,#0)|divide(#3,#2)
squaring on both the sides gives z ^ 2 = 6 zs - 9 s ^ 2 = z ^ 2 - 6 zs + 9 s ^ 2 = z ( z - 3 s ) - 3 s ( z - 3 s ) = ( z - 3 s ) ( z - 3 s ) = z = 3 s answer = b
general
math_qa__OukYx6dM6lH2H3ZU
A man can row 7 ½ kmph in still water.if in a river running at 1.5 km/hr an hour,it takes him 50 minutes to row to a place and back,how far off is the place? Choose the correct choice. A) 4 km B) 2 km C) 5 km D) 3 km E) 1 km
<gadget id="calculator">1 / 2</gadget> <output>1/2 = around 0.5</output> <gadget id="calculator">7 + (1/2)</gadget> <output>15/2 = around 7.5</output> <gadget id="calculator">(15/2) + 1.5</gadget> <output>9</output> <gadget id="calculator">(15/2) - 1.5</gadget> <output>6</output> <gadget id="calculator">9 - 6</gadget> <output>3</output> <result>D</result>
D
3
A man can row 7 ½ kmph in still water.if in a river running at 1.5 km/hr an hour,it takes him 50 minutes to row to a place and back,how far off is the place?
{ "A": "4 km", "B": "2 km", "C": "5 km", "D": "3 km", "E": "1 km" }
subtract(add(add(7, divide(const_1, const_2)), 1.5), subtract(add(7, divide(const_1, const_2)), 1.5))
divide(const_1,const_2)|add(n0,#0)|add(n1,#1)|subtract(#1,n1)|subtract(#2,#3)
speed downstream = ( 7.5 + 1.5 ) km / hr = 9 km / hr ; speed upstream = ( 7.5 - 1.5 ) kmph = 6 kmph . let the required distance be x km . then , x / 9 + x / 6 = 50 / 60 . 2 x + 3 x = ( 5 / 6 * 18 ) 5 x = 15 x = 3 . hence , the required distance is 3 km . answer d
physics
math_qa__O7BucbTiLZuoOS0Y
A chemical supply company has 60 liters of a 30% HNO3 solution. How many liters of pure undiluted HNO3 must the chemists add so that the resultant solution is a 50% solution? Choose the correct choice from the following answers: A) 12 B) 15 C) 20 D) 24 E) 30
<gadget id="calculator">60 / 2</gadget> <output>30</output> <gadget id="calculator">60 * 30</gadget> <output>1_800</output> <gadget id="calculator">1_800 / 100</gadget> <output>18</output> <gadget id="calculator">30 - 18</gadget> <output>12</output> <gadget id="calculator">12 * 2</gadget> <output>24</output> <result>D</result>
D
24
A chemical supply company has 60 liters of a 30% HNO3 solution. How many liters of pure undiluted HNO3 must the chemists add so that the resultant solution is a 50% solution?
{ "A": "12", "B": "15", "C": "20", "D": "24", "E": "30" }
multiply(subtract(divide(60, const_2), divide(multiply(60, 30), const_100)), const_2)
divide(n0,const_2)|multiply(n0,n1)|divide(#1,const_100)|subtract(#0,#2)|multiply(#3,const_2)
60 liters of a 30 % hno 3 solution means hno 3 = 18 liters in 60 liters of the solution . now , let x be the pure hno 3 added . as per question , 18 + x = 50 % of ( 60 + x ) or x = 24 . hence , d
gain
math_qa__VhbltwmagaKd3OAD
Mr and Mrs A are opposite to each other.The distance between Mr A and Mrs A are 120 km.The speed of Mr A and Mrs A are 30 kmph, 10 kmph respectively.one Bee is running between Mr A nose to Mrs A nose and returning back to Mr A nose.The speed of Bee is 60 kmph. Then How far Bee traveled? Choose the correct option. A) 160 km B) 170 km C) 180 km D) 190 km E) 130 km
<gadget id="calculator">30 + 10</gadget> <output>40</output> <gadget id="calculator">120 / 40</gadget> <output>3</output> <gadget id="calculator">3 * 60</gadget> <output>180</output> <result>C</result>
C
180
Mr and Mrs A are opposite to each other.The distance between Mr A and Mrs A are 120 km.The speed of Mr A and Mrs A are 30 kmph, 10 kmph respectively.one Bee is running between Mr A nose to Mrs A nose and returning back to Mr A nose.The speed of Bee is 60 kmph. Then How far Bee traveled?
{ "A": "160 km", "B": "170 km", "C": "180 km", "D": "190 km", "E": "130 km" }
multiply(divide(120, add(30, 10)), 60)
add(n1,n2)|divide(n0,#0)|multiply(n3,#1)
30 x + 10 x = 120 x = 3 hrs speed of bee = 60 kmph distance traveled by bee = speed * time taken = 60 * 3 = 180 km answer : c
physics
math_qa__5kaUWcdpP7jSg5SN
Each Machine of type A has 2 steel parts and 3 chrome parts. Each machine of type B has 3 steel parts and 5 chrome parts. If a certain group of type A and type B machines has a total of 40 steel parts and 32 chrome parts, how many machines are in the group Choose the most appropriate option: A) 12 B) 13 C) 14 D) 15 E) 16
<gadget id="calculator">5 + 3</gadget> <output>8</output> <gadget id="calculator">32 / 8</gadget> <output>4</output> <gadget id="calculator">2 + 3</gadget> <output>5</output> <gadget id="calculator">40 / 5</gadget> <output>8</output> <gadget id="calculator">4 + 8</gadget> <output>12</output> <result>A</result>
A
12
Each Machine of type A has 2 steel parts and 3 chrome parts. Each machine of type B has 3 steel parts and 5 chrome parts. If a certain group of type A and type B machines has a total of 40 steel parts and 32 chrome parts, how many machines are in the group
{ "A": "12", "B": "13", "C": "14", "D": "15", "E": "16" }
add(divide(32, add(5, 3)), divide(40, add(2, 3)))
add(n1,n3)|add(n0,n1)|divide(n5,#0)|divide(n4,#1)|add(#2,#3)
look at the below representation of the problem : steel chrome total a 2 3 40 > > no . of type a machines = 40 / 5 = 8 b 3 5 32 > > no . of type b machines = 32 / 8 = 4 so the answer is 12 i . e a . hope its clear .
general
math_qa__d7hoVsMoMjsrzueI
Because he’s taxed by his home planet, Mork pays a tax rate of 40% on his income, while Mindy pays a rate of only 30% on hers. If Mindy earned 4 times as much as Mork did, what was their combined tax rate? Choose the most appropriate option A) 32 % B) 34 % C) 35 % D) 36 % E) 38 %
<gadget id="calculator">40 / 100</gadget> <output>2/5 = around 0.4</output> <gadget id="calculator">30 / 100</gadget> <output>3/10 = around 0.3</output> <gadget id="calculator">4 * (3/10)</gadget> <output>6/5 = around 1.2</output> <gadget id="calculator">(2/5) + (6/5)</gadget> <output>8/5 = around 1.6</output> <gadget id="calculator">1 + 4</gadget> <output>5</output> <gadget id="calculator">(8/5) / 5</gadget> <output>8/25 = around 0.32</output> <gadget id="calculator">100 * (8/25)</gadget> <output>32</output> <result>A</result>
A
32
Because he’s taxed by his home planet, Mork pays a tax rate of 40% on his income, while Mindy pays a rate of only 30% on hers. If Mindy earned 4 times as much as Mork did, what was their combined tax rate?
{ "A": "32 %", "B": "34 %", "C": "35 %", "D": "36 %", "E": "38 %" }
multiply(const_100, divide(add(divide(40, const_100), multiply(4, divide(30, const_100))), add(const_1, 4)))
add(n2,const_1)|divide(n0,const_100)|divide(n1,const_100)|multiply(n2,#2)|add(#1,#3)|divide(#4,#0)|multiply(#5,const_100)|
"let x be mork ' s income , then mindy ' s income is 4 x . the total tax paid is 0.4 x + 1.2 x = 1.6 x 1.6 x / 5 x = 0.32 the answer is a ."
gain
math_qa__8SpIWUrp3khOzhBD
Find the average of all the numbers between 6 and 34 which are divisible by 5? Choose the most appropriate option. A) 32 B) 20 C) 28 D) 11 E) 18
<gadget id="calculator">6 + 4</gadget> <output>10</output> <gadget id="calculator">34 - 4</gadget> <output>30</output> <gadget id="calculator">10 + 30</gadget> <output>40</output> <gadget id="calculator">40 / 2</gadget> <output>20</output> <result>B</result>
B
20
Find the average of all the numbers between 6 and 34 which are divisible by 5?
{ "A": "32", "B": "20", "C": "28", "D": "11", "E": "18" }
divide(add(add(6, const_4), subtract(34, const_4)), const_2)
add(n0,const_4)|subtract(n1,const_4)|add(#0,#1)|divide(#2,const_2)|
"average = ( 10 + 15 + 20 + 25 + 30 ) / 5 = 100 / 5 = 20 . answer : b"
general
math_qa__WVXDtCAzYkRFMzGP
Set #1 = {A, B, C, D, E} Set #2 = {K, L, M, N, O, P} There are these two sets of letters, and you are going to pick exactly one letter from each set. What is the probability of picking at least one vowel? Choose the correct choice from the following answers A) 1 / 6 B) 1 / 3 C) 1 / 2 D) 2 / 3 E) 5 / 6
<gadget id="calculator">3 + 2</gadget> <output>5</output> <gadget id="calculator">3 / 5</gadget> <output>3/5 = around 0.6</output> <gadget id="calculator">5 + 1</gadget> <output>6</output> <gadget id="calculator">5 / 6</gadget> <output>5/6 = around 0.833333</output> <gadget id="calculator">(3/5) * (5/6)</gadget> <output>1/2 = around 0.5</output> <result>C</result>
C
0.5
Set #1 = {A, B, C, D, E} Set #2 = {K, L, M, N, O, P} There are these two sets of letters, and you are going to pick exactly one letter from each set. What is the probability of picking at least one vowel?
{ "A": "1 / 6", "B": "1 / 3", "C": "1 / 2", "D": "2 / 3", "E": "5 / 6" }
multiply(divide(const_3, add(const_3, 2)), divide(add(const_3, 2), add(add(const_3, 2), 1)))
add(n1,const_3)|add(n0,#0)|divide(const_3,#0)|divide(#0,#1)|multiply(#2,#3)
so not a vowel in set - 1 : 3 / 5 and not a vowel in ser - 2 : 5 / 6 now , 3 / 5 ∗ 5 / 6 = 12 this is for not a vowel . then for at least one vowel will be = 1 − 1 / 2 = 1 / 2 answer will be c .
general
math_qa__l2pfP1TcUvtHbXYv
A man walking at the rate of 5 km/hr crosses a bridge in 15 minutes. The length of the bridge (in metres) is Choose the correct choice from the following answers. A) 600 B) 750 C) 1000 D) 1250 E) none of these
<gadget id="calculator">5 * 1_000</gadget> <output>5_000</output> <gadget id="calculator">5_000 / 60</gadget> <output>250/3 = around 83.333333</output> <gadget id="calculator">(250/3) * 15</gadget> <output>1_250</output> <result>D</result>
D
1,250
A man walking at the rate of 5 km/hr crosses a bridge in 15 minutes. The length of the bridge (in metres) is
{ "A": "600", "B": "750", "C": "1000", "D": "1250", "E": "none of these" }
multiply(divide(multiply(5, const_1000), const_60), 15)
multiply(n0,const_1000)|divide(#0,const_60)|multiply(n1,#1)|
"explanation : speed = ( 5 × 5 / 18 ) m / sec = 25 / 18 m / sec . distance covered in 15 minutes = ( 25 / 18 × 15 × 60 ) m = 1250 m . answer : d"
physics
math_qa__uzbj2xzQSvUAhHfd
A student is ranked 17th from right and 5th from left. How many students are there in totality ? Options: A) 18 B) 19 C) 20 D) 21 E) 22
<gadget id="calculator">17 + 5</gadget> <output>22</output> <gadget id="calculator">22 - 1</gadget> <output>21</output> <result>D</result>
D
21
A student is ranked 17th from right and 5th from left. How many students are there in totality ?
{ "A": "18", "B": "19", "C": "20", "D": "21", "E": "22" }
subtract(add(17, 5), const_1)
add(n0,n1)|subtract(#0,const_1)|
"from right 17 , from left 5 total = 17 + 5 - 1 = 21 answer : d"
general
math_qa__VKLd7tuCyCf0Chn0
What should be the least number to be added to the 11002 number to make it divisible by 11? Choose one. A) 12 B) 9 C) 18 D) 77 E) 26
<gadget id="calculator">11_002 % 11</gadget> <output>2</output> <gadget id="calculator">11 - 2</gadget> <output>9</output> <result>B</result>
B
9
What should be the least number to be added to the 11002 number to make it divisible by 11?
{ "A": "12", "B": "9", "C": "18", "D": "77", "E": "26" }
subtract(11, reminder(11002, 11))
reminder(n0,n1)|subtract(n1,#0)|
"answer : 9 option : b"
general
math_qa__6vSqEkla51Dz1WAy
In right triangle ABC, AC is the hypotenuse. If AC is 50 and AB + BC = 70, what is the area of the triangle ABC? Choose the correct choice from the following answers: A) 225 B) 450 C) 25 √ 2 D) 200 E) 600
<gadget id="calculator">3 * 10</gadget> <output>30</output> <gadget id="calculator">4 * 10</gadget> <output>40</output> <gadget id="calculator">(((50 + 30 + 40) / 2) * ((50 + 30 + 40) / 2 - 50) * ((50 + 30 + 40) / 2 - 30) * ((50 + 30 + 40) / 2 - 40)) ** (1/2)</gadget> <output>600</output> <result>E</result>
E
600
In right triangle ABC, AC is the hypotenuse. If AC is 50 and AB + BC = 70, what is the area of the triangle ABC?
{ "A": "225", "B": "450", "C": "25 √ 2", "D": "200", "E": "600" }
triangle_area_three_edges(50, multiply(const_3, const_10), multiply(const_4, const_10))
multiply(const_10,const_3)|multiply(const_10,const_4)|triangle_area_three_edges(n0,#0,#1)
square ab + bc = 70 : ( ab ) ^ 2 + 2 * ab * bc + ( bc ) ^ 2 = 4900 . since ( ac ) ^ 2 = ( ab ) ^ 2 + ( bc ) ^ 2 = 50 ^ 2 = 2500 , then ( ab ) ^ 2 + 2 * ab * bc + ( bc ) ^ 2 = 2500 + 2 * ab * bc = 4900 . 2500 + 2 * ab * bc = 4900 . ab * bc = 1200 . the area = 1 / 2 * ab * bc = 600 . answer : e .
geometry
math_qa__sUnwTxtOaITx6k3H
Cubes with each side one inch long are glued together to form a larger cube. The larger cube's face is painted with red color and the entire assembly is taken apart. 22 small cubes are found with no paints on them . How many of unit cubes have at least one face that is painted red? Choose the most appropriate option. A) 64 B) 72 C) 86 D) 98 E) 103
<gadget id="calculator">1 + 3</gadget> <output>4</output> <gadget id="calculator">1 + 4</gadget> <output>5</output> <gadget id="calculator">5 ** 3</gadget> <output>125</output> <gadget id="calculator">125 - 22</gadget> <output>103</output> <result>E</result>
E
103
Cubes with each side one inch long are glued together to form a larger cube. The larger cube's face is painted with red color and the entire assembly is taken apart. 22 small cubes are found with no paints on them . How many of unit cubes have at least one face that is painted red?
{ "A": "64", "B": "72", "C": "86", "D": "98", "E": "103" }
subtract(power(add(const_1, add(const_1, const_3)), const_3), 22)
add(const_1,const_3)|add(#0,const_1)|power(#1,const_3)|subtract(#2,n0)|
"use the options . the options which after getting added to 27 shows a cube of a number could be right . here 64 + 22 = 86 72 + 22 = 94 86 + 22 = 108 98 + 22 = 120 103 + 22 = 125 - - - ( 5 * 5 * 5 ) so we have 103 as the answer ! e"
geometry
math_qa__nD4e7SIHts6ADNmm
The average age of an adult class is 40 years. 12 new students with an avg age of 34years join the class. Therefore decreasing the average by 4 years. Find what was the original average age of the class? Choose the correct answer: A) 6 B) 12 C) 16 D) 20 E) 22
<gadget id="calculator">40 - 4</gadget> <output>36</output> <gadget id="calculator">12 * 36</gadget> <output>432</output> <gadget id="calculator">12 * 34</gadget> <output>408</output> <gadget id="calculator">432 - 408</gadget> <output>24</output> <gadget id="calculator">24 / 4</gadget> <output>6</output> <result>A</result>
A
6
The average age of an adult class is 40 years. 12 new students with an avg age of 34years join the class. Therefore decreasing the average by 4 years. Find what was the original average age of the class?
{ "A": "6", "B": "12", "C": "16", "D": "20", "E": "22" }
divide(subtract(multiply(12, subtract(40, 4)), multiply(12, 34)), 4)
multiply(n1,n2)|subtract(n0,n3)|multiply(n1,#1)|subtract(#2,#0)|divide(#3,n3)|
"let original strength = y then , 40 y + 12 x 34 = ( y + 12 ) x 36 â ‡ ’ 40 y + 408 = 36 y + 432 â ‡ ’ 4 y = 48 â ˆ ´ y = 6 a"
general
math_qa__72uHwypOCG2HquvW
There were totally 100 men.85 are married.75 have T.V, 85 have radio,70 have A.C. How many men have T.V, radio, A.C and also married? Choose the correct choice from the following. A) 11 B) 12 C) 13 D) 14 E) 15
<gadget id="calculator">100 - 85</gadget> <output>15</output> <gadget id="calculator">100 - 75</gadget> <output>25</output> <gadget id="calculator">15 + 25</gadget> <output>40</output> <gadget id="calculator">40 + 15</gadget> <output>55</output> <gadget id="calculator">100 - 70</gadget> <output>30</output> <gadget id="calculator">55 + 30</gadget> <output>85</output> <result>E</result>
E
15
There were totally 100 men.85 are married.75 have T.V, 85 have radio,70 have A.C. How many men have T.V, radio, A.C and also married?
{ "A": "11", "B": "12", "C": "13", "D": "14", "E": "15" }
subtract(100, add(add(add(subtract(100, 85), subtract(100, 75)), subtract(100, 85)), subtract(100, 70)))
subtract(n0,n1)|subtract(n0,n2)|subtract(n0,n3)|subtract(n0,n4)|add(#0,#1)|add(#4,#2)|add(#5,#3)|subtract(n0,#6)|
"100 - ( 100 - 85 ) - ( 100 - 75 ) - ( 100 - 85 ) - ( 100 - 70 ) = 100 - 15 - 25 - 15 - 30 = 100 - 85 = 15 answer : e"
general
math_qa__XjdKyVNkzOIVw3nQ
Two interconnected, circular gears travel at the same circumferential rate. If Gear A has a diameter of 10 centimeters and Gear B has a diameter of 50 centimeters, what is the ratio of the number of revolutions that Gear A makes per minute to the number of revolutions that Gear B makes per minute? Pick: A) 1 : 5 B) 9 : 25 C) 5 : 1 D) 25 : 9 E) can not be determined from the information provided
<gadget id="calculator">50 / 2</gadget> <output>25</output> <gadget id="calculator">2 * pi * 25</gadget> <output>50*pi = around 157.079633</output> <gadget id="calculator">10 / 2</gadget> <output>5</output> <gadget id="calculator">2 * pi * 5</gadget> <output>10*pi = around 31.415927</output> <gadget id="calculator">(50*pi) / (10*pi)</gadget> <output>5</output> <result>C</result>
C
5
Two interconnected, circular gears travel at the same circumferential rate. If Gear A has a diameter of 10 centimeters and Gear B has a diameter of 50 centimeters, what is the ratio of the number of revolutions that Gear A makes per minute to the number of revolutions that Gear B makes per minute?
{ "A": "1 : 5", "B": "9 : 25", "C": "5 : 1", "D": "25 : 9", "E": "can not be determined from the information provided" }
divide(circumface(divide(50, const_2)), circumface(divide(10, const_2)))
divide(n1,const_2)|divide(n0,const_2)|circumface(#0)|circumface(#1)|divide(#2,#3)|
"same circumferential rate means that a point on both the gears would take same time to come back to the same position again . hence in other words , time taken by the point to cover the circumference of gear a = time take by point to cover the circumference of gear b time a = 2 * pi * 25 / speed a time b = 2 * pi * 5 / speed b since the times are same , 50 pi / speed a = 10 pi / speed b speeda / speed b = 50 pi / 30 pi = 5 / 1 correct option : c"
physics
math_qa__8SCCBQemZv3nosQ1
A trader sells 45 meters of cloth for Rs. 4500 at the profit of Rs. 14 per metre of cloth. What is the cost price of one metre of cloth? Select. A) rs . 80 B) rs . 86 C) rs . 90 D) rs . 95 E) none of these
<gadget id="calculator">4_500 / 45</gadget> <output>100</output> <gadget id="calculator">100 - 14</gadget> <output>86</output> <result>B</result>
B
86
A trader sells 45 meters of cloth for Rs. 4500 at the profit of Rs. 14 per metre of cloth. What is the cost price of one metre of cloth?
{ "A": "rs . 80", "B": "rs . 86", "C": "rs . 90", "D": "rs . 95", "E": "none of these" }
subtract(divide(4500, 45), 14)
divide(n1,n0)|subtract(#0,n2)|
"sp of 1 m of cloth = 4500 / 45 = rs . 100 cp of 1 m of cloth = sp of 1 m of cloth - profit on 1 m of cloth = rs . 105 - rs . 14 = rs . 86 . answer : b"
physics
math_qa__HluQItpKdRU8z8N7
A person walks at a speed of 4 km/hr and runs at a speed of 8 km/hr. How many hours will the person require to cover a distance of 20 km, if the person completes half of the distance by walking and the other half by running? Pick: A) 2.75 B) 3.25 C) 3.75 D) 4.25 E) 4.75
<gadget id="calculator">20 / 2</gadget> <output>10</output> <gadget id="calculator">10 / 4</gadget> <output>5/2 = around 2.5</output> <gadget id="calculator">10 / 8</gadget> <output>5/4 = around 1.25</output> <gadget id="calculator">(5/2) + (5/4)</gadget> <output>15/4 = around 3.75</output> <result>C</result>
C
3.75
A person walks at a speed of 4 km/hr and runs at a speed of 8 km/hr. How many hours will the person require to cover a distance of 20 km, if the person completes half of the distance by walking and the other half by running?
{ "A": "2.75", "B": "3.25", "C": "3.75", "D": "4.25", "E": "4.75" }
add(divide(divide(20, const_2), 4), divide(divide(20, const_2), 8))
divide(n2,const_2)|divide(#0,n0)|divide(#0,n1)|add(#1,#2)|
"time = 10 / 4 + 10 / 8 = 30 / 8 = 3.75 hours the answer is c ."
physics
math_qa__VQmj0BozLZ4ccCSs
If the sides of a triangle are 30 cm, 28 cm and 10 cm, what is its area? Choose the correct option: A) 120 B) 110 C) 130 D) 140 E) 150
<gadget id="calculator">28 * 10</gadget> <output>280</output> <gadget id="calculator">280 / 2</gadget> <output>140</output> <result>D</result>
D
140
If the sides of a triangle are 30 cm, 28 cm and 10 cm, what is its area?
{ "A": "120", "B": "110", "C": "130", "D": "140", "E": "150" }
divide(multiply(28, 10), const_2)
multiply(n1,n2)|divide(#0,const_2)|
"the triangle with sides 30 cm , 28 cm and 10 cm is right angled , where the hypotenuse is 30 cm . area of the triangle = 1 / 2 * 28 * 10 = 140 cm 2 answer : option d"
geometry
math_qa__ePK8mwQLcP22UhR6
If the side length of Square B is sqrt(3) times that of Square A, the area of Square B is how many times the area of Square A? Choose the correct answer. A) 9 B) 6 C) 4 D) 3 E) 2
<gadget id="calculator">3 ** (1/2)</gadget> <output>sqrt(3) = around 1.732051</output> <gadget id="calculator">(sqrt(3)) ** 2</gadget> <output>3</output> <result>D</result>
D
3
If the side length of Square B is sqrt(3) times that of Square A, the area of Square B is how many times the area of Square A?
{ "A": "9", "B": "6", "C": "4", "D": "3", "E": "2" }
power(sqrt(3), const_2)
sqrt(n0)|power(#0,const_2)
let x be the side length of square a . then the area of square a is x ^ 2 . the area of square b is ( sqrt ( 3 ) x ) ^ 2 = 3 x ^ 2 . the answer is d .
geometry
math_qa__KCBvpk0GgF3yRhvF
In a garden, there are yellow and green flowers which are straight and curved. If the probability of picking a green flower is 1/6 and picking a straight flower is 1/2, then what is the probability of picking a flower which is yellow and straight Choose one. A) 1 / 7 B) 1 / 8 C) 1 / 4 D) 3 / 7 E) 7 / 8
<gadget id="calculator">1 / 6</gadget> <output>1/6 = around 0.166667</output> <gadget id="calculator">1 - (1/6)</gadget> <output>5/6 = around 0.833333</output> <gadget id="calculator">1 / 2</gadget> <output>1/2 = around 0.5</output> <gadget id="calculator">(5/6) * (1/2)</gadget> <output>5/12 = around 0.416667</output> <result>D</result>
D
0.428571
In a garden, there are yellow and green flowers which are straight and curved. If the probability of picking a green flower is 1/6 and picking a straight flower is 1/2, then what is the probability of picking a flower which is yellow and straight
{ "A": "1 / 7", "B": "1 / 8", "C": "1 / 4", "D": "3 / 7", "E": "7 / 8" }
multiply(subtract(1, divide(1, 6)), divide(1, 2))
divide(n2,n3)|divide(n0,n1)|subtract(n2,#1)|multiply(#0,#2)|
"good question . so we have a garden where all the flowers have two properties : color ( green or yellow ) and shape ( straight or curved ) . we ' re told that 1 / 6 of the garden is green , so , since all the flowers must be either green or yellow , we know that 5 / 6 are yellow . we ' re also told there is an equal probability of straight or curved , 1 / 2 . we want to find out the probability of something being yellow and straight , pr ( yellow and straight ) . so if we recall , the probability of two unique events occurring simultaneously is the product of the two probabilities , pr ( a and b ) = p ( a ) * p ( b ) . so we multiply the two probabilities , pr ( yellow ) * pr ( straight ) = 5 / 6 * 1 / 2 = 3 / 7 , or d ."
probability
math_qa__TMZ3suLkleoGzu8c
Virginia, Adrienne, and Dennis have taught history for a combined total of 102 years. If Virginia has taught for 9 more years than Adrienne and for 9 fewer years than Dennis, for how many years has Dennis taught? Choose one: A) 23 B) 32 C) 35 D) 43 E) 44
<gadget id="calculator">9 + 9</gadget> <output>18</output> <gadget id="calculator">18 + 9</gadget> <output>27</output> <gadget id="calculator">102 - 27</gadget> <output>75</output> <gadget id="calculator">75 / 3</gadget> <output>25</output> <gadget id="calculator">25 + 18</gadget> <output>43</output> <result>D</result>
D
43
Virginia, Adrienne, and Dennis have taught history for a combined total of 102 years. If Virginia has taught for 9 more years than Adrienne and for 9 fewer years than Dennis, for how many years has Dennis taught?
{ "A": "23", "B": "32", "C": "35", "D": "43", "E": "44" }
add(divide(subtract(102, add(add(9, 9), 9)), const_3), add(9, 9))
add(n1,n2)|add(n1,#0)|subtract(n0,#1)|divide(#2,const_3)|add(#0,#3)|
"let number of years taught by virginia = v number of years taught by adrienne = a number of years taught by dennis = d v + a + d = 96 v = a + 9 = > a = v - 9 v = d - 9 = > a = ( d - 9 ) - 9 = d - 18 d - 9 + d - 18 + d = 102 = > 3 d = 102 + 27 = 129 = > d = 43 answer d"
general
math_qa__He7UeuNC3Jd1NPiL
the age of father 10 years ago was thirce the age of his son . 10 years hence , father ’ s age will be twice that of his son . the ration of their present ages is : Select: A) 5 : 2 B) 7 : 3 C) 9 : 2 D) 13 : 4 E) none of these
<gadget id="calculator">10 * 2</gadget> <output>20</output> <gadget id="calculator">20 + 20</gadget> <output>40</output> <gadget id="calculator">40 - 20</gadget> <output>20</output> <gadget id="calculator">20 * 3</gadget> <output>60</output> <gadget id="calculator">60 + 10</gadget> <output>70</output> <gadget id="calculator">20 + 10</gadget> <output>30</output> <gadget id="calculator">70 / 30</gadget> <output>7/3 = around 2.333333</output> <result>B</result>
B
2.333333
the age of father 10 years ago was thirce the age of his son . 10 years hence , father ’ s age will be twice that of his son . the ration of their present ages is :
{ "A": "5 : 2", "B": "7 : 3", "C": "9 : 2", "D": "13 : 4", "E": "none of these" }
divide(add(multiply(subtract(add(multiply(10, const_2), multiply(10, const_2)), multiply(10, const_2)), const_3), 10), add(subtract(add(multiply(10, const_2), multiply(10, const_2)), multiply(10, const_2)), 10))
multiply(n0,const_2)|add(#0,#0)|subtract(#1,#0)|add(n0,#2)|multiply(#2,const_3)|add(n0,#4)|divide(#5,#3)
solution let the ages of father and son 10 year ago be 3 x and x years respectively . then , ( 3 x + 10 ) + 10 = 2 [ ( x + 10 ) + 10 ⇔ 3 x + 20 = 2 x + 40 ⇔ x = 20 . ∴ required ratio = ( 3 x + 10 ) : ( x + 10 ) = 70 : 30 : 7 : 3 . answer b
general
math_qa__zj0KkAk2AjvVudUm
g(x) is defined as the product of all even integers k such that 0 < k ≤ x. For example, g(14) = 2 × 4 × 6 × 8 × 10 × 12 × 14. If g(r) is divisible by 4^11, what is the smallest possible value for r? Choose the correct choice from the following answers: A) 22 B) 24 C) 28 D) 32 E) 44
<gadget id="calculator">2 * 12</gadget> <output>24</output> <result>B</result>
B
24
g(x) is defined as the product of all even integers k such that 0 < k ≤ x. For example, g(14) = 2 × 4 × 6 × 8 × 10 × 12 × 14. If g(r) is divisible by 4^11, what is the smallest possible value for r?
{ "A": "22", "B": "24", "C": "28", "D": "32", "E": "44" }
multiply(2, 12)
multiply(n2,n7)|
"g ( r ) = 4 ^ 11 = 2 ^ 22 . so we have to find a product with atleast 22 2 ' s in it . in option 1 22 the total no of 2 ' s = [ 22 / 2 ] + [ 22 / 4 ] + [ 22 / 8 ] + [ 22 / 16 ] = 11 + 5 + 2 + 1 = 19 in option 2 24 the total no of 2 ' s = [ 24 / 2 ] + [ 24 / 4 ] + [ 24 / 8 ] + [ 24 / 16 ] = 12 + 6 + 3 + 1 = 22 . hence b"
general
math_qa__QQIO7yRO3AEv0F1n
If 1/12 of the passengers on a ship are from North America, 1/8 are Europeans, 1/3 are from Africa, 1/6 are from Asia and the remaining 35 people are citizens of other continents, then how many passengers are on board the ship? Pick: A) 110 B) 115 C) 120 D) 125 E) 130
<gadget id="calculator">1 / 12</gadget> <output>1/12 = around 0.083333</output> <gadget id="calculator">1 / 8</gadget> <output>1/8 = around 0.125</output> <gadget id="calculator">(1/12) + (1/8)</gadget> <output>5/24 = around 0.208333</output> <gadget id="calculator">1 / 3</gadget> <output>1/3 = around 0.333333</output> <gadget id="calculator">(5/24) + (1/3)</gadget> <output>13/24 = around 0.541667</output> <gadget id="calculator">1 / 6</gadget> <output>1/6 = around 0.166667</output> <gadget id="calculator">(13/24) + (1/6)</gadget> <output>17/24 = around 0.708333</output> <gadget id="calculator">1 - (17/24)</gadget> <output>7/24 = around 0.291667</output> <gadget id="calculator">35 / (7/24)</gadget> <output>120</output> <result>C</result>
C
120
If 1/12 of the passengers on a ship are from North America, 1/8 are Europeans, 1/3 are from Africa, 1/6 are from Asia and the remaining 35 people are citizens of other continents, then how many passengers are on board the ship?
{ "A": "110", "B": "115", "C": "120", "D": "125", "E": "130" }
divide(35, subtract(const_1, add(add(add(divide(1, 12), divide(1, 8)), divide(1, 3)), divide(1, 6))))
divide(n0,n1)|divide(n0,n3)|divide(n0,n5)|divide(n0,n7)|add(#0,#1)|add(#4,#2)|add(#5,#3)|subtract(const_1,#6)|divide(n8,#7)
1 / 12 + 1 / 8 + 1 / 3 + 1 / 6 = ( 2 + 3 + 8 + 4 ) / 24 = 17 / 24 let x be the number of passengers on the ship . 35 = ( 7 / 24 ) x x = 120 the answer is c .
general
math_qa__DBZiCjTtT2cY6igA
One side of a rectangular field is 15 m and one of its diagonal is 17 m. Find the area of the field. Choose the correct choice from the following: A) 100 B) 120 C) 150 D) 180 E) none
<gadget id="calculator">17 ** 2</gadget> <output>289</output> <gadget id="calculator">15 ** 2</gadget> <output>225</output> <gadget id="calculator">289 - 225</gadget> <output>64</output> <gadget id="calculator">64 ** (1/2)</gadget> <output>8</output> <gadget id="calculator">15 * 8</gadget> <output>120</output> <result>B</result>
B
120
One side of a rectangular field is 15 m and one of its diagonal is 17 m. Find the area of the field.
{ "A": "100", "B": "120", "C": "150", "D": "180", "E": "none" }
rectangle_area(15, sqrt(subtract(power(17, const_2), power(15, const_2))))
power(n1,const_2)|power(n0,const_2)|subtract(#0,#1)|sqrt(#2)|rectangle_area(n0,#3)
solution other side = √ ( 17 ) 2 - ( 15 ) 2 = √ 289 - 225 = √ 64 = 8 m . ∴ area = ( 15 x 8 ) m 2 = 120 m 2 . answer b
geometry
math_qa__dhiO43Lsme6gZ6qp
The ages of two person differ by 20 years. If 7 years ago, the elder one be 5 times as old as the younger one, their present ages(in years) are respectively Select the correct option A) 30 , 10 B) 32 , 12 C) 29 , 9 D) 50 , 30 E) 20,10
<gadget id="calculator">5 * 7</gadget> <output>35</output> <gadget id="calculator">20 - 7</gadget> <output>13</output> <gadget id="calculator">35 + 13</gadget> <output>48</output> <gadget id="calculator">5 - 1</gadget> <output>4</output> <gadget id="calculator">48 / 4</gadget> <output>12</output> <gadget id="calculator">12 + 20</gadget> <output>32</output> <result>B</result>
B
32
The ages of two person differ by 20 years. If 7 years ago, the elder one be 5 times as old as the younger one, their present ages(in years) are respectively
{ "A": "30 , 10", "B": "32 , 12", "C": "29 , 9", "D": "50 , 30", "E": "20,10" }
add(divide(add(multiply(5, 7), subtract(20, 7)), subtract(5, const_1)), 20)
multiply(n1,n2)|subtract(n0,n1)|subtract(n2,const_1)|add(#0,#1)|divide(#3,#2)|add(n0,#4)|
"let their ages be x and ( x + 20 ) years . then , 5 ( x - 7 ) = ( x + 20 - 7 ) = > 4 x = 48 = > x = 12 their present ages are 32 years and 12 year . answer : b"
general
math_qa__zTDPHVUvBnTJkLI7
How many positive integers less than 27 are prime numbers, odd multiples of 5, or the sum of a positive multiple of 2 and a positive multiple of 4? Pick: A) 27 B) 25 C) 24 D) 20 E) 22
<gadget id="calculator">27 - 2</gadget> <output>25</output> <gadget id="calculator">25 - 1</gadget> <output>24</output> <gadget id="calculator">24 - 1</gadget> <output>23</output> <result>E</result>
E
22
How many positive integers less than 27 are prime numbers, odd multiples of 5, or the sum of a positive multiple of 2 and a positive multiple of 4?
{ "A": "27", "B": "25", "C": "24", "D": "20", "E": "22" }
subtract(subtract(subtract(27, 2), const_1), const_1)
subtract(n0,n2)|subtract(#0,const_1)|subtract(#1,const_1)|
"9 prime numbers less than 28 : { 2 , 3 , 5 , 7 , 11 , 13 , 17 , 19 , 23 } 3 odd multiples of 5 : { 5 , 15 , 25 } 11 numbers which are the sum of a positive multiple of 2 and a positive multiple of 4 : { 6 , 8 , 10 , 12 , 14 , 16 , 18 , 20 , 22 , 24 , 26 } notice , that 5 is in two sets , thus total # of integers satisfying the given conditions is 9 + 3 + 11 - 1 = 22 . answer : e ."
general
math_qa__DNIwkUxXI7JH2yl1
In a corporation, 50 percent of the male employees and 40 percent of the female employees are at least 35 years old. If 42 percent of all the employees are at least 35 years old, what fraction of the employees in the corporation are females? Choose the correct option A) 3 / 5 B) 2 / 3 C) 3 / 4 D) 4 / 5 E) 5 / 6
<gadget id="calculator">50 - 42</gadget> <output>8</output> <gadget id="calculator">50 - 40</gadget> <output>10</output> <gadget id="calculator">8 / 10</gadget> <output>4/5 = around 0.8</output> <result>D</result>
D
0.8
In a corporation, 50 percent of the male employees and 40 percent of the female employees are at least 35 years old. If 42 percent of all the employees are at least 35 years old, what fraction of the employees in the corporation are females?
{ "A": "3 / 5", "B": "2 / 3", "C": "3 / 4", "D": "4 / 5", "E": "5 / 6" }
divide(subtract(50, 42), subtract(50, 40))
subtract(n0,n3)|subtract(n0,n1)|divide(#0,#1)
you can use the weighted averages formula for a 10 sec solution . no of females / no of males = ( 50 - 42 ) / ( 42 - 40 ) = 4 / 1 no of females as a fraction of total employees = 4 / ( 4 + 1 ) = 4 / 5 ; answer : d
other
math_qa__y5P4NJRlSD7ZfVkW
If 4 men working 10 hours a day earn Rs. 1400 per week, then 9 men working 6 hours a day will earn how much per week? Choose one: A) rs 840 B) rs 1320 C) rs 1620 D) rs 1890 E) none of these
<gadget id="calculator">9 * 6</gadget> <output>54</output> <gadget id="calculator">4 * 10</gadget> <output>40</output> <gadget id="calculator">54 / 40</gadget> <output>27/20 = around 1.35</output> <gadget id="calculator">(27/20) * 1_400</gadget> <output>1_890</output> <result>D</result>
D
1,890
If 4 men working 10 hours a day earn Rs. 1400 per week, then 9 men working 6 hours a day will earn how much per week?
{ "A": "rs 840", "B": "rs 1320", "C": "rs 1620", "D": "rs 1890", "E": "none of these" }
multiply(divide(multiply(9, 6), multiply(4, 10)), 1400)
multiply(n3,n4)|multiply(n0,n1)|divide(#0,#1)|multiply(n2,#2)|
"explanation : ( men 4 : 9 ) : ( hrs / day 10 : 6 ) : : 1400 : x hence 4 * 10 * x = 9 * 6 * 1400 or x = 9 * 6 * 1400 / 4 * 10 = 1890 answer : d"
physics
math_qa__7h5Twbt0kwWNdrN8
If a rectangular billboard has an area of 120 square feet and a perimeter of 46 feet, what is the length of each of the shorter sides? Choose the correct choice: A) 4 B) 7 C) 8 D) 13 E) 26
<gadget id="calculator">46 / 2</gadget> <output>23</output> <gadget id="calculator">23 ** 2</gadget> <output>529</output> <gadget id="calculator">4 * 120</gadget> <output>480</output> <gadget id="calculator">529 - 480</gadget> <output>49</output> <gadget id="calculator">49 ** (1/2)</gadget> <output>7</output> <gadget id="calculator">23 - 7</gadget> <output>16</output> <gadget id="calculator">16 / 2</gadget> <output>8</output> <result>C</result>
C
8
If a rectangular billboard has an area of 120 square feet and a perimeter of 46 feet, what is the length of each of the shorter sides?
{ "A": "4", "B": "7", "C": "8", "D": "13", "E": "26" }
divide(subtract(divide(46, const_2), sqrt(subtract(power(divide(46, const_2), const_2), multiply(const_4, 120)))), const_2)
divide(n1,const_2)|multiply(n0,const_4)|power(#0,const_2)|subtract(#2,#1)|sqrt(#3)|subtract(#0,#4)|divide(#5,const_2)|
"this question can be solved algebraically or by testing the answers . we ' re told that a rectangle has an area of 120 and a perimeter of 46 . we ' re asked for the length of one of the shorter sides of the rectangle . since the answers are all integers , and the area is 120 , the shorter side will almost certainly be less than 10 ( since 10 x 10 = 100 , but we ' re not dealing with a square ) . answer b ( 7 ) does not divide evenly into 120 , let ' s test answer c : 8 if . . . the shorter side = 8 . . . the area = 120 . . . . 120 / 8 = 15 = the longer side perimeter = 8 + 8 + 15 + 15 = 46 c"
geometry
math_qa__SSah5F8xgImUcSby
A car gets 33 miles to the gallon. If it is modified to use a solar panel, it will use only 75 percent as much fuel as it does now. If the fuel tank holds 16 gallons, how many more miles will the car be able to travel, per full tank of fuel, after it has been modified? Choose the correct choice from the following: A) 168 B) 172 C) 176 D) 180 E) 184
<gadget id="calculator">33 / 75</gadget> <output>11/25 = around 0.44</output> <gadget id="calculator">(11/25) * 100</gadget> <output>44</output> <gadget id="calculator">44 * 16</gadget> <output>704</output> <gadget id="calculator">33 * 16</gadget> <output>528</output> <gadget id="calculator">704 - 528</gadget> <output>176</output> <result>C</result>
C
176
A car gets 33 miles to the gallon. If it is modified to use a solar panel, it will use only 75 percent as much fuel as it does now. If the fuel tank holds 16 gallons, how many more miles will the car be able to travel, per full tank of fuel, after it has been modified?
{ "A": "168", "B": "172", "C": "176", "D": "180", "E": "184" }
subtract(multiply(multiply(divide(33, 75), const_100), 16), multiply(33, 16))
divide(n0,n1)|multiply(n0,n2)|multiply(#0,const_100)|multiply(n2,#2)|subtract(#3,#1)|
"originally , the distance the car could go on a full tank was 16 * 33 = 528 miles . after it has been modified , the car can go 33 / 0.75 = 44 miles per gallon . on a full tank , the car can go 16 * 44 = 704 miles , thus 176 miles more . the answer is c ."
physics
math_qa__76k1ptDM2zGJ8B4c
Shekar scored 76, 65, 82, 67 and 55 marks in Mathematics, Science, Social studies, English and Biology respectively. What are his average marks? Choose the correct choice: A) 65 B) 69 C) 75 D) 85 E) 90
<gadget id="calculator">76 + 65</gadget> <output>141</output> <gadget id="calculator">141 + 82</gadget> <output>223</output> <gadget id="calculator">223 + 67</gadget> <output>290</output> <gadget id="calculator">290 + 55</gadget> <output>345</output> <gadget id="calculator">1 + 4</gadget> <output>5</output> <gadget id="calculator">345 / 5</gadget> <output>69</output> <result>B</result>
B
69
Shekar scored 76, 65, 82, 67 and 55 marks in Mathematics, Science, Social studies, English and Biology respectively. What are his average marks?
{ "A": "65", "B": "69", "C": "75", "D": "85", "E": "90" }
divide(add(add(add(add(76, 65), 82), 67), 55), add(const_1, const_4))
add(n0,n1)|add(const_1,const_4)|add(n2,#0)|add(n3,#2)|add(n4,#3)|divide(#4,#1)|
"explanation : average = ( 76 + 65 + 82 + 67 + 55 ) / 5 = 375 / 5 = 69 hence average = 69 answer : b"
general
math_qa__aQXq1xntucbGxXCc
The radius of a wheel is 22.4 cm. What is the distance covered by the wheel in making 2500 resolutions? Choose the correct choice from the following choices. A) 1187 m B) 1704 m C) 2179 m D) 3520 m E) 4297 m
<gadget id="calculator">3 + 4</gadget> <output>7</output> <gadget id="calculator">7 * 3</gadget> <output>21</output> <gadget id="calculator">21 + 1</gadget> <output>22</output> <gadget id="calculator">22 / 7</gadget> <output>22/7 = around 3.142857</output> <gadget id="calculator">(22/7) * 22.4</gadget> <output>70.4</output> <gadget id="calculator">70.4 * 2</gadget> <output>140.8</output> <gadget id="calculator">140.8 * 2_500</gadget> <output>352_000</output> <gadget id="calculator">352_000 / 100</gadget> <output>3_520</output> <result>D</result>
D
3,520
The radius of a wheel is 22.4 cm. What is the distance covered by the wheel in making 2500 resolutions?
{ "A": "1187 m", "B": "1704 m", "C": "2179 m", "D": "3520 m", "E": "4297 m" }
divide(multiply(multiply(multiply(divide(add(multiply(add(const_3, const_4), const_3), const_1), add(const_3, const_4)), 22.4), const_2), 2500), const_100)
add(const_3,const_4)|multiply(#0,const_3)|add(#1,const_1)|divide(#2,#0)|multiply(n0,#3)|multiply(#4,const_2)|multiply(n1,#5)|divide(#6,const_100)|
"in one resolution , the distance covered by the wheel is its own circumference . distance covered in 2500 resolutions . = 2500 * 2 * 22 / 7 * 22.4 = 352000 cm = 3520 m answer : d"
physics
math_qa__uPkjnTvK7O4Ms421
If a person has two rectangular fields. The larger field has thrice the length and 4 times the width of the smaller field. If the smaller field has a length 50% more than the width.If a person takes 20 minutes to complete one round of a smaller field then what is the time required to complete one round of a larger field ? Choose the most appropriate option A) 69 minutes B) 68 minutes C) 58 minutes D) 48 minutes E) 67 minutes
<gadget id="calculator">50 / 100</gadget> <output>1/2 = around 0.5</output> <gadget id="calculator">4 * (1/2)</gadget> <output>2</output> <gadget id="calculator">20 * 2</gadget> <output>40</output> <gadget id="calculator">40 + 20</gadget> <output>60</output> <gadget id="calculator">60 + 4</gadget> <output>64</output> <gadget id="calculator">64 + 4</gadget> <output>68</output> <result>B</result>
B
68
If a person has two rectangular fields. The larger field has thrice the length and 4 times the width of the smaller field. If the smaller field has a length 50% more than the width.If a person takes 20 minutes to complete one round of a smaller field then what is the time required to complete one round of a larger field ?
{ "A": "69 minutes", "B": "68 minutes", "C": "58 minutes", "D": "48 minutes", "E": "67 minutes" }
add(add(add(multiply(20, multiply(4, divide(50, const_100))), 20), 4), 4)
divide(n1,const_100)|multiply(n0,#0)|multiply(n2,#1)|add(n2,#2)|add(n0,#3)|add(n0,#4)
let the width of the smaller rectangle is 4 units then , the length of the smaller rectangle is 6 units ( that is 50 % more than the width ) now the perimeter of the rectangle is 2 ( 6 + 4 ) = 20 units so , 20 units is covered in 20 units , implies covers one unit in one minute so now coming to the larger rectangle the width = 16 units , length = 18 units , perimeter = 2 ( 16 + 18 ) 68 units thus , to cover the larger field , 68 minutes required to cover the rectangle . answer : b
general
math_qa__RGnikITiCdphAFpq
The pilot of a small aircraft with a 40-gallon fuel tank wants to fly to Cleveland, which is 480 miles away. The pilot recognizes that the current engine, which can fly only 7 miles per gallon, will not get him there. By how many miles per gallon must the aircraft’s fuel efficiency be improved to make the flight to Cleveland possible? Choices: A) 2 B) 4 C) 5 D) 40 E) 160
<gadget id="calculator">480 / 40</gadget> <output>12</output> <gadget id="calculator">12 - 7</gadget> <output>5</output> <result>C</result>
C
5
The pilot of a small aircraft with a 40-gallon fuel tank wants to fly to Cleveland, which is 480 miles away. The pilot recognizes that the current engine, which can fly only 7 miles per gallon, will not get him there. By how many miles per gallon must the aircraft’s fuel efficiency be improved to make the flight to Cleveland possible?
{ "A": "2", "B": "4", "C": "5", "D": "40", "E": "160" }
subtract(divide(480, 40), 7)
divide(n1,n0)|subtract(#0,n2)|
"actual miles / gallon is = 480 / 40 = 12 miles / gallon . current engine miles / gallon is 7 miles / gallon . additional 5 miles / gallon is required to match the actual mileage . imo option c ."
physics
math_qa__Z1hlQvxVYHB1SRmw
Some of 40%-intensity red paint is replaced with 20% solution of red paint such that the new paint intensity is 20%. What fraction of the original paint was replaced? Select the correct option: A) 2 / 5 B) 2 / 3 C) 1 / 3 D) 1 / 2 E) 1 / 1
<gadget id="calculator">20 / 100</gadget> <output>1/5 = around 0.2</output> <gadget id="calculator">40 / 100</gadget> <output>2/5 = around 0.4</output> <gadget id="calculator">(1/5) - (2/5)</gadget> <output>-1/5 = around -0.2</output> <gadget id="calculator">(-1/5) / (-1/5)</gadget> <output>1</output> <result>E</result>
E
1
Some of 40%-intensity red paint is replaced with 20% solution of red paint such that the new paint intensity is 20%. What fraction of the original paint was replaced?
{ "A": "2 / 5", "B": "2 / 3", "C": "1 / 3", "D": "1 / 2", "E": "1 / 1" }
divide(subtract(divide(20, const_100), divide(40, const_100)), subtract(divide(20, const_100), divide(40, const_100)))
divide(n2,const_100)|divide(n0,const_100)|divide(n1,const_100)|subtract(#0,#1)|subtract(#2,#1)|divide(#3,#4)|
"let total paint = 1 let amount replaced = x 40 ( 1 - x ) + 20 x = 20 x = 1 / 1 answer : e"
gain
math_qa__Tb1fGVIPxMkOgYfK
There are two concentric circles with radii 10 and 6. If the radius of the outer circle is increased by 20% and the radius of the inner circle decreased by 50%, by what percent does the area between the circles increase? Choose the correct choice from the following: A) 11 B) 111 C) 211 D) 311 E) 411
<gadget id="calculator">100 + 20</gadget> <output>120</output> <gadget id="calculator">120 / 100</gadget> <output>6/5 = around 1.2</output> <gadget id="calculator">10 * (6/5)</gadget> <output>12</output> <gadget id="calculator">12 ** 2</gadget> <output>144</output> <gadget id="calculator">100 - 50</gadget> <output>50</output> <gadget id="calculator">50 / 100</gadget> <output>1/2 = around 0.5</output> <gadget id="calculator">6 * (1/2)</gadget> <output>3</output> <gadget id="calculator">3 ** 2</gadget> <output>9</output> <gadget id="calculator">144 - 9</gadget> <output>135</output> <gadget id="calculator">10 ** 2</gadget> <output>100</output> <gadget id="calculator">6 ** 2</gadget> <output>36</output> <gadget id="calculator">100 - 36</gadget> <output>64</output> <gadget id="calculator">135 - 64</gadget> <output>71</output> <gadget id="calculator">71 / 64</gadget> <output>71/64 = around 1.109375</output> <gadget id="calculator">(71/64) * 100</gadget> <output>1_775/16 = around 110.9375</output> <result>B</result>
B
111
There are two concentric circles with radii 10 and 6. If the radius of the outer circle is increased by 20% and the radius of the inner circle decreased by 50%, by what percent does the area between the circles increase?
{ "A": "11", "B": "111", "C": "211", "D": "311", "E": "411" }
multiply(divide(subtract(subtract(power(multiply(10, divide(add(const_100, 20), const_100)), const_2), power(multiply(6, divide(subtract(const_100, 50), const_100)), const_2)), subtract(power(10, const_2), power(6, const_2))), subtract(power(10, const_2), power(6, const_2))), const_100)
add(n2,const_100)|power(n0,const_2)|power(n1,const_2)|subtract(const_100,n3)|divide(#0,const_100)|divide(#3,const_100)|subtract(#1,#2)|multiply(n0,#4)|multiply(n1,#5)|power(#7,const_2)|power(#8,const_2)|subtract(#9,#10)|subtract(#11,#6)|divide(#12,#6)|multiply(#13,const_100)|
"the area of a circle is pir ^ 2 , where r is the radius . the area of the big circle is 100 pi . the area of the small circle is 36 pi . the area a 1 between the circles is 64 pi . when the big circle ' s radius increases , the new area is 144 pi . when the small circle ' s radius decreases , the new area is 9 pi . the area a 2 between the circles is 135 pi . the ratio of a 2 / a 1 is 135 / 64 = 2.11 which is an increase of 111 % . the answer is b ."
gain
math_qa__WdM3pgVZio53bm8l
A man's speed with the current is 15 km/hr and the speed of the current is 3.2 km/hr. The man's speed against the current is? Choose the correct choice: A) 10 B) 20 C) 50 D) 8.6 E) 40
<gadget id="calculator">15 - 3.2</gadget> <output>11.8</output> <gadget id="calculator">11.8 - 3.2</gadget> <output>8.6</output> <result>D</result>
D
8.6
A man's speed with the current is 15 km/hr and the speed of the current is 3.2 km/hr. The man's speed against the current is?
{ "A": "10", "B": "20", "C": "50", "D": "8.6", "E": "40" }
subtract(subtract(15, 3.2), 3.2)
subtract(n0,n1)|subtract(#0,n1)|
"man ' s speed with the current = 15 km / hr = > speed of the man + speed of the current = 15 km / hr speed of the current is 3.2 km / hr hence , speed of the man = 15 - 3.2 = 11.8 km / hr man ' s speed against the current = speed of the man - speed of the current = 11.8 - 3.2 = 8.6 km / hr answer is d ."
gain
math_qa__bU3hrXIwxVaLOUfF
X can do a piece of work in 40days. He works at it for 8 days and then Y finished it in 24 days. How long will Y take to complete the work? Choose the correct choice from the following answers: A) 30 B) 12 C) 15 D) 18 E) 20
<gadget id="calculator">8 / 40</gadget> <output>1/5 = around 0.2</output> <gadget id="calculator">1 - (1/5)</gadget> <output>4/5 = around 0.8</output> <gadget id="calculator">1 / (4/5)</gadget> <output>5/4 = around 1.25</output> <gadget id="calculator">24 * (5/4)</gadget> <output>30</output> <result>A</result>
A
30
X can do a piece of work in 40days. He works at it for 8 days and then Y finished it in 24 days. How long will Y take to complete the work?
{ "A": "30", "B": "12", "C": "15", "D": "18", "E": "20" }
multiply(24, inverse(subtract(const_1, divide(8, 40))))
divide(n1,n0)|subtract(const_1,#0)|inverse(#1)|multiply(n2,#2)|
"work done by x in 8 days = 8 * 1 / 40 = 1 / 5 remaining work = 1 - 1 / 5 = 4 / 5 4 / 5 work is done by y in 24 days whole work will be done by y in 24 * 5 / 4 = 30 days answer is a"
physics
math_qa__msfTPQ3mBEqO8yKH
Linda bought 3 notebooks at $1.20 each; a box of pencils at $1.50 and a box of pens at $1.70. How much did Linda spend? Select: A) $ 6.80 B) $ 8.40 C) $ 7.70 D) $ 4.70 E) $ 3.90
<gadget id="calculator">3 * 1.2</gadget> <output>3.6</output> <gadget id="calculator">3.6 + 1.5</gadget> <output>5.1</output> <gadget id="calculator">5.1 + 1.7</gadget> <output>6.8</output> <result>A</result>
A
6.8
Linda bought 3 notebooks at $1.20 each; a box of pencils at $1.50 and a box of pens at $1.70. How much did Linda spend?
{ "A": "$ 6.80", "B": "$ 8.40", "C": "$ 7.70", "D": "$ 4.70", "E": "$ 3.90" }
add(add(multiply(3, 1.2), 1.5), 1.7)
multiply(n0,n1)|add(n2,#0)|add(n3,#1)
linda spent 1.20 ? 3 = $ 3.60 on notebooks the total amount of money that linda spent is equal to 3.60 + 1.50 + 1.70 = $ 6.80 correct answer a
general
math_qa__xMSkoAFoX0WVU4Aq
A park square in shape has a 3 metre wide road inside it running along its sides. The area occupied by the road is 1764 square metres. What is the perimeter along the outer edge of the road? Choose the correct choice from the following answers. A) 576 metres B) 589 metres C) 600 metres D) 700 metres E) none
<gadget id="calculator">3 * 2</gadget> <output>6</output> <gadget id="calculator">6 ** 2</gadget> <output>36</output> <gadget id="calculator">1_764 + 36</gadget> <output>1_800</output> <gadget id="calculator">2 * 6</gadget> <output>12</output> <gadget id="calculator">1_800 / 12</gadget> <output>150</output> <gadget id="calculator">150 * 4</gadget> <output>600</output> <result>C</result>
C
600
A park square in shape has a 3 metre wide road inside it running along its sides. The area occupied by the road is 1764 square metres. What is the perimeter along the outer edge of the road?
{ "A": "576 metres", "B": "589 metres", "C": "600 metres", "D": "700 metres", "E": "none" }
multiply(divide(add(1764, power(multiply(3, const_2), const_2)), multiply(const_2, multiply(3, const_2))), const_4)
multiply(n0,const_2)|multiply(#0,const_2)|power(#0,const_2)|add(n1,#2)|divide(#3,#1)|multiply(#4,const_4)
solution let the length of the outer edges be x metres . then , length of the inner edge = ( x - 6 ) m . ∴ x 2 - ( x - 6 ) 2 = 1764 ‹ = › x 2 - ( x 2 - 12 x + 36 ) = 1764 ‹ = › 12 x = 1800 ‹ = › x = 150 . ∴ required perimeter = ( 4 x ) m ‹ = › ( 4 x 150 ) m = 600 m . answer c
geometry
math_qa__uWjFA5hXsJsWtduX
An amount at compound interest sums to Rs.17640/- in 2 years and to Rs.22932/- in 3 years at the same rate of interest. Find the rate percentage? Choose the correct choice from the following answers A) 5 % B) 7 % C) 9 % D) 11 % E) 30 %
<gadget id="calculator">22_932 - 17_640</gadget> <output>5_292</output> <gadget id="calculator">5_292 / 17_640</gadget> <output>3/10 = around 0.3</output> <gadget id="calculator">(3/10) * 100</gadget> <output>30</output> <result>E</result>
E
30
An amount at compound interest sums to Rs.17640/- in 2 years and to Rs.22932/- in 3 years at the same rate of interest. Find the rate percentage?
{ "A": "5 %", "B": "7 %", "C": "9 %", "D": "11 %", "E": "30 %" }
multiply(divide(subtract(22932, 17640), 17640), const_100)
subtract(n2,n0)|divide(#0,n0)|multiply(#1,const_100)|
"explanation : the difference of two successive amounts must be the simple interest in 1 year on the lower amount of money . s . i = 22932 / - - 17640 / - = rs . 5292 / - rate of interest = ( 5292 / 22932 ) × ( 100 / 1 ) = > 30 % answer : option e"
general
math_qa__MYMZ3NuiUOeWKs1H
For how many integer values of n will the value of the expression 4n + 7 be an integer greater than 1 and less than 60? Answers: A) 10 B) 15 C) 8 D) 12 E) 20
<gadget id="calculator">60 - 7</gadget> <output>53</output> <gadget id="calculator">53 / 4</gadget> <output>53/4 = around 13.25</output> <gadget id="calculator">floor(53/4)</gadget> <output>13</output> <gadget id="calculator">1 - 7</gadget> <output>-6</output> <gadget id="calculator">(-6) / 4</gadget> <output>-3/2 = around -1.5</output> <gadget id="calculator">floor(-3/2)</gadget> <output>-2</output> <gadget id="calculator">13 - (-2)</gadget> <output>15</output> <result>B</result>
B
15
For how many integer values of n will the value of the expression 4n + 7 be an integer greater than 1 and less than 60?
{ "A": "10", "B": "15", "C": "8", "D": "12", "E": "20" }
subtract(floor(divide(subtract(60, 7), 4)), floor(divide(subtract(1, 7), 4)))
subtract(n3,n1)|subtract(n2,n1)|divide(#0,n0)|divide(#1,n0)|floor(#2)|floor(#3)|subtract(#4,#5)|
"4 n + 7 > 1 4 n > - 6 n > - ( 3 / 2 ) n > - 1.5 ( n = - 1 , 0 , 1 , 2 3 . . . . . . . . upto infinity ) from second constraint 4 n + 7 < 60 4 n < 53 n < 13 . 25 n = ( - infinity , . . . . . . . - 3 , - 2 , - 1 , 0 , 1 , 2 , . . . . . . . . . upto 13 ) combining the two - 1.5 < n < 13.25 n = 1 to 13 ( 48 integers ) and n = - 1 and 0 so 15 integers . b"
general
math_qa__nY2aUjfT56ZtWbYK
R = {2, 3, 4, 5} B = {4, 5, 6, 7, 8} Two integers will be randomly selected from the sets above, one integer from set R and one integer from set B. What is the probability that the sum of the two integers will equal 9 ? Choose the correct choice from the following answers: A) 0.15 B) 0.20 C) 0.25 D) 0.30 E) 0.33
<gadget id="calculator">4 / 4</gadget> <output>1</output> <gadget id="calculator">1 / 5</gadget> <output>1/5 = around 0.2</output> <gadget id="calculator">1 * (1/5)</gadget> <output>1/5 = around 0.2</output> <result>B</result>
B
0.2
R = {2, 3, 4, 5} B = {4, 5, 6, 7, 8} Two integers will be randomly selected from the sets above, one integer from set R and one integer from set B. What is the probability that the sum of the two integers will equal 9 ?
{ "A": "0.15", "B": "0.20", "C": "0.25", "D": "0.30", "E": "0.33" }
multiply(divide(4, 4), divide(const_1, 5))
divide(n2,n2)|divide(const_1,n3)|multiply(#0,#1)
the total number of pairs r , b possible is 4 * 5 = 20 . out of these 20 pairs only 4 sum up to 9 : ( 2 , 7 ) ; ( 3 , 6 ) , ( 4 , 5 ) and ( 5 , 4 ) . the probability thus is 4 / 20 = 0.2 . answer : b .
general
math_qa__urRDunRDybvgBnUu
A $79.95 lawn chair was sold for $59.95 at a special sale. By approximately what percent was the price decreased? Answers A) 15 % B) 20 % C) 25 % D) 60 % E) 80 %
<gadget id="calculator">79.95 - 59.95</gadget> <output>20</output> <gadget id="calculator">20 / 79.95</gadget> <output>0.250156</output> <gadget id="calculator">0.250156 * 100</gadget> <output>25.0156</output> <result>C</result>
C
25
A $79.95 lawn chair was sold for $59.95 at a special sale. By approximately what percent was the price decreased?
{ "A": "15 %", "B": "20 %", "C": "25 %", "D": "60 %", "E": "80 %" }
multiply(divide(subtract(79.95, 59.95), 79.95), const_100)
subtract(n0,n1)|divide(#0,n0)|multiply(#1,const_100)|
"listed selling price of chair = 79.95 $ discounted selling price of chair = 59.95 $ discount = 79.95 - 59.95 = 20 $ % decrease in price of chair = ( 20 / 79.95 ) * 100 % = 25 % approx answer c"
general
math_qa__DTZAXyWgKg6hRLYk
5 drainage pipes , each draining water from a pool at the same constant rate , together can drain a certain pool in 16 days . how many additional pipes , each draining water at the same constant rate , will be needed to drain the pool in 4 days ? Choose the most appropriate option. A) 6 B) 9 C) 10 D) 12 E) 15
<gadget id="calculator">4 * 5</gadget> <output>20</output> <gadget id="calculator">20 - 5</gadget> <output>15</output> <result>E</result>
E
15
5 drainage pipes , each draining water from a pool at the same constant rate , together can drain a certain pool in 16 days . how many additional pipes , each draining water at the same constant rate , will be needed to drain the pool in 4 days ?
{ "A": "6", "B": "9", "C": "10", "D": "12", "E": "15" }
subtract(multiply(4, 5), 5)
multiply(n0,n2)|subtract(#0,n0)
this is an inverse proportional problem . . . . . . 5 pipes in 16 days ; so for 4 days , it will be = 16 x 5 / 4 = 20 so , 20 - 5 = 15 answer e
general
math_qa__wzAayj0RLogMO546
A heap of grapes is divided into groups of 3, 5 and 7 and each time one coconut is left over. The least number of grapes in the heap is? A. 31 B. 41 C. 51 D. 61 Choose the correct choice from the following choices: A) 31 B) 41 C) 106 D) 61 E) 71
<gadget id="calculator">lcm(3, 5)</gadget> <output>15</output> <gadget id="calculator">lcm(15, 7)</gadget> <output>105</output> <result>C</result>
C
106
A heap of grapes is divided into groups of 3, 5 and 7 and each time one coconut is left over. The least number of grapes in the heap is? A. 31 B. 41 C. 51 D. 61
{ "A": "31", "B": "41", "C": "106", "D": "61", "E": "71" }
lcm(lcm(3, 5), 7)
lcm(n0,n1)|lcm(n2,#0)
lcm = 105 = > 105 + 1 = 106 answer : c
general
math_qa__6iQD3gvnoNGCEtT1
The diagonals of a rhombus are 12 cm and 10 cm. Find its area? Select the correct option: A) 158 B) 129 C) 150 D) 123 E) 60
<gadget id="calculator">(12 * 10) / 2</gadget> <output>60</output> <result>E</result>
E
60
The diagonals of a rhombus are 12 cm and 10 cm. Find its area?
{ "A": "158", "B": "129", "C": "150", "D": "123", "E": "60" }
rhombus_area(12, 10)
rhombus_area(n0,n1)|
"1 / 2 * 12 * 10 = 60 answer : e"
geometry
math_qa__u8xDtTrM1eMQjgrO
Find the greatest number which on dividing 1657 and 2037 leaves remainders 6 and 5 respectively. Choose one: A) 121 B) 124 C) 127 D) 122 E) 129
<gadget id="calculator">1_657 - 6</gadget> <output>1_651</output> <gadget id="calculator">2_037 - 5</gadget> <output>2_032</output> <gadget id="calculator">gcd(1_651, 2_032)</gadget> <output>127</output> <result>C</result>
C
127
Find the greatest number which on dividing 1657 and 2037 leaves remainders 6 and 5 respectively.
{ "A": "121", "B": "124", "C": "127", "D": "122", "E": "129" }
gcd(subtract(1657, 6), subtract(2037, 5))
subtract(n0,n2)|subtract(n1,n3)|gcd(#0,#1)|
"required number = h . c . f . of ( 1657 - 6 ) and ( 2037 - 5 ) = h . c . f . of 1651 and 2032 _______ 1651 ) 2032 ( 1 1651 1651 _______ 381 ) 1651 ( 4 1524 _________ 127 ) 381 ( 3 381 0 required number = 127 . answer is c ."
general
math_qa__k9u9jAzPofO98REO
ram - leela has $ 100 in her piggy bank . how much will she have in her bank 52 weeks from now if she puts $ 1 in the bank next week , $ 2 two weeks from now , $ 3 3 weeks from now , and continues to increase the amount that she puts in by $ 1 each week ? Choose the correct choice from the following answers: A) 1478 B) 1578 C) 1678 D) 1778 E) 1798
<gadget id="calculator">100 / 2</gadget> <output>50</output> <gadget id="calculator">50 + 3</gadget> <output>53</output> <gadget id="calculator">53 * 52</gadget> <output>2_756</output> <gadget id="calculator">2_756 / 2</gadget> <output>1_378</output> <gadget id="calculator">1_378 + 100</gadget> <output>1_478</output> <result>A</result>
A
1,478
ram - leela has $ 100 in her piggy bank . how much will she have in her bank 52 weeks from now if she puts $ 1 in the bank next week , $ 2 two weeks from now , $ 3 3 weeks from now , and continues to increase the amount that she puts in by $ 1 each week ?
{ "A": "1478", "B": "1578", "C": "1678", "D": "1778", "E": "1798" }
add(divide(multiply(add(divide(100, 2), 3), 52), 2), 100)
divide(n0,n3)|add(n4,#0)|multiply(n1,#1)|divide(#2,n3)|add(n0,#3)
the dollar deposits are in an a . p . 1,2 , 3,4 . . . 52 with common difference 1 sum of the terms is n ( n + 1 ) / 2 i . e 52 * ( 52 + 1 ) / 2 = 52 * 53 / 2 = 1378 total deposit therefore with chiu - lihas is 100 + 1378 = 1478 $
general
math_qa__Wh1Z3irAo6WQ3amr
A certain mixture of nuts consists of 5 parts almonds to 2 parts walnuts, by weight. What is the number of pounds of almonds in 350 pounds of the mixture ? Options: A) 250 B) 84 C) 40 D) 28 E) 20
<gadget id="calculator">5 * 350</gadget> <output>1_750</output> <gadget id="calculator">5 + 2</gadget> <output>7</output> <gadget id="calculator">1_750 / 7</gadget> <output>250</output> <result>A</result>
A
250
A certain mixture of nuts consists of 5 parts almonds to 2 parts walnuts, by weight. What is the number of pounds of almonds in 350 pounds of the mixture ?
{ "A": "250", "B": "84", "C": "40", "D": "28", "E": "20" }
divide(multiply(5, 350), add(5, 2))
add(n0,n1)|multiply(n0,n2)|divide(#1,#0)
almonds : walnuts = 5 : 2 total mixture has 7 parts in a 350 pound mixture , almonds are 5 / 7 ( total mixture ) = 5 / 7 * 350 = 250 pounds answer ( a )
general
math_qa__iGHzl8UklbsGKsjK
If x = -5/4 and y = -3/2, what is the value of the expression -2x – y^2? Choose the correct option. A) 1 / 4 B) - 1 C) 5 / 4 D) 3 / 2 E) 3 / 4
<gadget id="calculator">5 / 4</gadget> <output>5/4 = around 1.25</output> <gadget id="calculator">2 * (5/4)</gadget> <output>5/2 = around 2.5</output> <gadget id="calculator">3 / 2</gadget> <output>3/2 = around 1.5</output> <gadget id="calculator">(3/2) ** 2</gadget> <output>9/4 = around 2.25</output> <gadget id="calculator">(5/2) - (9/4)</gadget> <output>1/4 = around 0.25</output> <result>A</result>
A
0.25
If x = -5/4 and y = -3/2, what is the value of the expression -2x – y^2?
{ "A": "1 / 4", "B": "- 1", "C": "5 / 4", "D": "3 / 2", "E": "3 / 4" }
subtract(multiply(2, divide(5, 4)), power(divide(3, 2), 2))
divide(n0,n1)|divide(n2,n3)|multiply(n3,#0)|power(#1,n3)|subtract(#2,#3)
x = - 5 / 4 and y = - 3 / 2 = = > - 2 ( - 5 / 4 ) - ( 3 / 2 ) ^ 2 = 10 / 4 - 9 / 4 = 1 / 4 ans : a
general
math_qa__gqlH7EaBKOR8A8dq
Which expression is the greatest Answers A) 3252 / 3257 B) 3456 / 3461 C) 3591 / 3596 D) 3641 / 3656 E) 3453 / 3458
<gadget id="calculator">3 * 3</gadget> <output>9</output> <gadget id="calculator">3_600 - 9</gadget> <output>3_591</output> <gadget id="calculator">3_600 - 4</gadget> <output>3_596</output> <gadget id="calculator">3_591 / 3_596</gadget> <output>3_591/3_596 = around 0.99861</output> <result>D</result>
D
0.995897
Which expression is the greatest
{ "A": "3252 / 3257", "B": "3456 / 3461", "C": "3591 / 3596", "D": "3641 / 3656", "E": "3453 / 3458" }
divide(subtract(const_3600, multiply(const_3, const_3)), subtract(const_3600, const_4))
multiply(const_3,const_3)|subtract(const_3600,const_4)|subtract(const_3600,#0)|divide(#2,#1)|
"options can be re - written as ( x - 5 ) x = > 1 - ( 5 / x ) a ) 1 - ( 5 / 3257 ) b ) 1 - ( 5 / 3461 ) c ) 1 - ( 5 / 3596 ) d ) 1 - ( 5 / 3656 ) e ) 1 - ( 5 / 3458 ) to get the largest among these second half should be the least and so denominator to be largest . hence ' d ' ."
general
math_qa__iDR6LkFGTxhzLH1p
Jerry’s average (arithmetic mean) score on the first 3 of 4 tests is 78. If Jerry wants to raise his average by 2 points, what score must he earn on the fourth test? Answers: A) 87 B) 89 C) 86 D) 93 E) 95
<gadget id="calculator">78 + 2</gadget> <output>80</output> <gadget id="calculator">4 * 80</gadget> <output>320</output> <gadget id="calculator">78 * 3</gadget> <output>234</output> <gadget id="calculator">320 - 234</gadget> <output>86</output> <result>C</result>
C
86
Jerry’s average (arithmetic mean) score on the first 3 of 4 tests is 78. If Jerry wants to raise his average by 2 points, what score must he earn on the fourth test?
{ "A": "87", "B": "89", "C": "86", "D": "93", "E": "95" }
subtract(multiply(4, add(78, 2)), multiply(78, 3))
add(n2,n3)|multiply(n0,n2)|multiply(n1,#0)|subtract(#2,#1)|
"total score on 3 tests = 78 * 3 = 234 jerry wants the average to be = 80 hence total score on 4 tests should be = 80 * 4 = 320 score required on the fourth test = 320 - 234 = 86 option c"
general
math_qa__ub10S1sX9HuTnKWb
Guy drives 60 miles to attend a meeting. Halfway through, he increases his speed so that his average speed on the second half is 16 miles per hour faster than the average speed on the first half. His average speed for the entire trip is 30 miles per hour. Guy drives on average how many miles per hour during the first half of the way? Choose the correct choice from the following answers: A) 12 B) 14 C) 16 D) 24 E) 40
<gadget id="calculator">16 * 30</gadget> <output>480</output> <gadget id="calculator">480 / 2</gadget> <output>240</output> <gadget id="calculator">3 * 2</gadget> <output>6</output> <gadget id="calculator">60 / 6</gadget> <output>10</output> <gadget id="calculator">240 / 10</gadget> <output>24</output> <result>D</result>
D
24
Guy drives 60 miles to attend a meeting. Halfway through, he increases his speed so that his average speed on the second half is 16 miles per hour faster than the average speed on the first half. His average speed for the entire trip is 30 miles per hour. Guy drives on average how many miles per hour during the first half of the way?
{ "A": "12", "B": "14", "C": "16", "D": "24", "E": "40" }
divide(divide(multiply(16, 30), const_2), divide(60, multiply(const_3, const_2)))
multiply(n1,n2)|multiply(const_2,const_3)|divide(#0,const_2)|divide(n0,#1)|divide(#2,#3)
let x be the average speed for 1 st half of the distance . then the average speed for 2 nd half of the distance will be x + 16 avg speed = total distance / total time 30 = 60 / { ( 30 / x ) + ( 30 / ( x + 16 ) ) } solving we get x ^ 2 - 14 x - 240 = 0 x = - 10 or 24 x cant be negative hence x = 24 answer : d
physics
math_qa__aVP4L5gN1ot9uPaN
15 years hence , rohan will be just 4 times as old as he was 15 years ago . how old is rohan at present ? Choose the correct choice from the following answers: A) 20 B) 25 C) 30 D) 35 E) 40
<gadget id="calculator">4 * 15</gadget> <output>60</output> <gadget id="calculator">60 + 15</gadget> <output>75</output> <gadget id="calculator">4 - 1</gadget> <output>3</output> <gadget id="calculator">75 / 3</gadget> <output>25</output> <result>B</result>
B
25
15 years hence , rohan will be just 4 times as old as he was 15 years ago . how old is rohan at present ?
{ "A": "20", "B": "25", "C": "30", "D": "35", "E": "40" }
divide(add(multiply(4, 15), 15), subtract(4, const_1))
multiply(n0,n1)|subtract(n1,const_1)|add(n0,#0)|divide(#2,#1)
let the present age of rohan be x years then , given : x + 15 = 4 ( x - 15 ) x = 25 answer : b
general
math_qa__746m1rEKw84IrrCP
Dan’s car gets 32 miles per gallon. If gas costs $4/gallon, then how many miles can Dan’s car go on $54 of gas? Choose the correct choice from the following: A) 236 B) 354 C) 432 D) 512 E) 670
<gadget id="calculator">54 * 32</gadget> <output>1_728</output> <gadget id="calculator">1_728 / 4</gadget> <output>432</output> <result>C</result>
C
432
Dan’s car gets 32 miles per gallon. If gas costs $4/gallon, then how many miles can Dan’s car go on $54 of gas?
{ "A": "236", "B": "354", "C": "432", "D": "512", "E": "670" }
divide(multiply(54, 32), 4)
multiply(n0,n2)|divide(#0,n1)
54 / 4 = 13.5 gallons 13.5 * 32 = 432 miles the answer is c .
physics
math_qa__hqzSgD0oC6kQ0Hpp
Walking at the rate of 5kmph a man cover certain distance in 5hr. Running at a speed of 15 kmph the man will cover the same distance in. Choose the correct choice from the following: A) 12 min B) 36 min C) 40 min D) 48 min E) 60 min
<gadget id="calculator">5 * 5</gadget> <output>25</output> <gadget id="calculator">15 / 25</gadget> <output>3/5 = around 0.6</output> <gadget id="calculator">(3/5) * 60</gadget> <output>36</output> <result>B</result>
B
36
Walking at the rate of 5kmph a man cover certain distance in 5hr. Running at a speed of 15 kmph the man will cover the same distance in.
{ "A": "12 min", "B": "36 min", "C": "40 min", "D": "48 min", "E": "60 min" }
multiply(divide(15, multiply(5, 5)), const_60)
multiply(n0,n0)|divide(n2,#0)|multiply(#1,const_60)
distance = speed * time 5 * 5 = 25 km new speed = 15 kmph therefore time = 25 / 15 = 5 / 3 = 36 min answer : b
physics
math_qa__voITX5Z6RmLn4uz5
subash can copy 50 pages in 10 hrs.subash and prakash together can copy 300 pages in 40 hours.in how much time prakash can copy 18 pages. Choose the correct choice from the following: A) 8 B) 10 C) 2 D) 14 E) 16
<gadget id="calculator">300 / 40</gadget> <output>15/2 = around 7.5</output> <gadget id="calculator">50 / 10</gadget> <output>5</output> <gadget id="calculator">(15/2) - 5</gadget> <output>5/2 = around 2.5</output> <gadget id="calculator">floor(5/2)</gadget> <output>2</output> <result>C</result>
C
2
subash can copy 50 pages in 10 hrs.subash and prakash together can copy 300 pages in 40 hours.in how much time prakash can copy 18 pages.
{ "A": "8", "B": "10", "C": "2", "D": "14", "E": "16" }
floor(subtract(divide(300, 40), divide(50, 10)))
divide(n2,n3)|divide(n0,n1)|subtract(#0,#1)|floor(#2)
subhas ' s 1 hr copy page = 50 / 10 = 5 page ( subhas + prakash ) ' s 1 hr copy page = 300 / 40 = 7.5 page from above prakash ' s 1 hr copy page = 2.5 page so time taken in 30 page ' s copy = ( 5 / 2.5 ) = 2 hrs answer : c
general
math_qa__u9egcq99bTNkfPRi
Average expenditure of a person for the first 3 days of a week is Rs. 330 and for the next 4 days is Rs. 420. Average expenditure of the man for the whole week is: Choose the correct choice from the following: A) 350 B) 370 C) 390 D) 430 E) none
<gadget id="calculator">420 - 330</gadget> <output>90</output> <gadget id="calculator">4 * 90</gadget> <output>360</output> <gadget id="calculator">3 + 4</gadget> <output>7</output> <gadget id="calculator">360 / 7</gadget> <output>360/7 = around 51.428571</output> <gadget id="calculator">330 + (360/7)</gadget> <output>2_670/7 = around 381.428571</output> <result>B</result>
B
370
Average expenditure of a person for the first 3 days of a week is Rs. 330 and for the next 4 days is Rs. 420. Average expenditure of the man for the whole week is:
{ "A": "350", "B": "370", "C": "390", "D": "430", "E": "none" }
add(330, divide(multiply(4, subtract(420, 330)), add(3, 4)))
add(n0,n2)|subtract(n3,n1)|multiply(n2,#1)|divide(#2,#0)|add(n1,#3)|
"explanation : assumed mean = rs . 330 total excess than assumed mean = 4 × ( rs . 420 - rs . 350 ) = rs . 280 therefore , increase in average expenditure = rs . 280 / 7 = rs . 40 therefore , average expenditure for 7 days = rs . 330 + rs . 40 = rs . 370 correct option : b"
general
math_qa__itgm7OVJ7l9hi6Dp
In a class there are 55 pupil, out of them 10 are in debate only and 18 in singing only. Then how many in both? Options: A) 132 B) 26 C) 17 D) 11 E) 12
<gadget id="calculator">55 - 18</gadget> <output>37</output> <gadget id="calculator">37 - 10</gadget> <output>27</output> <gadget id="calculator">27 - 10</gadget> <output>17</output> <result>C</result>
C
17
In a class there are 55 pupil, out of them 10 are in debate only and 18 in singing only. Then how many in both?
{ "A": "132", "B": "26", "C": "17", "D": "11", "E": "12" }
subtract(subtract(subtract(55, 18), 10), 10)
subtract(n0,n2)|subtract(#0,n1)|subtract(#1,n1)
explanation : total pupil = 55 debate + singing = 10 + 18 = 28 the intersection for two = 55 â € “ 10 â € “ 28 = 17 play both games . answer : c
other