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a ) 42 , b ) 70 , c ) 175 , d ) 165 , e ) 315 | c | multiply(multiply(7, 3), 5) | a certain university will select 1 of 5 candidates eligible to fill a position in the mathematics department and 4 of 7 candidates eligible to fill 2 identical positions in the computer science department . if none of the candidates is eligible for a position in both departments , how many different sets of 3 candidates are there to fill the 3 positions ? | "5 c 1 * 7 c 4 = 5 * 35 = 175 the answer is ( c )" | a = 7 * 3
b = a * 5
|
a ) 275 m , b ) 360 m , c ) 375 m , d ) 425 m , e ) 440 m | d | multiply(multiply(51, const_0_2778), 30) | if the speed of a man is 51 km per hour , then what is the distance traveled by him in 30 seconds ? | "the distance traveled in 30 sec = 51 * ( 5 / 18 ) * 30 = 425 m answer : d" | a = 51 * const_0_2778
b = a * 30
|
a ) 23 , b ) 1 : 2 , c ) 2 : 5 , d ) 3 : 5 , e ) 25 | b | divide(subtract(6, 4), 4) | the ratio between the sale price and the cost price of an article is 6 : 4 . what is the ratio between the profit and the cost price of that article ? | "c . p . = rs . 4 x and s . p . = rs . 6 x . then , gain = rs . 2 x required ratio = 2 x : 4 x = 1 : 2 b" | a = 6 - 4
b = a / 4
|
a ) $ 2000 , b ) $ 1800 , c ) $ 2500 , d ) $ 1500 , e ) $ 1600 | b | multiply(divide(3, add(add(2, 3), 4)), 5400) | a person want to give his money of $ 5400 to his 3 children a , b , c in the ratio 2 : 3 : 4 . what is the b ' s share ? | "b ' s share = 5400 * 3 / 9 = $ 1800 answer is b" | a = 2 + 3
b = a + 4
c = 3 / b
d = c * 5400
|
a ) 0 , b ) 1 , c ) 6 , d ) 2 , e ) 3 | a | divide(const_2, choose(add(const_3, const_3), const_3)) | what is the product of first three whole no . | "first three whole no . are 0 , 1,2 . remember whole no . start from 0 and natural no . from 1 so product will 0 only . answer a" | a = 3 + 3
b = math.comb(a, 3)
c = 2 / b
|
a ) 17 / 36 , b ) 36 / 17 , c ) 17 / 6 , d ) 17 / 1 , e ) 51 / 4 | d | subtract(divide(add(multiply(const_10, 2), 2), 3), divide(add(const_10, 1), 4)) | what is 2 2 / 3 - 1 1 / 4 divided by 1 / 4 - 1 / 6 ? | "2 2 / 3 - 1 1 / 4 = 8 / 3 - 5 / 4 = ( 32 - 15 ) / 12 = 17 / 12 1 / 4 - 1 / 6 = ( 6 - 4 ) / 24 = 2 / 24 = 1 / 12 so 17 / 12 / 1 / 12 = 17 / 12 * 12 = 17 / 1 answer - d" | a = 10 * 2
b = a + 2
c = b / 3
d = 10 + 1
e = d / 4
f = c - e
|
a ) 3005 , b ) 3098 , c ) 3300 , d ) 3010 , e ) 3000 | e | subtract(10000, multiply(divide(7, 10), 10000)) | income and expenditure of a person are in the ratio 10 : 7 . if the income of the person is rs . 10000 , then find his savings ? | "let the income and the expenditure of the person be rs . 10 x and rs . 7 x respectively . income , 10 x = 10000 = > x = 1000 savings = income - expenditure = 10 x - 7 x = 3 x = 3 ( 1000 ) so , savings = rs . 3000 . answer : e" | a = 7 / 10
b = a * 10000
c = 10000 - b
|
a ) 17.39 % , b ) 2 / 8 % , c ) 2 / 1 % , d ) 1 / 3 % , e ) 2 / 7 % | a | multiply(divide(15, add(const_100, 15)), const_100) | if the price of an article went up by 15 % , then by what percent should it be brought down to bring it back to its original price ? | "let the price of the article be rs . 100 . 15 % of 100 = 15 new price = 100 + 15 = rs . 115 required percentage = ( 115 - 100 ) / 115 * 100 = 20 / 115 * 100 = 17.39 % . answer : a" | a = 100 + 15
b = 15 / a
c = b * 100
|
a ) 250 / 3 , b ) 500 / 3 , c ) 300 , d ) 480 , e ) 600 | c | multiply(divide(subtract(25, 10), subtract(30, 25)), 100) | solution x is 10 percent alcohol by volume , and solution y is 30 percent alcohol by volume . how many milliliters of solution y must be added to 100 milliliters of solution x to create a solution that is 25 percent alcohol by volume ? | "we know that x is 10 % , y is 30 % and w . avg = 25 % . what does this mean with respect to w . avg technique ? w . avg is 1 portion away from y and 3 portion away from x so for every 1 portion of x we will have to add 3 portions of y . if x = 100 then y = 300 answer : c" | a = 25 - 10
b = 30 - 25
c = a / b
d = c * 100
|
a ) $ 7.15 , b ) $ 8.87 , c ) $ 28.96 , d ) $ 35.57 , e ) $ 40.92 | e | add(add(1.07, 5.35), multiply(0.023, divide(1.5, 0.001))) | one millisecond is 0.001 of a second . the costs for a single run of a computer program are $ 1.07 for operating - system overhead , $ 0.023 per millisecond of computer time , and $ 5.35 for the mounting of a data tape . what is the total of these 3 costs for 1 run of a program that requires 1.5 seconds of computer time ? | operating system overhead for 1 run = 1.07 $ mounting of data tape = 5.35 $ cost per 1 millisecond of computer time = . 023 $ total cost of 1 run of a program that requires 1.5 seconds of computer time = 1.07 + ( . 023 * 1500 ) + 5.35 = 1.07 + 34.5 + 5.35 = 40.92 $ answer e | a = 1 + 7
b = 1 / 5
c = 0 * 23
d = a + c
|
a ) 63 , b ) 72 , c ) 144 , d ) 216 , e ) 207 | e | multiply(divide(multiply(46, const_3), 20), 30) | if 20 typists can type 46 letters in 20 minutes , then how many letters will 30 typists working at the same rate complete in 1 hour ? | "20 typists can type 46 letters , so 30 typists can type = 46 * 30 / 20 46 * 30 / 20 letters can be typed in 20 mins . in 60 mins typist can type = 46 * 30 * 60 / 20 * 20 = 207 e is the answer" | a = 46 * 3
b = a / 20
c = b * 30
|
a ) 5 ½ ft , b ) 7 ½ ft , c ) 8 ½ ft , d ) 9 ½ ft , e ) 10 ft | b | subtract(divide(12, const_2), divide(const_1, const_2)) | the figure above shows the dimensions of a semicircular cross section of a one - way tunnel . the single traffic lane is 12 feet wide and is equidistant from the sides of the tunnel . if vehicles must clear the top of the tunnel by at least ½ foot when they are inside the traffic lane , what should be the limit h on the height of vehicles that are allowed to use the tunnel ? | "let ' s label the midpoint of the circle o . since the base of the semi - circle is 20 , we know that the diameter is 20 and , accordingly , the radius is 10 . we also know that the traffic lane is 12 feet long and there ' s an equal amount of space on either side , so the traffic lane extends 6 feet on either side of o . let ' s call the leftmost point on the base of the traffic lane a . so , the distance oa is 6 . now draw a line straight up from a to the top of the tunnel . let ' s label the point at which the line intersects the circle b . the answer to the question will , therefore , be the height ab - . 5 feet ( we need to leave . 5 feet of clearance ) . here ' s the key to solving the question : if we draw a line from o to b , that line is a radius of the circle and , therefore , has length 10 . we now have right triangle oab ( the right angle is at point a ) , with leg oa = 6 and hypotenuse ob = 10 . we can now solve for leg ab = 8 ( either by applying the pythagorean theorum or by applying the 3 / 4 / 5 special right triangle ratio ) . finally : ab = 8 , so the correct answer h is 8 - . 5 = 7.5 . . . choose ( b ) ! from a strategic guessing point of view , as soon as we realize that the height of the tunnel is 10 in the middle , we should quickly eliminate ( d ) and ( e ) as too big ; worse case you have a 1 / 3 shot at picking up the points . b" | a = 12 / 2
b = 1 / 2
c = a - b
|
a ) 2 , b ) 4 , c ) 0 , d ) 10 , e ) 3 | b | power(subtract(multiply(2, divide(add(34, 20), add(4, 2))), 20), 2) | if 4 x + y = 34 , 2 x - y = 20 , for integers of x and y , y ^ 2 = ? | 4 x + y = 34 2 x - y = 20 6 x = 54 x = 9 y = - 2 y ^ 2 = 4 answer is b | a = 34 + 20
b = 4 + 2
c = a / b
d = 2 * c
e = d - 20
f = e ** 2
|
a ) 50.2 , b ) 45.8 , c ) 54.7 , d ) 61.8 , e ) 10.5 | c | subtract(113, 59) | what is the sum of mean and median of 17 , 45 , 59 , 113 , 76 , 95 , 59 , 35 , 1236 ? | mean = ( 17 + 45 + 59 + 113 + 76 + 95 + 59 + 35 + 12 + 36 ) / 10 = 547 / 10 = 54.7 answer is c | a = 113 - 59
|
a ) 15 / 8 , b ) 14 / 3 , c ) 41 / 7 , d ) 3 / 18 , e ) 18 / 4 | a | multiply(multiply(divide(multiply(multiply(5, 1), 1), multiply(multiply(2, 2), 1)), divide(multiply(multiply(1, 1), 3), multiply(multiply(2, 1), 2))), divide(multiply(multiply(1, 3), 4), multiply(multiply(1, 2), 3))) | if a / b = 5 / 2 , b / c = 1 / 2 , c / d = 1 , d / e = 3 / 2 and e / f = 4 / 3 , then what is the value of abc / def ? | say a = 2 . then : a / b = 5 / 2 - - > b = 2 / 5 ; b / c = 1 / 2 - - > c = 4 / 5 ; c / d = 1 - - > d = 4 / 5 ; d / e = 3 / 2 - - > e = 8 / 15 ; e / f = 4 / 3 - - > f = 2 / 5 . abc / def = ( 1 * 2 / 5 * 4 / 5 ) / ( 4 / 5 * 8 / 15 * 2 / 5 ) = 15 / 8 . answer : a . | a = 5 * 1
b = a * 1
c = 2 * 2
d = c * 1
e = b / d
f = 1 * 1
g = f * 3
h = 2 * 1
i = h * 2
j = g / i
k = e * j
l = 1 * 3
m = l * 4
n = 1 * 2
o = n * 3
p = m / o
q = k * p
|
a ) $ 28 , b ) $ 187 , c ) $ 110 , d ) $ 138 , e ) $ 192 | b | divide(add(add(multiply(multiply(const_4, const_4), const_1000), multiply(2, const_100)), multiply(add(75, 2), 150)), 150) | a computer manufacturer produces a certain electronic component at a cost of $ 75 per component . shipping costs for delivering the components are $ 2 per unit . further , the manufacturer has costs of $ 16,500 a month related to the electronic component regardless of how many it produces . if the manufacturer produces and sells 150 components a month , what is the lowest price it can sell them for such that the costs do n ' t exceed the revenues ? | "this question can be solved easily using a equation model . 150 * p = 16500 ( fixed cost ) + 150 * 75 + 150 * 2 . = 16500 + 11250 + 300 p = $ 187 b" | a = 4 * 4
b = a * 1000
c = 2 * 100
d = b + c
e = 75 + 2
f = e * 150
g = d + f
h = g / 150
|
a ) $ 1.60 , b ) $ 16.00 , c ) $ 96.00 , d ) $ 108.00 , e ) $ 192.00 | e | multiply(divide(3.20, 10), surface_cube(10)) | if paint costs $ 3.20 per quart , and a quart covers 10 square feet , how much will it cost to paint the outside of a cube 10 feet on each edge ? | "total surface area = 6 a ^ 2 = 6 * 10 * 10 = 600 each quart covers 20 sqr ft thus total number of quarts = 600 / 10 = 60 cost will be 60 * 3.2 = $ 192 ans : e" | a = 3 / 20
b = a * surface_cube
|
a ) 21 , b ) 28 , c ) 99 , d ) 77 , e ) 66 | a | multiply(3, 7) | walking 7 / 6 of his usual rate , a boy reaches his school 3 min early . find his usual time to reach the school ? | "speed ratio = 1 : 7 / 6 = 6 : 7 time ratio = 7 : 6 1 - - - - - - - - 7 3 - - - - - - - - - ? = 21 m answer : a" | a = 3 * 7
|
['a ) 29', 'b ) 30', 'c ) 31', 'd ) 32', 'e ) 33'] | d | multiply(triangle_area(add(7, 1), 4), const_2) | in a rectangular coordinate system , what is the area of a triangle whose vertices have the coordinates ( - 1 , 0 ) , ( 7 , 4 ) , and ( 7 , - 4 ) ? | the triangle is symmetric about the x - axis . the part above the x - axis forms a triangle with a base of 8 and a height of 4 . the area of this part is ( 1 / 2 ) ( 8 ) ( 4 ) . we can double this to find the area of the whole triangle . the total area is ( 2 ) ( 1 / 2 ) ( 8 ) ( 4 ) = 32 . the answer is d . | a = 7 + 1
b = triangle_area * (
|
a ) a ) 125 , b ) b ) 627 , c ) c ) 187 , d ) d ) 721 , e ) e ) 159 | c | divide(multiply(850, subtract(const_100, add(add(40, 28), 10))), const_100) | in a school of 850 boys , 40 % of muslims , 28 % hindus , 10 % sikhs and the remaining of other communities . how many belonged to the other communities ? | "40 + 28 + 10 = 78 % 100 – 78 = 22 % 850 * 22 / 100 = 187 answer : c" | a = 40 + 28
b = a + 10
c = 100 - b
d = 850 * c
e = d / 100
|
a ) 24,000 , b ) 240,000 , c ) 18 , 000,000 , d ) 24 , 000,000 , e ) 240 , 000,000 | c | multiply(multiply(multiply(multiply(4, 100), divide(1, const_10)), multiply(5, 100)), multiply(9, 100)) | if a rectangular room measures 9 meters by 5 meters by 4 meters , what is the volume of the room in cubic centimeters ? ( 1 meter = 100 centimeters ) | "c . 180 , 000,000 9 * 100 * 5 * 100 * 4 * 100 = 180 , 000,000" | a = 4 * 100
b = 1 / 10
c = a * b
d = 5 * 100
e = c * d
f = 9 * 100
g = e * f
|
a ) 102 % , b ) 105 % , c ) 120 % , d ) 135 % , e ) 140 % | a | add(subtract(subtract(20, 15), divide(multiply(15, 20), const_100)), const_100) | the price of a certain painting increased by 20 % during the first year and decreased by 15 % during the second year . the price of the painting at the end of the 2 - year period was what percent of the original price ? | "assume that price is 100 price at the end of yr 1 : 100 + 20 = 120 price at the end of year 2 = 120 - 120 * 0.15 = 120 * 0.85 = 102 hence required answer = ( 102 / 100 ) * 100 % = 102 % answer is a ." | a = 20 - 15
b = 15 * 20
c = b / 100
d = a - c
e = d + 100
|
a ) a ) 30 , b ) b ) 45 , c ) c ) 50 , d ) d ) 55 , e ) e ) 60 | a | subtract(choose(7, 4), choose(5, 4)) | there are 7 books on a shelf , of which 2 are paperbacks and 5 are hardbacks . how many possible selections of 4 books from this shelf include at least one paperback ? | "approach 1 at - least 1 paper back = total - no paper back 7 c 4 - 5 c 4 = 30 approach 2 at - least 1 paper back = 1 paper back , 3 hard back or 2 paper back 2 hard back = 2 c 1 * 5 c 3 + 2 c 2 * 5 c 2 = 30 answer is a" | a = math.comb(7, 4)
b = math.comb(5, 4)
c = a - b
|
a ) s . 600 , b ) s . 800 , c ) s . 500 , d ) s . 900 , e ) s . 1200 | e | divide(25200, add(18, 3)) | a man sold 18 toys for rs . 25200 , gaining thereby the cost price of 3 toy find the cost price of a toy | let the cost of one toy = x . then , cost of 18 toys = 18 x . gain = 3 x . sp of 18 toys = rs . 25200 . gain = sp â € “ cp 3 x = 25200 â € “ 18 x 21 x = 25200 x = rs . 1200 . answer : option e | a = 18 + 3
b = 25200 / a
|
a ) 180 , b ) 270 , c ) 360 , d ) 500 , e ) 550 | b | multiply(divide(870, add(add(multiply(12, 8), multiply(16, 9)), multiply(18, 6))), multiply(16, 9)) | a , b and c rents a pasture for rs . 870 . a put in 12 horses for 8 months , b 16 horses for 9 months and 18 horses for 6 months . how much should c pay ? | "12 * 8 : 16 * 9 = 18 * 6 8 : 12 : 9 9 / 29 * 870 = 270 answer b" | a = 12 * 8
b = 16 * 9
c = a + b
d = 18 * 6
e = c + d
f = 870 / e
g = 16 * 9
h = f * g
|
a ) 9920 , b ) 96288 , c ) 26667 , d ) 1662 , e ) 2882 | a | add(multiply(multiply(add(divide(3, const_100), divide(divide(subtract(9200, 8000), 3), 8000)), 8000), 3), 8000) | sonika deposited rs . 8000 which amounted to rs . 9200 after 3 years at simple interest . had the interest been 3 % more . she would get how much ? | "( 8000 * 3 * 3 ) / 100 = 720 9200 - - - - - - - - 9920 answer : a" | a = 3 / 100
b = 9200 - 8000
c = b / 3
d = c / 8000
e = a + d
f = e * 8000
g = f * 3
h = g + 8000
|
a ) 32.2 , b ) 32.98 , c ) 32.3 , d ) 32.8 , e ) 27.8 | e | add(17, const_1) | the average of first five prime numbers greater than 17 is ? | "19 + 23 + 29 + 31 + 37 = 139 / 5 = 27.8 answer : e" | a = 17 + 1
|
a ) 144 , b ) 119 , c ) 113 , d ) 88 , e ) 31 | d | subtract(119, subtract(add(144, 119), 232)) | in a graduating class of 232 students , 144 took geometry and 119 took biology . what is the difference between the greatest possible number i and the smallest possible number of students that could have taken both geometry and biology ? | official solution : first of all , notice that since 144 took geometry and 119 took biology , then the number of students who took both geometry and biology can not be greater than 119 . { total } = { geometry } + { biology } - { both } + { neither } ; 232 = 144 + 119 - { both } + { neither } ; { both } = 31 + { neither } . { both } is minimized when { neither } is 0 . in this case { both } = 31 . the greatest possible number i of students that could have taken both geometry and biology , is 119 . thus , the answer is 119 - 31 = 88 . answer : d . | a = 144 + 119
b = a - 232
c = 119 - b
|
a ) 1 : 1 , b ) 2 : 3 , c ) 5 : 2 , d ) 10 : 11 , e ) 7 : 9 | d | divide(add(multiply(4, 7), multiply(5, divide(add(7, 5), const_2))), add(multiply(4, 5), multiply(5, divide(add(7, 5), const_2)))) | two alloys a and b are composed of two basic elements . the ratios of the compositions of the two basic elements in the two alloys are 7 : 5 and 1 : 2 , respectively . a new alloy x is formed by mixing the two alloys a and b in the ratio 4 : 3 . what is the ratio of the composition of the two basic elements in alloy x ? | "mixture a has a total of 7 + 5 = 12 parts . if in the final mixture this represents 6 parts , then the total number of parts in mixture b should be ( 12 / 6 ) * 3 = 6 . so , we should take of mixture b a quantity with 3 and 6 parts , respectively . this will give us in the final mixture ( 7 + 3 ) : ( 5 + 6 ) , which means 10 : 11 answer d ." | a = 4 * 7
b = 7 + 5
c = b / 2
d = 5 * c
e = a + d
f = 4 * 5
g = 7 + 5
h = g / 2
i = 5 * h
j = f + i
k = e / j
|
a ) 30 , b ) 18 , c ) 10 , d ) 9 , e ) 1 | e | subtract(divide(subtract(60, 50), subtract(55, 50)), const_1) | for the past n days , the average ( arithmetic mean ) daily production at a company was 50 units . if today ' s production of 60 units raises the average to 55 units per day , what is the value of n ? | "( average production for n days ) * n = ( total production for n days ) - - > 50 n = ( total production for n days ) ; ( total production for n days ) + 60 = ( average production for n + 1 days ) * ( n + 1 ) - - > 50 n + 60 = 55 * ( n + 1 ) - - > n = 1 . answer : e ." | a = 60 - 50
b = 55 - 50
c = a / b
d = c - 1
|
a ) 8.5 % , b ) 11.7 % , c ) 14.2 % , d ) 17.6 % , e ) 20.5 % | b | multiply(divide(70, multiply(const_100, const_2)), const_100) | sue ' s trail mix is 30 % nuts and 70 % dried fruit . jane ' s trail mix is 60 % nuts and 40 % chocolate chips . if the combined mixture of sue and jane ' s trails mix contains 55 % nuts , what percent of the combined mixture is dried fruit ? | "55 % is 25 % - points above 30 % and 5 % - points below 60 % . so the ratio of sue ' s mix to jane ' s mix is 1 : 5 . 1 / 6 * 70 % = 11.7 % the answer is b ." | a = 100 * 2
b = 70 / a
c = b * 100
|
a ) 24 , b ) 77 , c ) 297 , d ) 267 , e ) 29 | a | multiply(subtract(15, 9), 4) | think of a number , divide it by 4 and add 9 to it . the result is 15 . what is the number thought of ? | answer : a | a = 15 - 9
b = a * 4
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a ) 10 , b ) 11 , c ) 12 , d ) 13 , e ) 14 | d | subtract(subtract(98, 81), divide(98, add(const_1, const_10))) | what number is obtained by adding the units digits of 734 ^ 98 and 347 ^ 81 ? | "the units digit of 734 ^ 98 is 6 because 4 raised to the power of an even integer ends in 6 . the units digit of 347 ^ 81 is 7 because powers of 7 end in 7 , 9 , 3 or 1 cyclically . since 81 is in the form 4 n + 1 , the units digit is 7 . then 6 + 7 = 13 . the answer is d ." | a = 98 - 81
b = 1 + 10
c = 98 / b
d = a - c
|
a ) 8 , b ) 9 , c ) 10 , d ) 11 , e ) 16 | e | add(divide(subtract(166, const_1), add(10, const_1)), const_1) | in a new housing development , trees are to be planted along the sidewalk of a certain street . each tree takes up one square foot of sidewalk space , and there are to be 10 feet between each tree . how many trees can be planted if the road is 166 feet long ? | "let t be the number of trees . then the length required for trees on the sidewalk will be 1 * t = t to maximize the number of trees , the number of 10 feet spaces between trees should be 1 less than total number of trees . for example , if there are 3 trees , then there should be 2 spaces between them . so the number of 10 feet spaces will be t - 1 . then , the length of sidewalk required for 10 feet spaces will be 10 * ( t - 1 ) it is given that total lenght of sidewalk is 166 feet . or 10 ( t - 1 ) + t = 166 or 10 t - 10 + t = 166 or t = 16 answer : - e" | a = 166 - 1
b = 10 + 1
c = a / b
d = c + 1
|
a ) 12 , b ) 8 , c ) 6 , d ) 10 , e ) 16 | a | multiply(const_4, power(27, divide(const_1, const_3))) | a cube is painted red on all faces . it is then cut into 27 equal smaller cubes . how many l cubes are painted on only 2 faces ? | "1 ) draw a simple cube 2 ) draw 9 squares on each face of the cube ( so that it looks like a rubik ' s cube ) - this is what the cube will look like when it ' s cut into 27 equal smaller cubes . 3 ) remember that the outside of the cube is the part that ' s painted . . . . the mini - cubes with 2 painted sides are all on the edge of the cube , in themiddleof the edge . there are 4 in front , 4 in back and 4 more on thestripthat runs around the left / top / right / bottom of the cube . l = 4 + 4 + 4 = 12 . answer a" | a = 1 / 3
b = 27 ** a
c = 4 * b
|
a ) 4 , b ) 5 , c ) 6 , d ) 8 , e ) 9 | a | add(add(const_1, const_1), const_2) | let n be the greatest number that will divide 1305 , 4665 and 6905 , leaving the game remainder in each case . then sum of the digits in n is : | solution n = h . c . f . of ( 4665 - 1305 ) , ( 6905 - 4665 ) and ( 6905 - 1305 ) = h . c . f . of 3360 , 2240 and 5600 = 1120 . sum of digits in n = ( 1 + 1 + 2 + 0 ) = 4 . answer a | a = 1 + 1
b = a + 2
|
a ) 69 , b ) 75 , c ) 81 , d ) 87 , e ) 93 | c | divide(multiply(add(add(1, 8), add(2, 8)), subtract(12, 3)), 2) | in a rectangular coordinate system , what is the area of a quadrilateral whose vertices have the coordinates ( 3 , - 1 ) , ( 3 , 8 ) , ( 12 , 2 ) , ( 12 , - 7 ) ? | "by graphing the points , we can see that this figure is a trapezoid . a trapezoid is any quadrilateral that has one set of parallel sides , and the formula for the area of a trapezoid is : area = ( 1 / 2 ) × ( base 1 + base 2 ) × ( height ) , where the bases are the parallel sides . we can now determine the area of the quadrilateral : area = 1 / 2 × ( 9 + 9 ) × 9 = 81 . the answer is c ." | a = 1 + 8
b = 2 + 8
c = a + b
d = 12 - 3
e = c * d
f = e / 2
|
a ) 47 , b ) 49 , c ) 51 , d ) 53 , e ) 55 | d | divide(add(multiply(multiply(36, const_0_2778), 15), 380), multiply(36, const_0_2778)) | a train running at a speed of 36 km / h passes an electric pole in 15 seconds . in how many seconds will the whole train pass a 380 - meter long platform ? | "let the length of the train be x meters . when a train crosses an electric pole , the distance covered is its own length x . speed = 36 km / h = 36000 m / 3600 s = 10 m / s x = 15 * 10 = 150 m . the time taken to pass the platform = ( 150 + 380 ) / 10 = 53 seconds the answer is d ." | a = 36 * const_0_2778
b = a * 15
c = b + 380
d = 36 * const_0_2778
e = c / d
|
a ) 350 m , b ) 490 m , c ) 115 m , d ) 210 m , e ) 150 m | a | multiply(divide(multiply(60, const_1000), const_3600), 21) | a train running at the speed of 60 km / hr crosses a pole in 21 sec . what is the length of the train ? | "speed = 60 * 5 / 18 = 50 / 3 m / sec length of the train = speed * time = 50 / 3 * 21 = 350 m answer : a" | a = 60 * 1000
b = a / 3600
c = b * 21
|
a ) 4500 , b ) 4600 , c ) 4300 , d ) 4900 , e ) 5000 | d | multiply(multiply(70, const_2), divide(70, const_2)) | the sum of the first 70 positive even integers is 4,970 . what is the sum of the first 70 odd integers ? | sum of first n even numbers = n ( n + 1 ) = 4970 sum of first n odd numbers = n ^ 2 = 70 * 70 = 4900 ( here n = 70 ) answer : d | a = 70 * 2
b = 70 / 2
c = a * b
|
a ) 31 , b ) 32 , c ) 33 , d ) 34 , e ) 35 | b | divide(add(add(multiply(64, const_2), multiply(39, const_2)), multiply(6, 3)), add(3, const_4)) | a family consists of two grandparents , two parents , and 3 grandchildren . the average age of the grandparents is 64 years , the average age of the parents is 39 years , and the average age of the grandchildren is 6 years . what is the average age ( in years ) of the family ? | total age of the grandparents = 64 ã — 2 = 128 total age of the parents = 39 ã — 2 = 78 total age of the grandchildren = 6 ã — 3 = 18 average age of the family = ( 128 + 78 + 18 ) / 7 = 224 / 7 = 32 years the answer is b . | a = 64 * 2
b = 39 * 2
c = a + b
d = 6 * 3
e = c + d
f = 3 + 4
g = e / f
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a ) rs . 170 , b ) rs . 140 , c ) rs . 1.70 , d ) rs . 4.25 , e ) none | b | divide(70, 0.5) | if 0.5 % of a = 70 paise , then the value of a is ? | "answer ∵ 0.5 / 100 of a = 70 / 100 ∴ a = rs . ( 70 / 0.5 ) = rs . 140 correct option : b" | a = 70 / 0
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a ) 10.5 , b ) 15 , c ) 25.5 , d ) 30 , e ) 60 | a | subtract(subtract(divide(const_60, const_2), 15), divide(const_60, divide(20, 1.5))) | darcy lives 1.5 miles from work . she can walk to work at a constant rate of 3 miles per hour , or she can ride the train to work at a constant rate of 20 miles per hour . if she rides the train , there is an additional x minutes spent walking to the nearest train station , waiting for the train , and walking from the final train station to her work . if it takes darcy a total of 15 more minutes to commute to work by walking than it takes her to commute to work by riding the train , what is the value of x ? | the time it takes darcy to walk to work is ( 1.5 / 3 ) * 60 = 30 minutes the time it takes darcy to take the train is ( 1.5 / 20 ) * 60 + x = 4.5 + x minutes it takes 15 minutes longer to walk , so 30 = 4.5 + x + 15 x = 10.5 minutes answer : a | a = const_60 / 2
b = a - 15
c = 20 / 1
d = const_60 / c
e = b - d
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a ) 3698 , b ) 874 , c ) 3692 , d ) 1800 , e ) 3214 | d | multiply(add(5,40, const_1), const_2) | what is the least common multiple of 5,40 , 36,50 | "the given numbers are 5,40 , 36,50 thus the l . c . m is 5 * 2 * 2 * 1 * 2 * 9 * 5 = 1800 the answer is d" | a = 5 + 40
b = a * 2
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a ) rs 200 , b ) rs 220 , c ) rs 260 , d ) rs 280 , e ) none of these | a | divide(subtract(280, multiply(280, divide(12, const_100))), add(divide(25, const_100), const_1)) | the sale price of a trolley bag including the sale tax is rs . 280 . the rate of sale tax is 12 % . if the shopkeeper has made a profit of 25 % , the cost price of the trolley bag is : | "explanation : 112 % of s . p . = 280 s . p . = rs . ( 280 x 100 / 112 ) = rs . 250 . c . p . = rs ( 100 / 125 x 250 ) = rs 200 answer : a" | a = 12 / 100
b = 280 * a
c = 280 - b
d = 25 / 100
e = d + 1
f = c / e
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a ) 8 , b ) 2 , c ) 10 , d ) 4 , e ) 6 | c | sqrt(150) | the difference between c . i . and s . i . on an amount of rs . 15,000 for 2 years is rs . 150 . what is the rate of interest per annum ? | "explanation : [ 15000 * ( 1 + r / 100 ) 2 - 15000 ] - ( 15000 * r * 2 ) / 100 = 150 15000 [ ( 1 + r / 100 ) 2 - 1 - 2 r / 100 ] = 150 15000 [ ( 100 + r ) 2 - 10000 - 200 r ] / 10000 = 150 r 2 = ( 159 * 2 ) / 3 = 100 = > r = 10 rate = 10 % answer : option c" | a = math.sqrt(150)
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a ) 23.75 , b ) 22 , c ) 20 , d ) 19.2 , e ) none of these | e | add(divide(multiply(divide(add(multiply(80, 15), multiply(20, 20)), add(80, 20)), 50), const_100), divide(add(multiply(80, 15), multiply(20, 20)), add(80, 20))) | a trader mixes 80 kg of tea at 15 per kg with 20 kg of tea at cost price of 20 per kg . in order to earn a profit of 50 % , what should be the sale price of the mixed tea ? | "c . p . of mixture = 80 × 15 + 20 × 20 / 80 + 20 = 16 ∴ s . p . = ( 100 + 50 ) / 100 × 16 = 24 answer e" | a = 80 * 15
b = 20 * 20
c = a + b
d = 80 + 20
e = c / d
f = e * 50
g = f / 100
h = 80 * 15
i = 20 * 20
j = h + i
k = 80 + 20
l = j / k
m = g + l
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a ) 5 : 2 , b ) 2 : 3 , c ) 10 : 3 , d ) 3 : 7 , e ) 2 : 5 | c | divide(divide(10, const_100), divide(1, 3)) | in a school 10 % of the boys are same in number as 1 / 3 th of the girls . what is the ratio of boys to the girls in the school ? | "10 % of b = 1 / 3 g 10 b / 100 = g / 3 b = 10 g / 3 b / g = 10 / 3 b : g = 10 : 3 answer is c" | a = 10 / 100
b = 1 / 3
c = a / b
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a ) 6.18 , b ) 5.18 , c ) 4.18 , d ) 4.18 , e ) 7.18 | e | divide(120, multiply(60, const_0_2778)) | in what time will a train 120 meters long completely pass an electric pole , if it travels at a speed of 60 kmph . | "sol . speed = [ 60 x 5 / 18 ] m / sec = 16.7 m / sec . time taken = ( 120 / 16.7 ) sec = 7.18 sec . answer e" | a = 60 * const_0_2778
b = 120 / a
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a ) 81 , b ) 100 , c ) 120 , d ) 135 , e ) 160 | c | divide(multiply(add(90, divide(multiply(90, 20), const_100)), const_100), multiply(multiply(const_3, const_3), 10)) | a retailer bought a machine at a wholesale price of $ 90 and later on sold it after a 10 % discount of the retail price . if the retailer made a profit equivalent to 20 % of the whole price , what is the retail price e of the machine ? | "since the wholesale price was $ 90 and the profit was 20 % of the wholesale price ( [ . 2 ] [ 90 ] = $ 18 ) , the retail price would have to be above $ 108 , but not that much greater than that . let ' s start by testing answer c : $ 120 . . . . if . . . . . retail price e = $ 120 10 % discount off = $ 120 - ( . 1 ) ( 120 ) = 120 - 12 = 108 20 % profit on wholesale price = 90 + ( . 2 ) ( 90 ) = 90 + 18 = 108 these two numbers match , so this must be the answer ! final answer : [ reveal ] spoiler : c" | a = 90 * 20
b = a / 100
c = 90 + b
d = c * 100
e = 3 * 3
f = e * 10
g = d / f
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a ) 5 , b ) 7 , c ) 9 , d ) 3 , e ) 12 | d | add(divide(subtract(multiply(floor(divide(79, 11)), 11), multiply(add(floor(divide(49, 11)), const_1), 11)), 11), const_1) | how many numbers from 49 to 79 are exactly divisible by 11 ? | "49 / 11 = 4 and 79 / 11 = 7 = = > 7 - 4 = 3 numbers answer : d" | a = 79 / 11
b = math.floor(a)
c = b * 11
d = 49 / 11
e = math.floor(d)
f = e + 1
g = f * 11
h = c - g
i = h / 11
j = i + 1
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a ) 3 , b ) 5 , c ) 8 , d ) 13 , e ) 18 | e | add(subtract(multiply(40, 2), add(add(15, multiply(10, 2)), multiply(5, 3))), 3) | in a class of 40 students , 5 students did not borrow any books from the library , 15 students each borrowed 1 book , 10 students each borrowed 2 books , and the rest of the students each borrowed at least 3 books . if the average ( arithmetic mean ) number of books borrowed per student was 2 , what is the maximum number of books that any single student could have borrowed ? | "the average number of books per student was 2 means that total of 2 * 40 = 80 books were borrowed ; 5 + 15 + 10 = 30 students borrowed total of 5 * 0 + 15 * 1 + 10 * 2 = 35 books ; so 80 - 35 = 45 books are left to distribute among 40 - 30 = 10 students , these 10 arethe rest who borrowed at least 3 books ; tomaximizethe number of books one student from above 10 could have borrowed we shouldminimizethe number of books other 9 students from 10 could have borrowed . minimum these 9 students could have borrowed is 3 books per student , so total number of books they could have borrowed is 9 * 3 = 27 books . so the 10 th student could have borrowed is 45 - 27 = 18 books . answer : e ." | a = 40 * 2
b = 10 * 2
c = 15 + b
d = 5 * 3
e = c + d
f = a - e
g = f + 3
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a ) 600 , b ) 840 , c ) 1000 , d ) 1200 , e ) 1500 | b | multiply(divide(7, subtract(divide(60, 24), const_1)), 60) | working together , printer a and printer b would finish the task in 24 minutes . printer a alone would finish the task in 60 minutes . how many pages does the task contain if printer b prints 7 pages a minute more than printer a ? | answer : b . | a = 60 / 24
b = a - 1
c = 7 / b
d = c * 60
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a ) 2.9 min , b ) 3.9 min , c ) 4.2 min , d ) 4.8 min , e ) 5.6 min | d | divide(multiply(640, multiply(const_1, const_60)), add(multiply(4.2, const_1000), multiply(3.8, const_1000))) | the jogging track in a sports complex is 640 m in circumference . lata and geeta start from the same point and walk in opposite directions at 4.2 km / hr and 3.8 km / hr respectively . they will meet for the first time in ? | clearly , the two will meet when they are 640 m apart . to be ( 4.2 + 3.8 ) = 8.0 km apart , they take 1 hour . that is 60 min . to be 640 m apart , they take ( 640 / 8000 * 60 ) min = 4.8 min . answer : d | a = 1 * const_60
b = 640 * a
c = 4 * 2
d = 3 * 8
e = c + d
f = b / e
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a ) 15 , b ) 19 , c ) 11 , d ) 18 , e ) 13 | e | divide(subtract(68000, 42000), add(800, 1200)) | village x has a population of 68000 , which is decreasing at the rate of 1200 per year . village y has a population of 42000 , which is increasing at the rate of 800 per year . in how many years will the population of the two villages be equal ? | let the population of two villages be equal after p years then , 68000 - 1200 p = 42000 + 800 p 2000 p = 26000 p = 13 answer is e . | a = 68000 - 42000
b = 800 + 1200
c = a / b
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a ) 3 , b ) 5 , c ) 8 , d ) 11 , e ) 17 | d | divide(2145, multiply(multiply(add(const_2, const_3), add(add(const_2, const_3), const_2)), add(const_10, const_3))) | in a certain business school class , p students are accounting majors , q students are finance majors , r students are marketing majors , and s students are strategy majors . if pqrs = 2145 , and if 1 < p < q < r < s , how many students in the class are marketing majors ? | "pqrs = 2145 = 3 * 5 * 11 * 13 since 1 < p < q < r < s , the number of students who are marketing majors is r = 11 . the answer is d ." | a = 2 + 3
b = 2 + 3
c = b + 2
d = a * c
e = 10 + 3
f = d * e
g = 2145 / f
|
a ) 12 , b ) 13 , c ) 14 , d ) 15 , e ) 10 | a | divide(multiply(subtract(const_100, 4), 16), add(const_100, 28)) | if a man lost 4 % by selling oranges at the rate of 16 a rupee at how many a rupee must he sell them to gain 28 % ? | "96 % - - - - 16 128 % - - - - ? 96 / 128 * 16 = 12 answer : a" | a = 100 - 4
b = a * 16
c = 100 + 28
d = b / c
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a ) 4.37 % , b ) 2 % , c ) 6 % , d ) 8.75 % , e ) none of these | b | add(multiply(divide(subtract(divide(subtract(subtract(subtract(multiply(multiply(const_10, const_1000), const_10), const_1000), const_1000), multiply(add(1, const_3), const_100)), multiply(add(multiply(add(const_3, const_4), const_10), add(1, const_3)), const_1000)), 1), const_10), const_100), const_4) | the population of a town increased from 1 , 25,000 to 1 , 50,000 in a decade . the average percent increase of population per year is : | "solution increase in 10 year = ( 150000 - 125000 ) = 25000 . increase % = ( 25000 / 125000 x 100 ) % = 20 % â ˆ ´ required average = ( 20 / 10 ) % = 2 % answer b" | a = 10 * 1000
b = a * 10
c = b - 1000
d = c - 1000
e = 1 + 3
f = e * 100
g = d - f
h = 3 + 4
i = h * 10
j = 1 + 3
k = i + j
l = k * 1000
m = g / l
n = m - 1
o = n / 10
p = o * 100
q = p + 4
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a ) 47 , b ) 49 , c ) 54 , d ) 58 , e ) 62 | b | add(add(subtract(40, 6), 7), subtract(10, 7)) | 40 persons like apple . 7 like orange and mango dislike apple . 10 like mango and apple and dislike orange . 6 like all . how many people like apple ? | "orange + mango - apple = 7 mango + apple - orange = 10 apple = 40 orange + mango + apple = 6 40 + 10 + 6 - 7 = 49 like apple answer : b" | a = 40 - 6
b = a + 7
c = 10 - 7
d = b + c
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a ) 2388 , b ) 2337 , c ) 1192 , d ) 2827 , e ) 1180 | e | add(add(multiply(15, 36), multiply(12, 45)), multiply(10, 8)) | a man purchased 15 pens , 12 books , 10 pencils and 5 erasers . the cost of each pen is rs . 36 , each book is rs . 45 , each pencil is rs . 8 , and the cost of each eraser is rs . 40 less than the combined costs of pen and pencil . find the total amount spent ? | explanation : cost of each eraser = ( 36 + 8 - 40 ) = rs . 4 required amount = 15 * 36 + 12 * 45 + 10 * 8 + 5 * 4 540 + 540 + 80 + 20 = rs . 1180 answer : e | a = 15 * 36
b = 12 * 45
c = a + b
d = 10 * 8
e = c + d
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a ) 24 , b ) 26 , c ) 28 , d ) 21 , e ) 32 | d | multiply(divide(7, 9), add(22, const_4)) | john was 22 years old when he married betty . they just celebrated their fifth wedding anniversary , and betty ' s age is now 7 / 9 of john ' s . how old is betty ? | assume betty ' s age on marriage = x years . john ' s age on marriage = 22 john ' s age after 5 years = 27 years . betty ' s age after 5 years = x + 5 given : x + 5 = 7 / 9 ( 27 ) = 21 therefore betty ' s current age = 21 option d | a = 7 / 9
b = 22 + 4
c = a * b
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a ) 1024 , b ) 960 , c ) 277 , d ) 266 , e ) 121 | a | multiply(subtract(832, divide(subtract(832, 448), const_2)), add(const_1, divide(60, const_100))) | the profit earned by selling an article for rs . 832 is equal to the loss incurred when the same article is sold for rs . 448 . what should be the sale price for making 60 % profit ? | let c . p . = rs . x . then , 832 - x = x - 448 2 x = 1280 = > x = 640 required s . p . = 160 % of rs . 640 = 160 / 100 * 640 = rs . 1024 . answer : a | a = 832 - 448
b = a / 2
c = 832 - b
d = 60 / 100
e = 1 + d
f = c * e
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a ) 300 , b ) 800 , c ) 1100 , d ) 600 , e ) 1900 | d | subtract(subtract(1000, divide(1000, 5)), divide(subtract(1000, divide(1000, 5)), 4)) | workers at a campaign office have 1000 fliers to send out . if they send out 1 / 5 of them in the morning and 1 / 4 of the remaining ones out during the afternoon , how many are left for the next day ? | "( 1 / 5 ) * 1000 = 200 remaining = 1000 - 200 = 800 ( 1 / 4 ) of remaining = ( 1 / 4 ) * 800 = 200 remaining now = 800 - 200 = 600 answer : option d" | a = 1000 / 5
b = 1000 - a
c = 1000 / 5
d = 1000 - c
e = d / 4
f = b - e
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a ) 11 , b ) 20 , c ) 12 , d ) 40 , e ) 8 | e | multiply(divide(subtract(1080, 1000), 1000), const_100) | a cycle is bought for rs . 1000 and sold for rs . 1080 , find the gain percent ? | "1000 - - - - 80 100 - - - - ? = > 8 % answer : e" | a = 1080 - 1000
b = a / 1000
c = b * 100
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a ) 6 % , b ) 14 % , c ) 114 % , d ) 23 % , e ) 43 % | c | multiply(divide(subtract(divide(add(30, 7), 100), divide(7, 50)), divide(7, 50)), const_100) | a corporation paid $ 7 million in federal taxes on its first $ 50 million of gross profits and then $ 30 million in federal taxes on the next $ 100 million in gross profits . by approximately what percent did the ratio of federal taxes to gross profits increase from the first $ 50 million in profits to the next $ 100 million in profits ? | "difference in ratios = ( 30 / 100 ) - ( 7 / 50 ) = ( 8 / 50 ) % change = ( change ( 8 / 50 ) / original ratio ( 7 / 50 ) ) * 100 = 114 % answer - c" | a = 30 + 7
b = a / 100
c = 7 / 50
d = b - c
e = 7 / 50
f = d / e
g = f * 100
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a ) 10 , b ) 2 , c ) 12 , d ) 14 , e ) 15 | b | subtract(power(2, 2), 2) | if x ^ 2 + ( 1 / x ^ 2 ) = 2 , x ^ 4 + ( 1 / x ^ 4 ) = ? | - > x ^ 4 + ( 1 / x ^ 4 ) = ( x ^ 2 ) ^ 2 + ( 1 / x ^ 2 ) ^ 2 = ( x ^ 2 + 1 / x ^ 2 ) ^ 2 - 2 x ^ 2 ( 1 / x ^ 2 ) = 2 ^ 2 - 2 = 2 . thus , the answer is b . | a = 2 ** 2
b = a - 2
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a ) 5 : 8 , b ) 50 : 78 , c ) 2 : 3 , d ) it can not be determined from the information given . , e ) 6 : 7 | d | divide(add(5, 10), add(8, 10)) | the ratio of two quantities is 5 : 8 . if each of the quantities is increased by 10 , what is the ratio of the new quantities ? | since the ratio is 5 : 8 we can put the quantities as 5 k and 8 k . moreover increasing quantities implies that the quantities become 5 k + 10 and 8 k + 10 . so the ratio is ( 5 k + 10 ) : ( 8 k + 10 ) . the ratio value depend on the value of k . so it can not be determined from the information given . the answer is d | a = 5 + 10
b = 8 + 10
c = a / b
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a ) 10 , b ) 9 , c ) 8 , d ) 5 , e ) 12 | b | add(multiply(4, 2), const_1) | in the x - y plane , point ( x , y ) is a lattice point if both x and y are integers . a square has a center at ( 0 , 0 ) and side = 4 . some points , such as the center ( 0 , 0 ) , are inside the square , but a point such as ( 0 , 2 ) is on the square but not in the square . how many lattice points are in the square ? | the lattice points that are in the square , that lie on the x and y axes , are ( 0 , 0 ) , ( 0 , 1 ) , ( 1 , 0 ) , ( 0 , - 1 ) , and ( - 1 , 0 ) . the lattice points in the square and not on the x and y axes are ( 1 , 1 ) , ( - 1 , 1 ) , ( 1 , - 1 ) , and ( - 1 , - 1 ) . there are a total of 9 lattice points in the square . answer : b | a = 4 * 2
b = a + 1
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a ) 2.5 km , b ) 3 km , c ) 4 km , d ) 5.6 km , e ) 6.5 km | a | divide(add(divide(5, const_60), divide(10, const_60)), divide(const_1, 10)) | a boy is travelling from his home to school at 5 km / hr and reached 5 min late . next day he travelled at 10 km / hr and reached 10 min early . distance between home and school ? | "let the distance be x t 1 = x / 5 hr t 2 = x / 10 hr difference in time = 5 + 10 = 15 = 1 / 4 hr x / 5 - x / 10 = 1 / 4 x / 10 = 1 / 4 x = 2.5 km answer is a" | a = 5 / const_60
b = 10 / const_60
c = a + b
d = 1 / 10
e = c / d
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a ) 4 hours , b ) 5 hours , c ) 6 hours , d ) 7 hours , e ) 8 hours | e | divide(168, add(16, 5)) | a boat can travel with a speed of 16 km / hr in still water . if the rate of stream is 5 km / hr , then find the time taken by the boat to cover distance of 168 km downstream . | "explanation : it is very important to check , if the boat speed given is in still water or with water or against water . because if we neglect it we will not reach on right answer . i just mentioned here because mostly mistakes in this chapter are of this kind only . lets see the question now . speed downstream = ( 16 + 5 ) = 21 kmph time = distance / speed = 168 / 21 = 8 hours option e" | a = 16 + 5
b = 168 / a
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a ) 1898 , b ) 1098 , c ) 1000 , d ) 2008 , e ) 1082 | c | divide(power(power(10, const_2), const_3), power(10, const_3)) | a cube of side one meter length is cut into small cubes of side 10 cm each . how many such small cubes can be obtained ? | along one edge , the number of small cubes that can be cut = 100 / 10 = 10 along each edge 10 cubes can be cut . ( along length , breadth and height ) . total number of small cubes that can be cut = 10 * 10 * 10 = 1000 answer : c | a = 10 ** 2
b = a ** 3
c = 10 ** 3
d = b / c
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a ) 72.5 , b ) 55.5 , c ) 62.5 , d ) 82.5 , e ) 65.9 | e | multiply(divide(divide(multiply(47.50, add(const_100, 25)), const_100), subtract(const_100, 10)), const_100) | at what price must an book costing $ 47.50 be marked in order that after deducting 10 % from the list price . it may be sold at a profit of 25 % on the cost price ? | "e $ 62.50 cp = 47.50 sp = 47.50 * ( 125 / 100 ) = 59.375 mp * ( 90 / 100 ) = 59.375 mp = 65.9 e" | a = 100 + 25
b = 47 * 50
c = b / 100
d = 100 - 10
e = c / d
f = e * 100
|
a ) 22 , b ) 60 , c ) 24 , d ) 76 , e ) 21 | c | divide(multiply(multiply(4, 6), 8), const_2) | a gardener wants to plant trees in his garden in such a way that the number of trees in each row should be the same . if there are 8 rows or 6 rows or 4 rows , then no tree will be left . find the least number of trees required | "explanation : the least number of trees that are required = lcm ( 8 , 6,4 ) = 24 . answer : c" | a = 4 * 6
b = a * 8
c = b / 2
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a ) 120 cm 2 , b ) 765 cm 2 , c ) 1080 cm 2 , d ) 197 cm 2 , e ) 275 cm 2 | c | divide(multiply(72, 30), const_2) | if the sides of a triangle are 78 cm , 72 cm and 30 cm , what is its area ? | "the triangle with sides 78 cm , 72 cm and 30 cm is right angled , where the hypotenuse is 78 cm . area of the triangle = 1 / 2 * 72 * 30 = 1080 cm 2 answer : c" | a = 72 * 30
b = a / 2
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a ) 4 : 5 , b ) 5 : 6 , c ) 6 : 5 , d ) 5 : 4 , e ) 2 : 5 | b | divide(divide(const_1, const_4), divide(60, const_100)) | if 60 % of a number is equal to one half of another number , what is the ratio of first number to the second number ? | "let 60 % of a = 1 / 2 b . then , 60 a / 100 = 1 b / 2 = > 3 a / 5 = 1 b / 2 a / b = ( 1 / 2 * 5 / 3 ) = 5 / 6 a : b = 5 : 6 . answer : b" | a = 1 / 4
b = 60 / 100
c = a / b
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a ) 25 minutes . , b ) 30 minutes . , c ) 40 minutes . , d ) 1 hour and 30 minutes , e ) 1 hour and 20 minutes | d | multiply(divide(subtract(const_1, add(divide(const_1, 2), divide(const_1, 5))), divide(const_1, 5)), const_60) | it takes avery 2 hours to build a brick wall while tom can do it in 5 hours . if the two start working together and after an hour avery leaves , how much time will it take tom to complete the wall on his own ? | "avery ' s efficiency is 100 / 2 = 50 % tom ' s = 100 / 5 = 20 % they worked together for 1 hour and finished 70 % of the job remaining = 30 % tom will complete 20 % in 60 minutes , and 10 % in 60 * 10 / 20 minutes = 30 minutes time taken by tom to finish the remaining on his own = 60 + 30 = 90 minutes answer : d" | a = 1 / 2
b = 1 / 5
c = a + b
d = 1 - c
e = 1 / 5
f = d / e
g = f * const_60
|
a ) 23777 , b ) 30000 , c ) 29977 , d ) 26777 , e ) 19871 | b | divide(subtract(multiply(100000, divide(add(9, divide(3, 5)), const_100)), multiply(100000, divide(9, const_100))), subtract(divide(11, const_100), divide(9, const_100))) | an amount of rs . 100000 is invested in two types of shares . the first yields an interest of 9 % p . a and the second , 11 % p . a . if the total interest at the end of one year is 9 3 / 5 % , then the amount invested at 11 % was ? | "let the sum invested at 9 % be rs . x and that invested at 11 % be rs . ( 100000 - x ) . then , ( x * 9 * 1 ) / 100 + [ ( 100000 - x ) * 11 * 1 ] / 100 = ( 100000 * 48 / 5 * 1 / 100 ) ( 9 x + 1100000 - 11 x ) = 960000 x = 70000 sum invested at 9 % = rs . 70000 sum invested at 11 % = rs . ( 100000 - 70000 ) = rs . 30000 . answer : b" | a = 3 / 5
b = 9 + a
c = b / 100
d = 100000 * c
e = 9 / 100
f = 100000 * e
g = d - f
h = 11 / 100
i = 9 / 100
j = h - i
k = g / j
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a ) 12 , 8,8 , b ) 4 , 4,22 , c ) 9 , 3,32 , d ) 9 , 6,12 , e ) 9 , 2,23 | a | divide(multiply(const_4.0, 3), 3) | find the numbers which are in the ratio 3 : 2 : 2 such that the sum of the first and the second added to the difference of the third and the second is 20 ? | "let the numbers be a , b and c . a : b : c = 3 : 2 : 2 given , ( a + b ) + ( c - b ) = 20 = > a + c = 20 = > 3 x + 2 x = 20 = > x = 4 a , b , c are 3 x , 2 x , 2 x a , b , c are 12 , 8 , 8 . answer : a" | a = 4 * 0
b = a / 3
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a ) s . 247 , b ) s . 248 , c ) s . 240 , d ) s . 229 , e ) s . 212 | c | add(divide(170, subtract(const_1, divide(15, const_100))), multiply(divide(170, subtract(const_1, divide(15, const_100))), divide(20, const_100))) | a shopkeeper loses 15 % , if an article is sold for rs . 170 . what should be the selling price of the article to gain 20 % ? | "given that sp = rs . 170 and loss = 15 % cp = [ 100 ( sp ) ] / ( 100 - l % ) = ( 100 * 170 ) / 85 = 20 * 6 = rs . 200 . to get 20 % profit , new sp = [ ( 100 + p % ) cp ] / 100 = ( 200 * 120 ) / 100 = rs . 240 answer : c" | a = 15 / 100
b = 1 - a
c = 170 / b
d = 15 / 100
e = 1 - d
f = 170 / e
g = 20 / 100
h = f * g
i = c + h
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a ) 124 % , b ) 120 % , c ) 96 % , d ) 90 % , e ) 64 % | d | multiply(multiply(subtract(const_1, divide(40, const_100)), add(const_1, divide(50, const_100))), const_100) | mary ' s income is 50 percent more than tim ' s income , and tim ' s income is 40 percent less than juan ' s income . what percent of juan ' s income is mary ' s income ? | "juan ' s income = 100 ( assume ) ; tim ' s income = 60 ( 40 percent less than juan ' s income ) ; mary ' s income = 90 ( 50 percent more than tim ' s income ) . thus , mary ' s income ( 90 ) is 90 % of juan ' s income ( 100 ) . answer : d ." | a = 40 / 100
b = 1 - a
c = 50 / 100
d = 1 + c
e = b * d
f = e * 100
|
a ) 653 , b ) 664 , c ) 698 , d ) 744 , e ) 700 | a | subtract(800, multiply(divide(subtract(854, 800), subtract(divide(4, const_100), divide(3, const_100))), divide(3, const_100))) | peter invests a sum of money and gets back an amount of $ 800 in 3 years . david invests an equal amount of money and gets an amount of $ 854 in 4 years . if both amounts were invested at the same rate ( simple interest ) what was the sum of money invested ? | "since both peter and david invested the same amount of money at the same rate , they would earn same interest per year . david invested for one year more than peter and hence he got interest amount for one more year . interest earned per year = amount received by david - amount received by peter = 854 - 800 = 54 interest earned for 3 years = 54 * 3 = 162 amount invested = 815 - 162 = 653 answer : a" | a = 854 - 800
b = 4 / 100
c = 3 / 100
d = b - c
e = a / d
f = 3 / 100
g = e * f
h = 800 - g
|
a ) 271.34 m , b ) 281.34 m , c ) 291.34 m , d ) 301.34 m , e ) 311.34 m | b | 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), 200), const_100) | the radius of a wheel is 22.4 cm . what is the distance covered by the wheel in making 200 resolutions . | "in one resolution , the distance covered by the wheel is its own circumference . distance covered in 200 resolutions . = 200 * 2 * 22 / 7 * 22.4 = 28134 cm = 281.34 m answer : b" | a = 3 + 4
b = a * 3
c = b + 1
d = 3 + 4
e = c / d
f = e * 22
g = f * 2
h = g * 200
i = h / 100
|
a ) − 0.3 , b ) 0.6 , c ) 0.3 , d ) 1.08 , e ) 2.46 | b | subtract(multiply(divide(divide(subtract(power(3, 2), power(1.8, 0.6)), const_1000), const_1000), 3), divide(divide(subtract(power(3, 2), power(1.8, 0.6)), const_1000), const_1000)) | what is the value of 3 x ^ 2 − 1.8 x + 0.6 for x = 0.6 ? | "3 x ^ 2 - 1.8 x + 0.6 for x = 0.6 = 3 ( 0.6 * 0.6 ) - 3 * 0.6 * ( 0.6 ) + 0.6 = 0 + 0.6 = 0.6 answer : b" | a = 3 ** 2
b = 1 ** 8
c = a - b
d = c / 1000
e = d / 1000
f = e * 3
g = 3 ** 2
h = 1 ** 8
i = g - h
j = i / 1000
k = j / 1000
l = f - k
|
a ) $ 900 , b ) $ 720 , c ) $ 600 , d ) $ 300 , e ) $ 60 | a | divide(multiply(multiply(divide(add(multiply(multiply(4, const_100), const_100), multiply(multiply(const_100, const_0_25), const_100)), const_100), 4), 12), multiply(const_3, 4)) | mr . hernandez , who was a resident of state x for only 12 months last year , had a taxable income of $ 22,500 for the year . if the state tax rate were 4 percent of the year ’ s taxable income prorated for the proportion of the year during which the taxpayer was a resident , what would be the amount of mr . hernandez ’ s state x tax for last year ? | "total tax for the year = 22,500 x 4 % = 900 as stated annual tax is prorated as per the duration of stay . prorated tax = 900 ( 12 / 12 ) = 900 answer a" | a = 4 * 100
b = a * 100
c = 100 * const_0_25
d = c * 100
e = b + d
f = e / 100
g = f * 4
h = g * 12
i = 3 * 4
j = h / i
|
a ) 85 , b ) 93 , c ) 83 , d ) 72 , e ) none | b | add(multiply(divide(add(12, 6), const_2), 12), subtract(12, divide(add(12, 6), const_2))) | the sum of digits of a two digit number is 12 , the difference between the digits is 6 . find the number | "description : = > x + y = 12 , x - y = 6 adding these 2 x = 18 = > x = 9 , y = 3 . thus the number is 93 answer b" | a = 12 + 6
b = a / 2
c = b * 12
d = 12 + 6
e = d / 2
f = 12 - e
g = c + f
|
a ) 200 , b ) 240 , c ) 300 , d ) 360 , e ) 120 | b | multiply(5, const_4) | how many 4 - digit numbers can be formed from the digits 0,2 , 3 , 5 , 6 , 7 and 9 , which are divisible by 5 and if the repetition is not allowed ? | "since , each desired number is divisible by 5 , so we must have either 0 or 5 at the unit place . so , the tens place can now be filled by any of the remaining 6 digits ( 2 , 3 , 6 , 7 , 9 , 0 or 5 ) the hundreds place can now be filled by any of the remaining 5 digits therefore the 3 - digit no can be formed by ( 4 * 5 * 6 * 2 ) = 240 ways ans - b" | a = 5 * 4
|
a ) 4 , b ) 7 , c ) 8 , d ) 12 , e ) 14 | c | multiply(divide(multiply(8, 8), 8), divide(7, 7)) | if 8 workers can build 8 cars in 8 days , then how many days would it take 7 workers to build 7 cars ? | "8 workers can build 1 car per day on average . 1 worker can build 1 / 8 of a car per day . 7 workers can build 7 / 8 car per day . the time required to build 7 cars is 7 / ( 7 / 8 ) = 8 days the answer is c ." | a = 8 * 8
b = a / 8
c = 7 / 7
d = b * c
|
a ) 20 ft , b ) 25 ft , c ) 450 ft , d ) 900 ft , e ) 1000 ft | c | multiply(30, add(divide(multiply(30, divide(const_10, const_2)), const_3), divide(const_10, const_2))) | the circumference of the front wheel of a cart is 30 ft long and that of the back wheel is 45 ft long . what is the distance traveled by the cart , when the front wheel has done five more revolutions than the rear wheel ? | "point to note : both the wheels would have traveled the same distance . now consider , no . of revolutions made by back wheel as x , which implies that the number of revolutions made by the front wheel is ( x + 5 ) . equating the distance traveled by front wheel to back wheel : ( x + 5 ) * 30 = x * 45 . ( formula for calculating the distance traveled by each wheel is : # of revolutions * circumference . ) solving this eqn . gives x = 10 . sub x = 10 either in ( x + 5 ) * 30 or in x * 45 to get the distance , which is 450 . so the correct choice is c ." | a = 10 / 2
b = 30 * a
c = b / 3
d = 10 / 2
e = c + d
f = 30 * e
|
a ) 130 , b ) 132 , c ) 134 , d ) 136 , e ) 138 | e | divide(1242, subtract(43, 34)) | a girl was asked to multiply a certain number by 43 . she multiplied it by 34 and got his answer less than the correct one by 1242 . find the number to be multiplied . | "let the required number be x . then , 43 x – 34 x = 1242 or 9 x = 1242 or x = 138 . required number = 138 . answer : e" | a = 43 - 34
b = 1242 / a
|
a ) 330000 , b ) 340000 , c ) 347000 , d ) 356000 , e ) 404600 | e | multiply(multiply(560000, subtract(const_1, divide(15, const_100))), divide(85, const_100)) | in an election , candidate a got 85 % of the total valid votes . if 15 % of the total votes were declared invalid and the total numbers of votes is 560000 , find the number of valid vote polled in favor of candidate . | "total number of invalid votes = 15 % of 560000 = 15 / 100 × 560000 = 8400000 / 100 = 84000 total number of valid votes 560000 – 84000 = 476000 percentage of votes polled in favour of candidate a = 85 % therefore , the number of valid votes polled in favour of candidate a = 85 % of 476000 = 85 / 100 × 476000 = 40460000 / 100 = 404600 e )" | a = 15 / 100
b = 1 - a
c = 560000 * b
d = 85 / 100
e = c * d
|
a ) 306.09 , b ) 306.07 , c ) 306.04 , d ) 306.03 , e ) 306.01 | c | subtract(multiply(5000, power(add(1, divide(4, const_100)), divide(const_3, 2))), 5000) | find out the c . i on rs . 5000 at 4 % p . a . compound half - yearly for 1 1 / 2 years | "a = 5000 ( 51 / 50 ) 3 = 5306.04 5000 - - - - - - - - - - - 306.04 answer : c" | a = 4 / 100
b = 1 + a
c = 3 / 2
d = b ** c
e = 5000 * d
f = e - 5000
|
a ) 26 , b ) 37.5 , c ) 42 , d ) 44 , e ) 50 | d | multiply(subtract(multiply(add(const_1, divide(80, const_100)), subtract(const_1, divide(20, const_100))), const_1), const_100) | a retailer purchases shirts from a wholesaler and then sells the shirts in her store at a retail price that is 80 percent greater than the wholesale price . if the retailer decreases the retail price by 20 percent this will have the same effect as increasing the wholesale price by what percent ? | "answer : d = 44 . assume rs . 100 to be the price at which the retailer buys from wholesaler . 80 % increase makes retail price = 180 . now 20 % decrease - > ( 1 - 20 / 100 ) * 180 = 144 . now compared to the wholesale price of 100 , 44 % increase is what will have the same effect as increasing the wholesale price ." | a = 80 / 100
b = 1 + a
c = 20 / 100
d = 1 - c
e = b * d
f = e - 1
g = f * 100
|
a ) 426 , b ) 284 , c ) 483 , d ) 256 , e ) 428 | c | multiply(multiply(const_pi, 7), 22) | the slant height of a cone is 22 cm and radius of the base is 7 cm , find the curved surface of the cone ? | "π * 22 * 7 = 483 answer : c" | a = math.pi * 7
b = a * 22
|
a ) 90 , b ) 300 , c ) 270 , d ) 500 , e ) 1,000 | b | divide(divide(240, const_2), divide(40, const_100)) | one night 40 percent of the female officers on a police force were on duty . if 240 officers were on duty that night and half of these were female officers , how many female officers were on the police force ? | "let total number of female officers in the police force = f total number of officers on duty on that night = 240 number of female officers on duty on that night = 240 / 2 = 120 ( 40 / 100 ) * f = 120 = > f = 300 answer b" | a = 240 / 2
b = 40 / 100
c = a / b
|
a ) 1 / 13 , b ) 1 / 14 , c ) 1 / 2 , d ) 2 / 15 , e ) 2 / 16 | d | divide(choose(4, const_2), choose(add(4, 6), const_2)) | there are 4 red shoes & 6 green shoes . if two of red shoes are drawn what is the probability of getting red shoes | "taking 4 red shoe the probablity is 4 c 2 from 10 shoes probablity of taking 2 red shoe is 4 c 2 / 10 c 2 = 2 / 15 answer : d" | a = math.comb(4, 2)
b = 4 + 6
c = math.comb(b, 2)
d = a / c
|
a ) 25 liters , b ) 27 liters , c ) 26 liters , d ) 32 liters , e ) 35 liters | c | subtract(divide(multiply(const_2, const_100), subtract(20, multiply(divide(75, const_100), 20))), 14) | how much water should be added to 14 liters of a 20 % - solution of alcohol to reduce the concentration of alcohol in the solution by 75 % ? | "let x ltr water to be added 2 ltr alcohol to be represented as ( 20 ( 1 - 3 / 4 ( new soln . = 14 + x ) ) ) 2 = 5 % * ( 14 + x ) - - - - - - - - > x = 26 ans c" | a = 2 * 100
b = 75 / 100
c = b * 20
d = 20 - c
e = a / d
f = e - 14
|
a ) 18 , b ) 20 , c ) 22 , d ) 24 , e ) 25 | d | multiply(multiply(8, const_2), divide(const_3, const_2)) | a group of hikers is planning a trip that will take them up a mountain using one route and back down using another route . they plan to travel down the mountain at a rate of one and a half times the rate they will use on the way up , but the time each route will take is the same . if they will go up the mountain at a rate of 8 miles per day and it will take them two days , how many miles long is the route down the mountain ? | on the way down , the rate is 1.5 * 8 = 12 miles per day . the distance of the route down the mountain is 2 * 12 = 24 miles . the answer is d . | a = 8 * 2
b = 3 / 2
c = a * b
|
a ) 0 , b ) 2 , c ) 4 , d ) 7 , e ) 9 | b | divide(1, 37) | what is the 20 th digit to the right of the decimal point in the decimal expansion of 1 / 37 ? | "1 / 37 = 0.027027 . . . so , we have a repeating cycle of 027 . every third digit ( 2 nd , 4 th , 6 th , . . . ) to the right of the decimal point is alternating by 2 , 0 , 7 thus 20 th digit is 2 . answer : b ." | a = 1 / 37
|
a ) rs . 72 , b ) rs . 36 , c ) rs . 55 , d ) rs . 50 , e ) none | c | divide(6.6, divide(12, const_100)) | the banker ' s gain on a bill due due 1 year hence at 12 % per annum is rs . 6.6 . the true discount is | solution t . d = [ b . g x 100 / r x t ] = rs . ( 6.6 x 100 / 12 x 1 ) = rs . 55 . answer c | a = 12 / 100
b = 6 / 6
|
a ) 15 , b ) 25 , c ) 30 , d ) 45 , e ) 55 | c | divide(subtract(multiply(92, 5), multiply(5, 20)), subtract(92, 80)) | the average mark of the students of a class in a particular exam is 80 . if 5 students whose average mark in that exam is 20 are excluded , the average mark of the remaining will be 92 . find the number of students who wrote the exam . | "let the number of students who wrote the exam be x . total marks of students = 80 x . total marks of ( x - 5 ) students = 92 ( x - 5 ) 80 x - ( 5 * 20 ) = 92 ( x - 5 ) 360 = 12 x = > x = 30 answer : c" | a = 92 * 5
b = 5 * 20
c = a - b
d = 92 - 80
e = c / d
|
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