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a ) 16 cm , b ) 24 cm , c ) 28 cm , d ) 36 cm , e ) 39 cm | d | divide(multiply(const_4, divide(power(12, const_3), power(8, const_2))), const_3) | a metallic sphere of radius 12 cm is melted and drawn into a wire , whose radius of cross section is 8 cm . what is the length of the wire ? | "volume of the wire ( in cylindrical shape ) is equal to the volume of the sphere . Ο ( 8 ) ^ 2 * h = ( 4 / 3 ) Ο ( 12 ) ^ 3 = > h = 36 cm answer : d" | a = 12 ** 3
b = 8 ** 2
c = a / b
d = 4 * c
e = d / 3
|
a ) 2 : 3 , b ) 3 : 4 , c ) 3 : 20 , d ) 20 : 3 , e ) 22 : 1 | c | divide(multiply(0.06, const_100), multiply(0.4, const_100)) | if 0.4 of a number is equal to 0.06 of another number , the ratio of the numbers is : | "expl : 0.4 a = 0.06 b - > a / b = 0.06 / 0.40 = 6 / 40 = 3 / 20 : . a : b = 3 : 20 answer : c" | a = 0 * 6
b = 0 * 4
c = a / b
|
a ) 1 , b ) 2 , c ) 3 , d ) 4 , e ) 5 | e | subtract(subtract(subtract(18, 5), 4), 4) | a group of people participate in some curriculum , 25 of them practice yoga , 18 study cooking , 10 study weaving , 4 of them study cooking only , 5 of them study both the cooking and yoga , 4 of them participate all curriculums . how many people study both cooking and weaving ? | "both cooking and weaving = 18 - ( 4 + 4 + 5 ) = 5 so , the correct answer is e ." | a = 18 - 5
b = a - 4
c = b - 4
|
a ) 29 % , b ) 20 % , c ) 27 % , d ) 25 % , e ) 12 % | c | multiply(divide(subtract(multiply(add(500, multiply(const_3, 500)), divide(22, const_100)), multiply(500, divide(7, const_100))), multiply(const_3, 500)), const_100) | a $ 500 investment and a $ 1,500 investment have a combined yearly return of 22 percent of the total of the two investments . if the $ 500 investment has a yearly return of 7 percent , what percent yearly return does the $ 1,500 investment have ? | "the equation we can form the question : return on total investment = sum of individual investments ( 500 + 1500 ) ( 22 ) = ( 500 Γ’ Λ β 7 ) + ( 1500 x ) , where x is the return on investment of 1500 . solving the equation , we get x = 27 % ( option c ) answer : c" | a = 3 * 500
b = 500 + a
c = 22 / 100
d = b * c
e = 7 / 100
f = 500 * e
g = d - f
h = 3 * 500
i = g / h
j = i * 100
|
a ) 3 , b ) 3.5 , c ) 4 , d ) 4.5 , e ) 5 | b | divide(subtract(198, 170), divide(subtract(222, 198), 3)) | joe went on a diet 3 months ago when he weighed 222 pounds . if he now weighs 198 pounds and continues to lose at the same average monthly rate , in approximately how many months will he weigh 170 pounds ? | "222 - 198 = 24 pounds lost in 3 months 24 / 3 = 8 , so joe is losing weight at a rate of 8 pounds per month . . . . in approximately how many months will he weigh 170 pounds ? a simple approach is to just list the weights . now : 198 lbs in 1 month : 190 lbs in 2 months : 182 lbs in 3 months : 174 lbs in 4 months : 166 lbs since 170 pounds is halfway between 174 and 166 , the correct answer must be 3.5 months . answer : b" | a = 198 - 170
b = 222 - 198
c = b / 3
d = a / c
|
a ) 0.1 , b ) 0.6 , c ) 1 , d ) 1.2 , e ) 3 | e | divide(30, subtract(50, 40)) | two cars are traveling in the same direction along the same route . the red car travels at a constant speed of 40 miles per hour , and the black car is traveling at a constant speed of 50 miles per hour . if the red car is 30 miles ahead of the black car , how many hours will it take the black car to overtake the red car ? | option e 20 + 40 t = 50 t t = 3 | a = 50 - 40
b = 30 / a
|
a ) 50 % , b ) 53 % , c ) 54 % , d ) 55 % , e ) 57 % | a | add(multiply(60, divide(70, const_100)), multiply(subtract(const_100, 60), divide(20, const_100))) | in a certain city , 60 percent of the registered voters are democrats and the rest are republicans . in a mayoral race , if 70 percent of the registered voters who are democrats and 20 percent of the registered voters who are republicans are expected to vote for candidate a , what percent of the registered voters are expected to vote for candidate a ? | "say there are total of 100 registered voters in that city . thus 60 are democrats and 40 are republicans . 60 * 0.70 = 42 democrats are expected to vote for candidate a ; 40 * 0.20 = 8 republicans are expected to vote for candidate a . thus total of 42 + 8 = 50 registered voters are expected to vote for candidate a , which is 50 % of the total number of registered voters . answer : a" | a = 70 / 100
b = 60 * a
c = 100 - 60
d = 20 / 100
e = c * d
f = b + e
|
a ) 553681 , b ) 555181 , c ) 555681 , d ) 556581 , e ) 555581 | c | multiply(subtract(subtract(divide(559981, 987), const_4), const_0_33), 987) | a boy multiplied 987 by a certain number and obtained 559981 as his answer . if in the answer both 98 are wrong and other digits are correct , then the correct answer would be : | "987 = 3 x 7 x 47 . so , the required number must be divisible by each one of 3 , 7 , 47 553681 - - > sum of digits = 28 , not divisible by 3 555181 sum of digits = 25 , not divisible by 3 555681 is divisible by each one of 3 , 7 , 47 . 556581 sum of digits = 30 , not divisible by 7 555581 sum of digits = 29 , not divisible by 3 so the answer is c ." | a = 559981 / 987
b = a - 4
c = b - const_0_33
d = c * 987
|
a ) 2 , b ) 3 , c ) 4 , d ) 5 , e ) 6 | d | divide(subtract(add(multiply(2, 3), 11), add(multiply(2, 2), 3)), subtract(multiply(2, 2), multiply(2, const_1))) | given f ( x ) = 2 x β 3 , for what value of x does 2 * [ f ( x ) ] β 11 = f ( x β 2 ) ? | "2 ( 2 x - 3 ) - 11 = 2 ( x - 2 ) - 3 2 x = 10 x = 5 the answer is d ." | a = 2 * 3
b = a + 11
c = 2 * 2
d = c + 3
e = b - d
f = 2 * 2
g = 2 * 1
h = f - g
i = e / h
|
a ) 45 minutes , b ) 14 minutes , c ) 39 minutes , d ) 40 minutes 20 seconds , e ) none of these | a | multiply(divide(750, subtract(add(40, 30), 20)), const_3) | pipe a fills a tank of capacity 750 liters at the rate of 40 liters a minute . another pipe b fills the same tank at the rate of 30 liters a minute . a pipe at the bottom of the tank drains the tank at the rate of 20 liters a minute . if pipe a is kept open for a minute and then closed and pipe b is open for a minute and then closed and then pipe c is open for a minute and then closed and the cycle is repeated , when will the tank be full ? | "in one cycle they fill 40 + 30 - 20 = 50 liters 750 = 50 * n = > n = 15 here n = number of cycles . total time = 15 * 3 = 45 as in one cycle there are 3 minutes . thus 45 minutes answer : a" | a = 40 + 30
b = a - 20
c = 750 / b
d = c * 3
|
a ) 33 , b ) 35 , c ) 37 , d ) 39 , e ) 41 | d | multiply(divide(21, 6), const_12) | the first doughnut is priced at $ 1 and then if you purchase additional doughnuts as dozens then the price is $ 6 / dozen . what is the total number of doughnuts purchased if you paid $ 21 ? | "$ 21 = 3 * $ 6 + $ 3 the number of doughnuts is 3 * 12 + 3 = 39 the answer is d ." | a = 21 / 6
b = a * 12
|
a ) 1200 , b ) 1723 , c ) 1129 , d ) 2613 , e ) 1372 | a | divide(150, subtract(inverse(const_2), subtract(const_1, divide(62.5, const_100)))) | all the milk in container a which was filled to its brim was poured into two containers b and c . the quantity of milk in container b was 62.5 % less than the capacity of container a . if 150 liters was now transferred from c to b , then both the containers would have equal quantities of milk . what was the initial quantity of milk in container a ? | "a b has 62.5 % or ( 5 / 8 ) of the milk in a . therefore , let the quantity of milk in container a ( initially ) be 8 k . quantity of milk in b = 8 k - 5 k = 3 k . quantity of milk in container c = 8 k - 3 k = 5 k container : a b c quantity of milk : 8 k 3 k 5 k it is given that if 150 liters was transferred from container c to container b , then both the containers would have equal quantities of milk . 5 k - 150 = 3 k + 150 = > 2 k = 300 = > k = 150 the initial quantity of milk in a = 8 k = 8 * 150 = 1200 liters ." | a = 1/(2)
b = 62 / 5
c = 1 - b
d = a - c
e = 150 / d
|
a ) 240 meters , b ) 260 meters , c ) 420 meters , d ) 600 meters , e ) can not be determined | b | subtract(multiply(divide(multiply(72, const_1000), const_3600), 30), multiply(divide(multiply(72, const_1000), const_3600), 17)) | a train traveling at 72 kmph crosses a platform in 30 seconds and a man standing on the platform in 17 seconds . what is the length of the platform in meters ? | "speed of the train in metres / sec = 72000 / 3600 = 20 distance travelled by train to cross the platform = 30 * 20 = 600 = length of train + length of platform distance travelled by train to cross the man = 17 * 20 = 340 = length of train length of platform = 600 - 340 = 260 answer : b" | a = 72 * 1000
b = a / 3600
c = b * 30
d = 72 * 1000
e = d / 3600
f = e * 17
g = c - f
|
a ) 140 , b ) 150 , c ) 160 , d ) 170 , e ) 183 | e | divide(2562, 14) | two numbers have a h . c . f of 14 and a product of two numbers is 2562 . find the l . c . m of the two numbers ? | "l . c . m of two numbers is given by ( product of the two numbers ) / ( h . c . f of the two numbers ) = 2562 / 14 = 183 . answer : e" | a = 2562 / 14
|
a ) 2 days , b ) 4 days , c ) 6 days , d ) 7 days , e ) 10 days | b | add(multiply(10, 2), divide(10, 2)) | a can complete a work in 10 days and b can do the same work in 5 days . if a after doing 2 days , leaves the work , find in how many days b will do the remaining work ? | "the required answer = ( 10 - 2 ) * 5 / 10 = 40 / 10 = 4 days answer is b" | a = 10 * 2
b = 10 / 2
c = a + b
|
a ) 14 , b ) 20 , c ) 15 , d ) 28 , e ) 30 | c | divide(180, subtract(13, const_1)) | let the number which when multiplied by 13 is increased by 180 . | "solution let the number be x . then , 13 x - x = 180 βΉ = βΊ 12 x = 180 x βΉ = βΊ 15 . answer c" | a = 13 - 1
b = 180 / a
|
a ) 1 , b ) 100 , c ) 10000 , d ) 100000 , e ) 1000 | e | power(10, subtract(655, 652)) | 10 ^ ( 655 ) Γ£ Β· 10 ^ ( 652 ) = ? | "10 ^ ( 655 ) Γ£ Β· 10 ^ ( 652 ) = 10 ^ ( 655 - 652 ) = 10 ^ 3 = 1000 answer : e" | a = 655 - 652
b = 10 ** a
|
a ) 110 , b ) 130 , c ) 150 , d ) 170 , e ) 190 | e | divide(factorial(20), multiply(factorial(subtract(20, const_2)), factorial(const_2))) | if 20 lines are drawn in a plane such that no two of them are parallel and no three are concurrent , then in how many points do they intersect ? | if two lines are not parallel , then they will intersect in exactly one point . lines can be extended infinitely on both ends so somewhere they will intersect with each other if they are not parallel . we are also given that no three lines are concurrent . this means that no three lines intersect at the same point . so every pair of two lines we select will have a unique point of intersection which they will not share with any third line . the number of ways to select 2 lines from 20 lines is 20 c 2 = 190 the answer is e . | a = math.factorial(20)
b = 20 - 2
c = math.factorial(b)
d = math.factorial(2)
e = c * d
f = a / e
|
a ) 32 min , b ) 40 min , c ) 35 min , d ) 25 min , e ) 20 min | a | add(20, 12) | the jogging track in a sports complex is 1000 meters in circumference . deepak and his wife start from the same point and walk in opposite directions at 20 km / hr and 12 km / hr respectively . they will meet for the first time in ? | "clearly , the two will meet when they are 1000 m apart to be 20 + 12 = 32 km apart , they take 1 hour to be 1000 m apart , they take 32 * 1000 / 1000 = 32 min . answer is a" | a = 20 + 12
|
a ) 12 sec , b ) 20 sec , c ) 15 sec , d ) 18 sec , e ) 10 sec | e | divide(180, add(15, 3)) | an escalator moves towards the top level at the rate of 15 ft . sec and its length is 180 feet . if a person walks on the moving escalator at the rate of 3 feet per second towards the top level , how much time does he take to cover the entire length . | "explanation : time taken to cover the entire length = tot . dist / resultant speed = 180 / ( 15 + 3 ) = 10 sec answer : e" | a = 15 + 3
b = 180 / a
|
a ) $ 1,395 , b ) $ 1,733 , c ) $ 3,466 , d ) $ 13,333 , e ) $ 20,796 | a | subtract(9, multiply(4, const_2)) | a new home buyer pays 4 % annual interest on her first mortgage and 9 % annual interest on her second mortgage . if she borrowed a total of $ 335,000 , 80 % of which was in the first mortgage , what is her approximate monthly interest payment ? | "0.04 x + 0.09 y = 335000 [ 1 ] 0.04 x = 0.80 * 335000 = 268000 [ 2 ] 268000 + 0.09 y = 320000 - - > 0.09 y = 67000 [ 3 ] 268000 / 12 = 22333.3333 [ 4 ] 67000 / 12 = 5583.333 [ 5 ] adding [ 4,5 ] we get : 27916 [ 6 ] dividing [ 6 ] / 2 to get an average we get 1.395 , ans a" | a = 4 * 2
b = 9 - a
|
a ) 10 , b ) 20 , c ) 30 , d ) 40 , e ) 50 | d | divide(divide(add(200, 300), const_1000), divide(45, const_3600)) | a train 200 meters long completely crosses a 300 meters long bridge in 45 seconds . what is the speed of the train is ? | "s = ( 200 + 300 ) / 45 = 500 / 45 * 18 / 5 = 40 answer : d" | a = 200 + 300
b = a / 1000
c = 45 / 3600
d = b / c
|
a ) 32 % , b ) 34.4 % , c ) 35 % , d ) 35.6 % , e ) 36.4 % | d | multiply(divide(add(multiply(divide(30, const_100), 56000), multiply(divide(40, const_100), 72000)), add(72000, 56000)), const_100) | john and ingrid pay 30 % and 40 % tax annually , respectively . if john makes $ 56000 and ingrid makes $ 72000 , what is their combined tax rate ? | "( 1 ) when 30 and 40 has equal weight or weight = 1 / 2 , the answer would be 35 . ( 2 ) when 40 has larger weight than 30 , the answer would be in between 35 and 40 . unfortunately , we have 2 answer choices d and e that fit that condition so we need to narrow down our range . ( 3 ) get 72000 / 128000 = 72 / 128 = 9 / 16 . 9 / 16 is a little above 8 / 16 = 1 / 2 . thus , our answer is just a little above 35 . answer : d" | a = 30 / 100
b = a * 56000
c = 40 / 100
d = c * 72000
e = b + d
f = 72000 + 56000
g = e / f
h = g * 100
|
a ) 8000 , b ) 8500 , c ) 9000 , d ) 9500 , e ) 10000 | e | add(divide(multiply(7000, 30), const_100), 7000) | john ' s bank ' s saving amount is decreased 30 % due to loan payment and current balance is rs . 7000 . find the actual balance before deduction ? | "cp * ( 70 / 100 ) = 7000 cp = 100 * 100 = > cp = 10000 answer : e" | a = 7000 * 30
b = a / 100
c = b + 7000
|
a ) 80 % , b ) 100 % , c ) 109 % , d ) 120 % , e ) 140 % | c | multiply(divide(multiply(subtract(const_1, divide(add(divide(multiply(add(10, subtract(10, const_1)), subtract(const_100, const_10)), const_100), 6), 25)), const_100), multiply(subtract(const_1, divide(add(6, divide(multiply(add(10, const_4), subtract(const_100, const_10)), const_100)), 20)), const_100)), const_100) | during a special promotion , a certain filling station is offering a 10 percent discount on gas purchased after the first 6 gallons . if kim purchased 20 gallons of gas , and isabella purchased 25 gallons of gas , then isabella β s total per - gallon discount is what percent of kim β s total per - gallon discount ? | kim purchased 20 gallons of gas . she paid for 6 + 0.9 * 14 = 18.6 gallons , so the overall discount she got was 1.4 / 20 = 7 % . isabella purchased 25 gallons of gas . she paid for 6 + 0.9 * 19 = 23.1 gallons , so the overall discount she got was 1.9 / 25 = 7.6 % . 7.6 is 7.6 / 7 * 100 = 109 % of 7 . answer : c . | a = 10 - 1
b = 10 + a
c = 100 - 10
d = b * c
e = d / 100
f = e + 6
g = f / 25
h = 1 - g
i = h * 100
j = 10 + 4
k = 100 - 10
l = j * k
m = l / 100
n = 6 + m
o = n / 20
p = 1 - o
q = p * 100
r = i / q
s = r * 100
|
a ) 90 , b ) 150 , c ) 270 , d ) 300 , e ) 450 | b | subtract(multiply(add(add(multiply(const_100, const_10), multiply(const_3, const_100)), multiply(3, const_10)), divide(3, add(add(3, 2), 2))), multiply(add(add(multiply(const_100, const_10), multiply(const_3, const_100)), multiply(3, const_10)), divide(2, add(add(3, 2), 2)))) | a farmer with 1,350 acres of land had planted his fields with corn , sugar cane , and tobacco in the ratio of 3 : 2 : 4 , respectively , but he wanted to make more money , so he shifted the ratio to 2 : 2 : 5 , respectively . how many more acres of land were planted with tobacco under the new system ? | "originally ( 4 / 9 ) * 1350 = 600 acres were planted with tobacco . in the new system ( 5 / 9 ) * 1350 = 750 acres were planted with tobacco . thus 750 - 600 = 150 more acres were planted with tobacco . the answer is b ." | a = 100 * 10
b = 3 * 100
c = a + b
d = 3 * 10
e = c + d
f = 3 + 2
g = f + 2
h = 3 / g
i = e * h
j = 100 * 10
k = 3 * 100
l = j + k
m = 3 * 10
n = l + m
o = 3 + 2
p = o + 2
q = 2 / p
r = n * q
s = i - r
|
a ) 1 / 2 , b ) 1 / 3 , c ) 1 / 4 , d ) 1 / 5 , e ) w = 1 / 6 | e | divide(const_1, divide(divide(factorial(4), factorial(const_2)), factorial(const_2))) | if two of the 4 expressions x + y , x + 5 y , x - y , and 5 x - y are chosen at random , what is the probability w that their product will be of the form of x ^ 2 - ( by ) ^ 2 , where b is an integer ? | only ( x + y ) ( x - y ) pair will give the form x ^ 2 - ( by ) ^ 2 the probability of selecting these two pairs are 1 / 4 * 1 / 3 = 1 / 12 , assuming x + y is picked first , then x - y , but x - y can be picked first followed by x + y . so the probability w = 1 / 12 * 2 = 1 / 6 ans e | a = math.factorial(4)
b = math.factorial(2)
c = a / b
d = math.factorial(2)
e = c / d
f = 1 / e
|
a ) rs 840 , b ) rs 1320 , c ) rs 1620 , d ) rs 1680 , e ) none of these | c | multiply(divide(multiply(9, 6), multiply(4, 10)), 1200) | if 4 men working 10 hours a day earn rs . 1200 per week , then 9 men working 6 hours a day will earn how much per week ? | "explanation : ( men 4 : 9 ) : ( hrs / day 10 : 6 ) : : 1200 : x hence 4 * 10 * x = 9 * 6 * 1200 or x = 9 * 6 * 1200 / 4 * 10 = 1620 answer : c" | a = 9 * 6
b = 4 * 10
c = a / b
d = c * 1200
|
a ) 29 , b ) 33 , c ) 35 , d ) 40 , e ) 42 | a | add(add(divide(subtract(180, 40), 5), 1), 1) | a test has 180 questions . each question has 5 options , but only 1 option is correct . if test - takers mark the correct option , they are awarded 1 point . however , if an answer is incorrectly marked , the test - taker loses 0.25 points . no points are awarded or deducted if a question is not attempted . a certain group of test - takers attempted different numbers of questions , but each test - taker still received the same net score of 40 . what is the maximum possible number of such test - takers ? | "a correct answers get you 1 point , an incorrect answer gets you minus 1 / 4 point and a skipped question gets you 0 points . since there are 200 total questions , there are a variety of ways to get a total of 40 points . let c be the number of correct answers and let i be the number of incorrect answers . to get 40 points , a test taker must have at least 40 correct answers . then c = > 40 . for every correct question above 40 , the test taker has 4 incorrect answers . then , the i = 4 * ( c - 40 ) . also , i + c < = 180 . thus 5 c < = 340 and so c < = 68 . then 40 < = c < = 68 and c can have 29 possible values . the answer is a ." | a = 180 - 40
b = a / 5
c = b + 1
d = c + 1
|
a ) 1 / 49 , b ) 4 / 7 , c ) 3 / 7 , d ) 16 / 49 , e ) 40 / 49 | c | subtract(const_1, sqrt(divide(16, 49))) | jean drew a gumball at random from a jar of pink and blue gumballs . since the gumball she selected was blue and she wanted a pink one , she replaced it and drew another . the second gumball also happened to be blue and she replaced it as well . if the probability of her drawing the two blue gumballs was 16 / 49 what is the probability that the next one she draws will be pink ? | "the probability of drawing a pink gumball both times is the same . the probability that she drew two blue gumballs = 16 / 49 = ( 4 / 7 ) * ( 4 / 7 ) therefore probability that the next one she draws is pink = 3 / 7 option ( c )" | a = 16 / 49
b = math.sqrt(a)
c = 1 - b
|
a ) 110 , b ) 70.4 , c ) 86 , d ) 105.6 , e ) 108 | a | add(88, multiply(divide(25, const_100), 88)) | if x is 25 percent greater than 88 , then x = | "x = 88 * 1.25 = 110 so the answer is a ." | a = 25 / 100
b = a * 88
c = 88 + b
|
a ) 40 , b ) 48 , c ) 54 , d ) 62 , e ) 76 | d | add(add(multiply(8, 4), multiply(const_2, multiply(4, add(1, divide(25, const_100))))), multiply(const_2, multiply(8, add(1, divide(25, const_100))))) | a cistern 8 meters long and 4 meters wide contains water up to a depth of 1 meter 25 cm . what is the total area of the wet surface ? | "area of the wet surface = [ 2 ( lb + bh + lh ) - lb ] = 2 ( bh + lh ) + lb = [ 2 ( 4 x 1.25 + 8 x 1.25 ) + 8 x 4 ] = 62 the answer is d ." | a = 8 * 4
b = 25 / 100
c = 1 + b
d = 4 * c
e = 2 * d
f = a + e
g = 25 / 100
h = 1 + g
i = 8 * h
j = 2 * i
k = f + j
|
a ) 1 , b ) 2 , c ) 3 , d ) 4 , e ) 5 | e | divide(subtract(add(multiply(divide(subtract(multiply(60, 10), multiply(54, 10)), subtract(60, 40)), 40), multiply(subtract(10, divide(subtract(multiply(60, 10), multiply(54, 10)), subtract(60, 40))), 60)), multiply(48, 10)), subtract(60, 48)) | at a certain food stand , the price of each apple is 40 Β’ and the price of each orange is 60 Β’ . mary selects a total of 10 apples and oranges from the food stand , and the average ( arithmetic mean ) price of the 10 pieces of fruit is 54 Β’ . how many oranges must mary put back so that the average price of the pieces of fruit that she keeps is 48 Β’ ? | "if the average price is 54 , then mary has 7 oranges and 3 apples ( a ratio of 7 : 3 ) . for the average price to be 48 , the ratio should be 2 : 3 . mary must put back 5 oranges . the answer is e ." | a = 60 * 10
b = 54 * 10
c = a - b
d = 60 - 40
e = c / d
f = e * 40
g = 60 * 10
h = 54 * 10
i = g - h
j = 60 - 40
k = i / j
l = 10 - k
m = l * 60
n = f + m
o = 48 * 10
p = n - o
q = 60 - 48
r = p / q
|
a ) $ 200 , b ) $ 500 , c ) $ 600 , d ) $ 800 , e ) $ 1,200 | b | divide(subtract(1800, 800), const_2) | david has $ 1800 at the beginning of his trip , after spending money , he still has exactly $ 800 less than he spent on the trip . how much money does john still have ? | suppose total money spent = x not spend ( money he still has ) = x - 800 x + x - 800 = 1800 x = 1300 money not spend = 1300 - 800 = 500 answer : b | a = 1800 - 800
b = a / 2
|
['a ) 4 : 5', 'b ) 1 : 5', 'c ) 3 : 5', 'd ) 1.5 : 5', 'e ) 2 : 5'] | e | divide(multiply(power(3, const_2), 10), multiply(power(5, const_2), 9)) | two cylinders of the radius in the ratio 3 : 5 and heights in the ratio 10 : 9 . then find the volumes ratio ? | Ο r ( power 2 ) h : Ο r ( power 2 ) h 9 Γ 10 : 25 Γ 9 90 : 225 2 : 5 answer is e . | a = 3 ** 2
b = a * 10
c = 5 ** 2
d = c * 9
e = b / d
|
a ) 23,000 , b ) 24,500 , c ) 25,500 , d ) 26,500 , e ) 27,500 | a | floor(divide(divide(subtract(540, multiply(1,000, divide(8, const_100))), subtract(divide(10, const_100), divide(8, const_100))), 1,000)) | angelo and isabella are both salespersons . in any given week , angelo makes $ 540 in base salary plus 8 percent of the portion of his sales above $ 1,000 for that week . isabella makes 10 percent of her total sales for any given week . for what amount of weekly sales would angelo and isabella earn the same amount of money ? | "let the weekly sales of both = x 540 + ( x β 1000 ) 8 / 100 = 10 / 100 x x = 23000 answer : a" | a = 8 / 100
b = 1 * 0
c = 540 - b
d = 10 / 100
e = 8 / 100
f = d - e
g = c / f
h = g / 1
i = math.floor(h)
|
a ) 525 , b ) 545 , c ) 565 , d ) 575 , e ) 585 | e | divide(add(divide(multiply(1500, 30), const_100), 1500), multiply(divide(1500, const_100), const_2)) | a computer store offers employees a 30 % discount off the retail price . if the store purchased a computer from the manufacturer for $ 1500 dollars and marked up the price 30 % to the final retail price , how much would an employee save if he purchased the computer at the employee discount ( 30 % off retail price ) as opposed to the final retail price . | "cost price = 1500 profit = 30 % = 30 % of 1500 = 450 selling price = cp + profit sp = 1950 a discount of 30 % to employees means 30 % off on 1950 so 30 % of 1950 = 585 ans e" | a = 1500 * 30
b = a / 100
c = b + 1500
d = 1500 / 100
e = d * 2
f = c / e
|
a ) 11 : 6 , b ) 12 : 7 , c ) 13 : 7 , d ) 15 : 6 , e ) 65 : 56 | e | divide(multiply(65, 5), multiply(70, 4)) | car a runs at the speed of 65 km / hr & reaches its destination in 5 hr . car b runs at the speed of 70 km / h & reaches its destination in 4 h . what is the respective ratio of distances covered by car a & car b ? | sol . distance travelled by car a = 65 Γ£ β 5 = 325 km distance travelled by car b = 70 Γ£ β 4 = 280 km ratio = 325 / 280 = 65 : 56 e | a = 65 * 5
b = 70 * 4
c = a / b
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a ) - 4 , b ) - 2 , c ) 0 , d ) 2 , e ) 4 | c | multiply(negate(multiply(divide(70, 2), 2)), 11) | if 9 a - b = 10 b + 70 = - 12 b - 2 a , what is the value of 11 a + 11 b ? | "( i ) 9 a - 11 b = 70 ( ii ) 2 a + 22 b = - 70 adding ( i ) and ( ii ) : 11 a + 11 b = 0 the answer is c ." | a = 70 / 2
b = a * 2
c = negate * (
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a ) 15 , b ) 16 , c ) 17 , d ) 18 , e ) 19 | a | add(multiply(3, 4), const_1) | how many distinct integer values of n satisfy the inequality | | n - 3 | + 4 | β€ 17 ? | "so i can write this as in - 3 i + 4 < = 17 or in - 3 i < = 13 so n can have - 10 to 16 = 15 true values . . . . a" | a = 3 * 4
b = a + 1
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a ) 2 , b ) 3 , c ) 4 , d ) 5 , e ) 7 | b | subtract(15, 12) | there are 250 men and 150 women in a committee , if all will work they will complete 12 units per day , if all men work they will complete 15 units per day , how many units will women complete per day ? | i think there is a mistake in this question . if all men and women together complete 12 units , how only men can do 15 units of work a day ? forgetting about the reality , women can do - 3 units a day . answer : b | a = 15 - 12
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a ) 52 : 56 , b ) 55 : 53 , c ) 52 : 50 , d ) 22 : 56 , e ) 52 : 51 | b | divide(add(const_100, 10), add(const_100, 6)) | the cash difference between the selling prices of an article at a profit of 10 % and 6 % is rs . 3 . the ratio of the two selling prices is ? | "let c . p . of the article be rs . x . then , required ratio = 110 % of x / 106 % of x = 110 / 106 = 55 / 53 = 55 : 53 answer : b" | a = 100 + 10
b = 100 + 6
c = a / b
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a ) 5363 , b ) 6240 , c ) 2368 , d ) 1987 , e ) 2732 | b | multiply(divide(96, 10), 650) | in order to obtain an income of rs . 650 from 10 % stock at rs . 96 , one must make an investment of | to obtain rs . 10 , investment = rs . 96 . to obtain rs . 650 , investment = = rs . 6240 . answer : b | a = 96 / 10
b = a * 650
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a ) 152 , b ) 209 , c ) 57 , d ) 171 , e ) 220 | e | multiply(multiply(8, subtract(11, 8)), 11) | there are 380 doctors and nurses in a hospital . if the ratio of the doctors to the nurses is 8 : 11 , then how many nurses are there in the hospital ? | "given , the ratio of the doctors to the nurses is 8 : 11 number of nurses = 11 / 19 x 380 = 220 answer : e" | a = 11 - 8
b = 8 * a
c = b * 11
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a ) $ 200 , b ) $ 240 , c ) $ 280 , d ) $ 320 , e ) $ 360 | a | divide(subtract(multiply(multiply(const_100, multiply(add(const_2, const_3), const_2)), add(divide(5, const_100), const_1)), add(add(multiply(const_100, multiply(add(const_2, const_3), const_2)), multiply(multiply(add(const_2, const_3), const_2), 3)), multiply(const_2, const_3))), subtract(add(divide(5, const_100), const_1), add(divide(3, const_100), const_1))) | we invested a total of $ 1,000 . we invested one part of the money at 3 % and the rest of the money at 5 % . the total investment with interest at the end of the year was $ 1,046 . how much money did we invest at 3 % ? | "let x be the money invested at 3 % . 1.03 x + 1.05 ( 1000 - x ) = 1046 . 0.02 x = 1050 - 1046 . 0.02 x = 4 . 2 x = 400 . x = 200 . the answer is a ." | a = 2 + 3
b = a * 2
c = 100 * b
d = 5 / 100
e = d + 1
f = c * e
g = 2 + 3
h = g * 2
i = 100 * h
j = 2 + 3
k = j * 2
l = k * 3
m = i + l
n = 2 * 3
o = m + n
p = f - o
q = 5 / 100
r = q + 1
s = 3 / 100
t = s + 1
u = r - t
v = p / u
|
a ) 122 , b ) 210 , c ) 216 , d ) 217 , e ) 225 | c | add(factorial(5), multiply(4, factorial(4))) | a 5 - digit number divisible by 3 is to be formed using numerical 0 , 1 , 2 , 3 , 4 and 5 without repetition . the total number e of ways this can be done is : | we should determine which 5 digits from given 6 , would form the 5 digit number divisible by 3 . we have six digits : 0 , 1 , 2 , 3 , 4 , 5 . their sum = 15 . for a number to be divisible by 3 the sum of the digits must be divisible by 3 . as the sum of the six given numbers is 15 ( divisible by 3 ) only 5 digits good to form our 5 digit number would be 15 - 0 = { 1 , 2 , 3 , 4 , 5 } and 15 - 3 = { 0 , 1 , 2 , 4 , 5 } . meaning that no other 5 from given six will total the number divisible by 3 . second step : we have two set of numbers : 1 , 2 , 3 , 4 , 5 and 0 , 1 , 2 , 4 , 5 . how many 5 digit numbers can be formed using these two sets : 1 , 2 , 3 , 4 , 5 - - > 5 ! as any combination of these digits would give us 5 digit number divisible by 3 . 5 ! = 120 . 0 , 1 , 2 , 4 , 5 - - > here we can not use 0 as the first digit , otherwise number wo n ' t be any more 5 digit and become 4 digit . so , desired # would be total combinations 5 ! , minus combinations with 0 as the first digit ( combination of 4 ) 4 ! - - > 5 ! - 4 ! = 4 ! ( 5 - 1 ) = 4 ! * 4 = 96 120 + 96 = 216 = e answer : c . | a = math.factorial(5)
b = math.factorial(4)
c = 4 * b
d = a + c
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a ) s . 15,550 , b ) s . 15,400 , c ) s . 16,500 , d ) s . 17,600 , e ) s . 17,900 | b | multiply(700, multiply(5.5, 4)) | the lenght of a room is 5.5 m and width is 4 m . find the cost of paving the floor by slabs at the rate of rs . 700 per sq . metre . | "area of the floor = ( 5.5 Γ£ β 4 ) m 2 = 22 m 2 . cost of paving = rs . ( 800 Γ£ β 22 ) = rs . 15400 answer : option b" | a = 5 * 5
b = 700 * a
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a ) 10 kmph , b ) 20 kmph , c ) 25 kmph , d ) 30 kmph , e ) 27 kmph | d | divide(270, divide(multiply(6, 3), 2)) | a car takes 6 hours to cover a distance of 270 km . how much should the speed in kmph be maintained to cover the same direction in 3 / 2 th of the previous time ? | "time = 6 distence = 270 3 / 2 of 6 hours = 6 * 3 / 2 = 9 hours required speed = 270 / 9 = 30 kmph d )" | a = 6 * 3
b = a / 2
c = 270 / b
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a ) $ 20 , b ) $ 30 , c ) $ 50 , d ) $ 90 , e ) $ 110 | b | divide(11, subtract(1, add(add(divide(1, 10), divide(1, 3)), divide(1, 5)))) | at a supermarket , john spent 1 / 5 of his money on fresh fruits and vegetables , 1 / 3 on meat products , and 1 / 10 on bakery products . if he spent the remaining $ 11 on candy , how much did john spend at the supermarket ? | "let ' s let t = total number of dollars spent at the supermarket . with this variable we can set up an equation and determine t . we are given that john spent 1 / 5 of his money on fresh fruits and vegetables , or ( 1 / 5 ) t , 1 / 3 on meat products , or ( 1 / 3 ) t , and 1 / 10 on bakery products , or ( 1 / 10 ) t . we are also given that he spent the remaining $ 11 on candy . since we know where all his money was allocated , we can sum these values together and set the sum to t . so we have : ( 1 / 5 ) t + ( 1 / 3 ) t + ( 1 / 10 ) t + 11 = t to get rid of the fractions we can multiply the entire equation by 30 , and we obtain : 6 t + 10 t + 3 t + 330 = 30 t 19 t + 330 = 30 t 330 = 11 t t = 30 john spent $ 90 at the supermarket . answer : b" | a = 1 / 10
b = 1 / 3
c = a + b
d = 1 / 5
e = c + d
f = 1 - e
g = 11 / f
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a ) 40 days , b ) 30 days , c ) 60 days , d ) 70 days , e ) 50 days | c | divide(multiply(12, 15), subtract(15, 12)) | a and b finish the job in 15 days . while a , b and c can finish it in 12 days . c alone will finish the job in | "explanation : 12 = ( 15 * x ) / ( 15 + x ) 180 + 12 x = 15 x 3 x = 180 x = 60 answer : option c" | a = 12 * 15
b = 15 - 12
c = a / b
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a ) 80 cm , b ) 90 cm , c ) 100 cm , d ) 120 cm , e ) 130 cm | c | divide(250, add(const_2, divide(50, const_100))) | one ball will drop from a certain height . the height it will reach after rebounding from the floor is 50 percent of the previous height . the total travel is 250 cm when it touches the floor on third time . what is the value of the original height ? | "when ball comes down , then i have indicated the distance covered in green when ball goes up , then i have indicated the distance covered in red distance travelled uptil the ball touches the floor 3 rd time : h + 0.5 h + 0.5 h + 0.5 * 0.5 h + 0.5 * 0.5 h h + 2 * 0.5 * h + 2 * 0.25 * h = h ( 1 + 2 * 0.5 + 2 * 0.25 ) = h ( 1 + 1 + 0.5 ) = 250 2.5 h = 250 h = 100 . c is the answer ." | a = 50 / 100
b = 2 + a
c = 250 / b
|
a ) 5 , b ) 7 , c ) 9 , d ) 10 , e ) 11 | a | divide(subtract(17, 8), subtract(17, 8)) | a number divided by 44 leaves remainder 17 what is the remainder when same number divided by 8 | "add 44 + 17 = 61 now 61 divided by 8 so we get 5 as reaminder answer : a" | a = 17 - 8
b = 17 - 8
c = a / b
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a ) 50 % , b ) 53 % , c ) 54 % , d ) 55 % , e ) 57 % | e | add(multiply(60, divide(75, const_100)), multiply(subtract(const_100, 60), divide(30, const_100))) | in a certain city , 60 percent of the registered voters are democrats and the rest are republicans . in a mayoral race , if 75 percent of the registered voters who are democrats and 30 percent of the registered voters who are republicans are expected to vote for candidate a , what percent of the registered voters are expected to vote for candidate a ? | "say there are total of 100 registered voters in that city . thus 60 are democrats and 40 are republicans . 60 * 0.75 = 45 democrats are expected to vote for candidate a ; 40 * 0.30 = 12 republicans are expected to vote for candidate a . thus total of 45 + 12 = 57 registered voters are expected to vote for candidate a , which is 57 % of the total number of registered voters . answer : e ." | a = 75 / 100
b = 60 * a
c = 100 - 60
d = 30 / 100
e = c * d
f = b + e
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a ) $ 1520 , b ) $ 1640 , c ) $ 1780 , d ) $ 1850 , e ) $ 1960 | a | multiply(surface_rectangular_prism(4, 5, 2), 20) | a rectangular tank needs to be coated with insulation . the tank has dimensions of 4 feet , 5 feet , and 2 feet . each square foot of insulation costs $ 20 . how much will it cost to cover the surface of the tank with insulation ? | "the total surface area is 2 ( 2 * 4 + 4 * 5 + 2 * 5 ) = 76 square feet the total cost is 76 * $ 20 = $ 1520 the answer is a ." | a = surface_rectangular_prism * (
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a ) 2.0 , b ) 2.8 , c ) 2.2 , d ) 2.5 , e ) 3.0 | c | multiply(divide(divide(multiply(divide(10, const_100), 400), 20), multiply(divide(10, const_100), 400)), const_100) | a reduction of 10 % in the price of salt enables a lady to obtain 20 kgs more for rs . 400 , find the original price per kg ? | "answer : 400 * ( 10 / 100 ) = 40 - - - 20 ? - - - 1 = > rs . 2 400 - - - 360 ? - - - 2 = > rs . 2.22 . answer : c" | a = 10 / 100
b = a * 400
c = b / 20
d = 10 / 100
e = d * 400
f = c / e
g = f * 100
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a ) s . 4528 , b ) s . 1812 , c ) s . 4527 , d ) s . 4530 , e ) s . 4521 | b | multiply(subtract(subtract(multiply(multiply(const_2, 12), add(15, 25)), multiply(6, 3)), multiply(3, multiply(4, 3))), 2) | the dimensions of a room are 25 feet * 15 feet * 12 feet . what is the cost of white washing the four walls of the room at rs . 2 per square feet if there is one door of dimensions 6 feet * 3 feet and three windows of dimensions 4 feet * 3 feet each ? | "area of the four walls = 2 h ( l + b ) since there are doors and windows , area of the walls = 2 * 12 ( 15 + 25 ) - ( 6 * 3 ) - 3 ( 4 * 3 ) = 906 sq . ft . total cost = 906 * 2 = rs . 1812 answer : b" | a = 2 * 12
b = 15 + 25
c = a * b
d = 6 * 3
e = c - d
f = 4 * 3
g = 3 * f
h = e - g
i = h * 2
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a ) 100 , b ) 200 , c ) 300 , d ) 600 , e ) 900 | d | multiply(subtract(36, 300), 300) | what is the greatest positive integer n such that 3 ^ n is a factor of 36 ^ 300 ? | "36 = 3 ^ 2 * 2 ^ 2 . 36 ^ 300 = 3 ^ 600 * 2 ^ 600 the answer is d ." | a = 36 - 300
b = a * 300
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a ) 5 square inches , b ) 10 square inches , c ) 16 square inches , d ) 25 square inches , e ) 350 square inches | c | subtract(multiply(power(12, const_2), const_3), add(add(power(8, const_2), power(12, const_2)), add(power(8, const_2), power(12, const_2)))) | huey ' s hip pizza sells two sizes of square pizzas : a small pizza that measures 8 inches on a side and costs $ 10 , and a large pizza that measures 12 inches on a side and costs $ 20 . if two friends go to huey ' s with $ 30 apiece , how many more square inches of pizza can they buy if they pool their money than if they each purchase pizza alone ? | "in the first case each can buy one pizza of $ 10 and one pizza of $ 20 . in square inches that would be ( 8 * 8 = 64 ) for the small pizza and ( 12 * 12 = 144 ) for the large pizza . in total sq inches that would be ( 64 + 144 ) * 2 = 416 sq inches . in the second case if they pool their money together they can buy 3 large pizzas . in terms of square inches that would be 3 * 144 = 432 sq inches . hence , the difference is 16 square inches more ( 432 - 416 ) . the correct answer is c" | a = 12 ** 2
b = a * 3
c = 8 ** 2
d = 12 ** 2
e = c + d
f = 8 ** 2
g = 12 ** 2
h = f + g
i = e + h
j = b - i
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a ) 87 days , b ) 14 days , c ) 55 days , d ) 44 days , e ) 22 days | b | divide(subtract(multiply(30, 40), multiply(40, 16)), 40) | 30 men can do a work in 40 days . when should 16 men leave the work so that the entire work is completed in 40 days after they leave the work ? | "total work to be done = 30 * 40 = 1200 let 16 men leave the work after ' p ' days , so that the remaining work is completed in 40 days after they leave the work . 40 p + ( 16 * 40 ) = 1200 40 p = 560 = > p = 14 days answer : b" | a = 30 * 40
b = 40 * 16
c = a - b
d = c / 40
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a ) $ 155 , b ) $ 165 , c ) $ 175 , d ) $ 185 , e ) $ 195 | c | divide(126, multiply(divide(subtract(const_100, 10), const_100), divide(subtract(const_100, 20), const_100))) | what is the normal price of an article sold at $ 126 after two successive discounts of 10 % and 20 % ? | "0.8 * 0.9 * cost price = $ 126 cost price = $ 175 the answer is c ." | a = 100 - 10
b = a / 100
c = 100 - 20
d = c / 100
e = b * d
f = 126 / e
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a ) 18 % , b ) 20 % , c ) 21 % , d ) 33 % , e ) can not be determined | d | add(divide(multiply(40, 4), 2), add(40, 5)) | two kinds of vodka are mixed in the ratio 1 : 2 and 2 : 1 and they are sold fetching the profit 40 % and 20 % respectively . if the vodkas are mixed in equal ratio and the individual profit percent on them are increased by 4 / 3 and 5 / 3 times respectively , then the mixture will fetch the profit of | answer : d . | a = 40 * 4
b = a / 2
c = 40 + 5
d = b + c
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a ) 600 , b ) 650 , c ) 700 , d ) 750 , e ) none of these | c | divide(280, divide(2, 5)) | there are 280 female managers in a certain company . find the total number of female employees in the company , if 2 / 5 of all the employees are managers and 2 / 5 of all male employees are managers . | as per question stem 2 / 5 m ( portion of men employees who are managers ) + 280 ( portion of female employees who are managers ) = 2 / 5 t ( portion of total number of employees who are managers ) , thus we get that 2 / 5 m + 280 = 2 / 5 t , or 2 / 5 ( t - m ) = 280 , from here we get that t - m = 700 , that would be total number of female employees and the answer ( c ) | a = 2 / 5
b = 280 / a
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a ) 3050 , b ) 3000 , c ) 4000 , d ) 4050 , e ) 3100 | b | subtract(add(2050, 6200), 5250) | the average monthly income of p and q is rs . 2050 . the average monthly income of q and r is rs . 5250 and the average monthly income of p and r is rs . 6200 . the monthly income of p is : | "explanation : let p , q and r represent their respective monthly incomes . then , we have : p + q = ( 2050 x 2 ) = 4100 . . . . ( i ) q + r = ( 5250 x 2 ) = 10500 . . . . ( ii ) p + r = ( 6200 x 2 ) = 12400 . . . . ( iii ) adding ( i ) , ( ii ) and ( iii ) , we get : 2 ( p + q + r ) = 27000 or p + q + r = 13500 . . . . ( iv ) subtracting ( ii ) from ( iv ) , we get p = 3000 . p ' s monthly income = rs . 3000 . answer : b" | a = 2050 + 6200
b = a - 5250
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a ) 911 , b ) 100 , c ) 101 , d ) 160 , e ) 785 | d | multiply(multiply(divide(32, 16), 10), 8) | running at the same constant rate , 16 identical machines can produce a total of 32 shirt per minute . at this rate , how many shirt could 8 such machines produce in 10 minutes ? | "let ' s take the approach that uses the answer choices to eliminate wasted time . 32 / 16 = 2 shirt per minute per machine . 8 machines = 16 per minute . 10 minutes worth = 160 shirt . looking at the answers it is clear . . . we can only choose ( d ) the correct answer is d ." | a = 32 / 16
b = a * 10
c = b * 8
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a ) 77 / 2 , b ) 1 / 7 , c ) 78 / 85 , d ) 1 / 5 , e ) 47 / 85 | d | multiply(divide(add(const_2, const_1), add(multiply(14, const_2), const_2)), const_2) | the events a and b are independent , the probability that event a occurs is greater than 0 , and the probability that event a occurs is twice the probability that event b occurs . the probability that at least one of events a and b occurs is 14 times the probability that both events a and b occur . what is the probability that event a occurs ? | "let us say probability of a occuring is a . let us say probability of b occuring is b . a = 2 b probability ( either a or b or both ) = 14 times probability ( a and b ) a * ( 1 - b ) + b * ( 1 - a ) + ab = 14 * ab substituting a = 2 b in the second equation : 2 b * ( 1 - b ) + b * ( 1 - 2 b ) + 2 b * b = 14 * 2 b * b 3 b - 2 b ^ 2 = 28 b ^ 2 3 b = 30 b ^ 2 b = 3 / 30 = 1 / 10 so , a = 2 b = 1 / 5 the correct answer is d ." | a = 2 + 1
b = 14 * 2
c = b + 2
d = a / c
e = d * 2
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a ) 6 , b ) 12 , c ) 18 , d ) 26 , e ) 28 | c | multiply(3, 6) | three numbers are in the ratio of 3 : 4 : 6 and their product is 1944 . the largest of these numbers is | "solution let the numbers be 3 x , 4 x and 6 x . then , 3 x Γ 4 x Γ 6 x = 1944 βΉ = βΊ 72 x 3 = 1944 βΉ = βΊ x 3 = 27 βΉ = βΊ x = 3 therefore , largest number = 6 x = 18 . answer c" | a = 3 * 6
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a ) 10 am , b ) 12 noon , c ) 10.30 am , d ) 12.30 am , e ) 11 am | b | add(divide(add(200, 25), add(20, 25)), 7) | two stations p and q are 200 km apart on a straight track . one train starts from p at 7 a . m . and travels towards q at 20 kmph . another train starts from q at 8 a . m . and travels towards p at a speed of 25 kmph . at what time will they meet ? | "assume both trains meet after x hours after 7 am distance covered by train starting from p in x hours = 20 x km distance covered by train starting from q in ( x - 1 ) hours = 25 ( x - 1 ) total distance = 200 = > 20 x + 25 ( x - 1 ) = 200 = > 45 x = 225 = > x = 5 means , they meet after 5 hours after 7 am , ie , they meet at 12 noon answer is b ." | a = 200 + 25
b = 20 + 25
c = a / b
d = c + 7
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a ) 10 m , b ) 15 m , c ) 20 m , d ) 25 m , e ) 12 m | a | multiply(1, 20) | walking at 1 / 3 th of its usual speed a cab is 20 mnts late . find its usual time to cover the journey ? | "new speed = 1 / 3 th of usual speed new time = 3 of usual time 3 ut - ut = 20 m 2 ut = 20 m ut = 10 m answer is a" | a = 1 * 20
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a ) 89 men , b ) 120 men , c ) 90 men , d ) 60 men , e ) 134 men | e | subtract(divide(multiply(760, subtract(22, const_2)), 17), 760) | there is food for 760 men for 22 days . how many more men should join after two days so that the same food may last for 17 days more ? | "760 - - - - 22 760 - - - - 20 x - - - - - 17 x * 17 = 760 * 20 x = 894 760 - - - - - - - 134 answer : e" | a = 22 - 2
b = 760 * a
c = b / 17
d = c - 760
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a ) 1209 , b ) 1324 , c ) 1245 , d ) 1140 , e ) 1635 | d | multiply(divide(subtract(1015, 15), subtract(9, const_1)), 9) | find large number from below question the difference of two numbers is 1015 . on dividing the larger number by the smaller , we get 9 as quotient and the 15 as remainder | "let the smaller number be x . then larger number = ( x + 1015 ) . x + 1015 = 9 x + 15 8 x = 1000 x = 125 large number = 125 + 1015 = 1140 answer : d" | a = 1015 - 15
b = 9 - 1
c = a / b
d = c * 9
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a ) $ 14,755 , b ) $ 15,205 , c ) $ 16,000 , d ) $ 16,225 , e ) $ 17,155 | b | multiply(divide(const_3, const_4), const_1000) | a store owner estimates that the average price of type a products will increase by 35 % next year and that the price of type b products will increase by 10 % next year . this year , the total amount paid for type a products was $ 4500 and the total price paid for type b products was $ 8300 . according to the store owner ' s estimate , and assuming the number of products purchased next year remains the same as that of this year , how much will be spent for both products next year ? | "cost of type a products next year = 1.35 * 4500 = 6075 cost of type b products next year = 1.1 * 8300 = 9130 total 6075 + 9130 = 15205 option b" | a = 3 / 4
b = a * 1000
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a ) 8 , b ) 3 , c ) 7 , d ) 9 , e ) 10 | a | add(divide(subtract(floor(divide(add(sqrt(add(multiply(42, const_4), const_2)), const_1), const_2)), const_1), const_2), divide(subtract(sqrt(subtract(add(multiply(42, const_4), const_2), power(floor(divide(add(sqrt(add(multiply(42, const_4), const_2)), const_1), const_2)), const_2))), const_1), const_2)) | in a classroom , the average age of boys ( b ) is g and the average age of girls ( g ) is b . the average age of all is b + g . at the time of calculation , the class teacher , who is 42 years old was also present in the class . can you find the value of b + g ? | a b + g = 8 for b in range ( 199 ) : for g in range ( 199 ) : sum 1 = 2 * b * g + 42 sum 2 = ( b + g ) * ( b + g + 1 ) if ( sum 1 = = sum 2 ) : print ( b , g , sum 1 ) ( b , g ) = ( 35 ) = > b + g = 8 | a = 42 * 4
b = a + 2
c = math.sqrt(b)
d = c + 1
e = d / 2
f = math.floor(e)
g = f - 1
h = g / 2
i = 42 * 4
j = i + 2
k = 42 * 4
l = k + 2
m = math.sqrt(l)
n = m + 1
o = n / 2
p = math.floor(o)
q = p ** 2
r = j - q
s = math.sqrt(r)
t = s - 1
u = t / 2
v = h + u
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a ) $ 32000 , b ) $ 36000 , c ) $ 42000 , d ) $ 44000 , e ) $ 45000 | c | divide(subtract(multiply(divide(17, const_100), 100000), 200), add(divide(17, const_100), divide(23, const_100))) | mr . tom invested in fund x and fund y . the total amount she invested , in both funds combined , was $ 100000 . in one year , fund x paid 23 % and fund y paid 17 % . the interest earned in fund y was exactly $ 200 greater than the interest earned in fund x . how much did ms . tom invest in fund x ? | x + y = 100000 0.17 y = 0.23 a + 200 take away decimals first : 17 y = 23 x + 20000 isolate first equation to solve for x ( your goal ) : y = 100000 - y plug in for b : 17 ( 100000 - x ) = 23 x + 20000 1 , 700000 - 17 x = 23 x + 20000 1 , 680000 = 40 x 1 , 680000 / 40 = x x = 42000 = answer choice c | a = 17 / 100
b = a * 100000
c = b - 200
d = 17 / 100
e = 23 / 100
f = d + e
g = c / f
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a ) 5 % , b ) 8 % , c ) 3 % , d ) 9 % , e ) 5.5 % | e | divide(multiply(const_100, 176), multiply(800, 4)) | what is the rate percent when the simple interest on rs . 800 amount to rs . 176 in 4 years ? | "176 = ( 180 * 4 * r ) / 100 r = 5.5 % answer : e" | a = 100 * 176
b = 800 * 4
c = a / b
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a ) a . 0.6 , b ) b . 1 , c ) c . 2.1 , d ) d . 1.8 , e ) e . 5.4 | d | subtract(6, multiply(const_2, multiply(divide(35, const_100), 6))) | a 6 litre sol is 35 % alcohol . how many litres of pure alcohol must be added to produce a sol that is 50 % alcohol ? | "35 % of 6 = 2.1 50 % of 6 = 3 shortage is 0.9 so we need to have 0.9 / 50 % to get 50 % alcohol content . = 1.8 d" | a = 35 / 100
b = a * 6
c = 2 * b
d = 6 - c
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a ) 17 , b ) 77 , c ) 66 , d ) 55 , e ) 31 | a | add(add(add(multiply(1, const_3), 1), multiply(multiply(1, const_3), add(multiply(1, const_3), 1))), 1) | sushil got thrice as many marks in english as in science . his total marks in english , science and maths are 170 . if the ratio of his marks in english and maths is 1 : 4 , find his marks in science ? | s : e = 1 : 3 e : m = 1 : 4 - - - - - - - - - - - - s : e : m = 1 : 4 : 12 1 / 17 * 170 = 17 answer : a | a = 1 * 3
b = a + 1
c = 1 * 3
d = 1 * 3
e = d + 1
f = c * e
g = b + f
h = g + 1
|
a ) 80 , b ) 63 , c ) 420 , d ) 160 , e ) 1260 | c | multiply(divide(multiply(6, subtract(6, const_1)), const_2), divide(multiply(8, subtract(8, const_1)), const_2)) | if 6 parallel lines in a plane is intersected by a family of another 8 parallel lines , how many parallelograms are there in the network thus formed ? | "parallelogram can formed by 2 horizontal and 2 vertical lines for horizontal 6 c 2 for vertical 8 c 2 total parallelogram is 6 c 2 * 8 c 2 = 15 * 28 = 420 answer : c" | a = 6 - 1
b = 6 * a
c = b / 2
d = 8 - 1
e = 8 * d
f = e / 2
g = c * f
|
a ) 7 , b ) 1 , c ) 9 , d ) 10 , e ) 11 | b | subtract(divide(100, const_2), multiply(7, 7)) | what is the remainder if 7 ^ 8 is divided by 100 ? | "7 ^ 8 can be written as ( 7 ^ 4 ) ^ 2 if we divide 7 ^ 4 by 100 the reminder is 1 so , ( 7 ^ 4 ) ^ 2 by 100 , the reminder is 1 ^ 2 = 1 answer : b" | a = 100 / 2
b = 7 * 7
c = a - b
|
a ) 100 , b ) 190 , c ) 150 , d ) 180 , e ) 199 | b | divide(multiply(multiply(divide(617.50, const_100), 20), const_100), 65) | 65 % of x = 20 % of 617.50 . find the value of x ? | "65 % of x = 20 % of 615.50 then , 65 / 100 * x = 20 / 100 * 6175 / 10 x = 190 answer is b" | a = 617 / 50
b = a * 20
c = b * 100
d = c / 65
|
a ) 11952 , b ) 11852 , c ) 11752 , d ) 11652 , e ) 11552 | a | add(subtract(multiply(const_10, multiply(const_100, const_100)), const_100), 48,64) | find the smallest number of five digits exactly divisible by 24 , 48,64 and 88 . | "smallest number of five digits is 10000 . required number must be divisible by l . c . m . of 24,48 , 64,88 i . e 2012 , on dividing 10000 by 2012 , we get 60 as remainder . therefore , required number = 10000 + ( 2012 Γ’ β¬ β 60 ) = 11952 . answer is a ." | a = 100 * 100
b = 10 * a
c = b - 100
d = c + 48
|
a ) 5 , b ) 7 , c ) 9 , d ) 11 , e ) 12 | d | add(divide(subtract(multiply(floor(divide(82, 6)), 6), multiply(add(floor(divide(12, 6)), const_1), 6)), 6), const_1) | how many numbers from 12 to 82 are exactly divisible by 6 ? | "option ' d ' 12 / 6 = 2 and 82 / 6 = 13 = = > 13 - 2 = 11 numbers" | a = 82 / 6
b = math.floor(a)
c = b * 6
d = 12 / 6
e = math.floor(d)
f = e + 1
g = f * 6
h = c - g
i = h / 6
j = i + 1
|
a ) 125 days , b ) 150 days , c ) 90 days , d ) 225 days , e ) none of these | d | inverse(divide(subtract(divide(const_1, 6), multiply(10, divide(const_1, 100))), 15)) | 10 men and 15 women finish a work in 6 days . one man alone finishes that work in 100 days . in how many days will a woman finish the work ? | 15 women ' s work of a day = 1 β 6 - 1 β 10 β 1 β 15 part β΄ for 1 whole part a woman will take = 15 Γ 15 = 225 days . answer d | a = 1 / 6
b = 1 / 100
c = 10 * b
d = a - c
e = d / 15
f = 1/(e)
|
a ) 20 , b ) 36 , c ) 48 , d ) 60 , e ) 84 | c | add(divide(multiply(subtract(100, 60), subtract(24, 6)), 30), 24) | a certain quantity is measured on two different scales , the r - scale and the s - scale , that are related linearly . measurements on the r - scale of 6 and 24 correspond to measurements on the s - scale of 30 and 60 , respectively . what measurement on the r - scale corresponds to a measurement of 100 on the s - scale ? | question says they are both related linearly so they the relationships can be represented by standard linear definition y = mx + b . let s scale = y . and r scale = x . 30 = 6 m + b eqn 1 60 = 24 m + b eqn 2 eqn 2 - eqn 1 = > 30 = 18 m = > m = 5 / 3 solving for b using either equation gives us b = 20 linear relationship is represented by y = ( 5 / 3 ) x + 20 solve for 100 : 100 = 5 / 3 x + 20 80 = 5 / 3 x x = 48 ans = c | a = 100 - 60
b = 24 - 6
c = a * b
d = c / 30
e = d + 24
|
a ) 16 , b ) 18 , c ) 20 , d ) 13 , e ) 14 | b | add(13, divide(subtract(add(11, 12), 13), const_2)) | a family x went for a vacation . unfortunately it rained for 13 days when they were there . but whenever it rained in the mornings , they had clear afternoons and vice versa . in all they enjoyed 11 mornings and 12 afternoons . how many days did they stay there totally ? | explanation : clearly 11 mornings and 12 afternoons = 23 half days = > since 13 days raining means 13 half days . = > so 23 - 13 = 10 halfdays ( not effecetd by rain ) = > so 10 halfdays = 5 fulldays hence , total no . of days = 13 + 5 = 18 days answer : b | a = 11 + 12
b = a - 13
c = b / 2
d = 13 + c
|
a ) 6.9 , b ) 69.0 , c ) 0.736 , d ) 0.6859 , e ) 0.69 | c | divide(multiply(92, add(add(multiply(multiply(add(const_3, const_2), const_2), multiply(multiply(const_3, const_4), const_100)), multiply(multiply(add(const_3, const_4), add(const_3, const_2)), multiply(add(const_3, const_2), const_2))), add(const_3, const_3))), const_100) | what is 92 % of 4 / 5 ? | "92 % * ( 4 / 5 ) = 0.92 * 0.8 = 0.736 answer : c" | a = 3 + 2
b = a * 2
c = 3 * 4
d = c * 100
e = b * d
f = 3 + 4
g = 3 + 2
h = f * g
i = 3 + 2
j = i * 2
k = h * j
l = e + k
m = 3 + 3
n = l + m
o = 92 * n
p = o / 100
|
a ) 13000 , b ) 7000 , c ) 10000 , d ) 2800 , e ) none of these | d | subtract(subtract(multiply(multiply(5, const_1000), const_100), add(multiply(75000, const_2), 75000)), subtract(subtract(multiply(divide(subtract(125, 1), 125), multiply(multiply(5, const_1000), const_100)), multiply(multiply(75000, const_2), divide(subtract(125, 1), 125))), 75000)) | a textile manufacturing firm employees 125 looms . it makes fabrics for a branded company . the aggregate sales value of the output of the 125 looms is rs 5 , 00,000 and the monthly manufacturing expenses is rs 1 , 50,000 . assume that each loom contributes equally to the sales and manufacturing expenses are evenly spread over the number of looms . monthly establishment charges are rs 75000 . if one loom breaks down and remains idle for one month , the decrease in profit is : | "explanation : profit = 5 , 00,000 Γ’ Λ β ( 1 , 50,000 + 75,000 ) = rs . 2 , 75,000 . since , such loom contributes equally to sales and manufacturing expenses . but the monthly charges are fixed at rs 75,000 . if one loan breaks down sales and expenses will decrease . new profit : - = > 500000 Γ£ β ( 124 / 125 ) Γ’ Λ β 150000 Γ£ β ( 124 / 125 ) Γ’ Λ β 75000 . = > rs 2 , 72,200 . decrease in profit = > 2 , 75,000 Γ’ Λ β 2 , 72,200 = > rs . 2,800 . answer : d" | a = 5 * 1000
b = a * 100
c = 75000 * 2
d = c + 75000
e = b - d
f = 125 - 1
g = f / 125
h = 5 * 1000
i = h * 100
j = g * i
k = 75000 * 2
l = 125 - 1
m = l / 125
n = k * m
o = j - n
p = o - 75000
q = e - p
|
a ) 20 % , b ) 45 % , c ) 33.33 % , d ) 18 % , e ) none of these | b | multiply(divide(subtract(multiply(add(add(add(20, 25), const_10), add(divide(25, const_2), const_3)), 18), multiply(20, 18)), multiply(20, 18)), const_100) | a milk man has 20 liters of milk . if he mixes 25 liters of water , which is freely available , in 20 liters of pure milk . if the cost of pure milk is rs . 18 per liter , then the profit of the milkman , when he sells all the mixture at cost price is : | "explanation : when the water is freely available and all the water is sold at the price of the milk , then the water gives the profit on the cost of 20 liters of milk . therefore , profit percentage = 45 % . answer : b" | a = 20 + 25
b = a + 10
c = 25 / 2
d = c + 3
e = b + d
f = e * 18
g = 20 * 18
h = f - g
i = 20 * 18
j = h / i
k = j * 100
|
a ) 350 m , b ) 200 m , c ) 400 m , d ) 500 m , e ) none of them | c | divide(multiply(100, 8), subtract(10, 8)) | a thief is spotted by a policeman from a distance of 100 meters . when the policeman starts the chase , the thief also starts running . if the speed of the thief be 8 km / hr and that of the policeman 10 km / hr , how far the thief will have run before he is overtaken ? | "relative speed of the policeman = ( 10 - 8 ) km / hr = 2 km / hr . time taken by police man to cover ( 100 m / 1000 ) x 1 / 2 hr = 1 / 20 hr . in 1 / 20 hrs , the thief covers a distance of 8 x 1 / 20 km = 2 / 5 km = 400 m answer is c ." | a = 100 * 8
b = 10 - 8
c = a / b
|
a ) 29 % , b ) 41 % , c ) 58 % , d ) 69 % , e ) 70 % | c | multiply(divide(add(multiply(75, 175), multiply(60, 220)), add(add(multiply(75, 175), multiply(60, 220)), multiply(150, 125))), const_100) | a major airplane manufacturer announced the sale of 150 small airliners at $ 125 million each , 75 medium sized airliners at $ 175 million each , and 60 large airliners at $ 220 million each . what percentage of the company ' s income came from large and medium airliners ? | answer is ( money from mid and large plane ) / ( total money from all the planes ) x 100 = ( 175 β 75 + 220 β 60 ) / ( 125 β 150 + 175 β 75 + 220 β 60 ) β 100 ( 175 β 75 + 220 β 60 ) / ( 125 β 150 + 175 β 75 + 220 β 60 ) β 100 = 58.4 % you could just multiply add divide to get answer . however sometimes its much better to make it easy we should see if we have any common terms 125 * 150 = ( 5 * 5 * 5 ) * ( 2 * 3 * 5 * 5 ) 175 * 75 = ( 5 * 5 * 7 ) * ( 3 * 5 * 5 ) 220 * 60 = ( 2 * 2 * 11 * 5 ) * ( 2 * 2 * 3 * 5 ) 3 * 5 * 5 is common cancel it ans becomes ( 175 + 176 ) / ( 176 + 175 + 250 ) * 100 = ~ = ~ 350 / 600 * 100 = ~ = ~ 7 / 12 * 100 = 60 % > > > 58 % is closest . answer : c | a = 75 * 175
b = 60 * 220
c = a + b
d = 75 * 175
e = 60 * 220
f = d + e
g = 150 * 125
h = f + g
i = c / h
j = i * 100
|
a ) 25 % , b ) ( 8 ) 20 % , c ) 30 % , d ) 50 % , e ) 65 % | a | subtract(add(add(75, 30), 20), const_100) | if 75 percent of a class answered the first question on a certain test correctly , 30 percent answered the second question on the test correctly , and 20 percent answered neither of the questions correctly , what percent answered both correctly ? | "i did n ' t understand how to connect 20 percent with the whole equation . why 20 is out of the percentile diagram ( circles ) but inside of 100 ? 20 % appeared in the exam ; however did not answer question aquestion b correctly so they are out of the two circles , however as they have appeared in the exam , they have to be taken into consideration for calculation purpose i am doing it this way : suppose the total class size is 100 , then 20 percent of the class answered incorrectly and rest 80 percent answered correctly in question 1 or 2 or both . now , 100 - [ ( 75 - x ) + x + ( 30 - x ) ] = 20 . . . . . . . . . . values are in percent x = 20 - 100 + 105 x = 25 ans : a" | a = 75 + 30
b = a + 20
c = b - 100
|
a ) 0.0039 , b ) 0.0625 , c ) 0.16 , d ) 0.25 , e ) 0.5 | a | power(divide(1, 4), 4) | what is the decimal equivalent of ( 1 / 4 ) ^ 4 ? | "( 1 / 4 ) ^ 4 = 1 / 256 = 0.0039 answer : a" | a = 1 / 4
b = a ** 4
|
a ) 2 / 10 , b ) 5 / 10 , c ) 10 / 5 , d ) 7 / 6 , e ) 6 / 7 | b | divide(5, const_10) | ( ( a + b ) / c ) / 2 in the expression above , a , b , and c are different numbers and each is one of the numbers 2 , 3 , or 5 . what is the least possible value of the expression ? | ( ( a + b ) / c ) / 2 = ( a + b ) / 2 c the expression will have the least value when numerator ( a + b ) is the smallest . = ( 2 + 3 ) / 2 * 5 = 5 / 10 answer b | a = 5 / 10
|
a ) 95000 , b ) 97500 , c ) 100000 , d ) 105000 , e ) 102500 | c | multiply(divide(const_100, 85), 85000) | 85 % of the population of a city is 85000 . the total population of the city is ? | "x * ( 85 / 100 ) = 85000 x = 1000 * 100 x = 100000 answer : c" | a = 100 / 85
b = a * 85000
|
a ) 33 , b ) 28 , c ) 27 , d ) 24 , e ) 25 | e | divide(add(24, 26), const_2) | if the median of a list of numbers is m , the first quartile of the list is the median of the numbers in the list that are less than m . what is the first quartile of the list of numbers 42 , 24 , 30 , 22 , 26 , 27 , 33 and 35 ? | it is given that a quartile is the middle number of all numbers less than median . . so lets arrange the number in ascending order - 42 , 24 , 30 , 22 , 26 , 27 , 33 and 35 22 , 24 , 26 , 27 , 30 , 33 , 35 , 42 , . . . numbers less than median are 22 , 24 , 26 , 27 . . the median of these numbers = center of 24 and 26 = 25 e | a = 24 + 26
b = a / 2
|
['a ) 3 p / 2', 'b ) 3 p ^ 2 / 4', 'c ) 3 p', 'd ) 3 p ^ 2', 'e ) 4 p / 3'] | a | multiply(divide(sqrt(9), sqrt(64)), const_4) | what is the perimeter of a square with area 9 p ^ 2 / 64 ? | area of square , ( side ) ^ 2 = ( 3 p / 8 ) ^ 2 therefore side of the square = 3 p / 8 perimeter of square = 4 * side = 4 * ( 3 p / 8 ) = 3 p / 2 answer is a . | a = math.sqrt(9)
b = math.sqrt(64)
c = a / b
d = c * 4
|
a ) 7 , b ) 9 , c ) 8 , d ) 5 , e ) 4 | a | subtract(subtract(subtract(power(25, const_2), multiply(144, const_2)), multiply(144, const_2)), subtract(subtract(subtract(subtract(power(25, const_2), multiply(144, const_2)), multiply(144, const_2)), const_4), const_3)) | 14 . the sum and the product of two numbers are 25 and 144 respectively , the difference of the number is ? | x + y = 25 xy = 144 ( x - y ) 2 = ( x + y ) 2 Γ’ β¬ β 4 xy ( x - y ) 2 = 625 Γ’ β¬ β 576 = > ( x Γ’ β¬ β y ) = 7 answer : a | a = 25 ** 2
b = 144 * 2
c = a - b
d = 144 * 2
e = c - d
f = 25 ** 2
g = 144 * 2
h = f - g
i = 144 * 2
j = h - i
k = j - 4
l = k - 3
m = e - l
|
a ) 87501 , b ) 87599 , c ) 87529 , d ) 87520 , e ) 87521 | c | multiply(subtract(subtract(add(90510, 7819), 9011), 1789), divide(const_60, const_2)) | ( x ) + 1789 + 9011 - 7819 = 90510 . calculate the value of x | "x + 1789 + 9011 - 7819 = 90510 = x + 1789 + 9011 = 90510 + 7819 = x + 10800 = 98329 = x = 98329 - 10800 = 87529 answer is c" | a = 90510 + 7819
b = a - 9011
c = b - 1789
d = const_60 / 2
e = c * d
|
a ) 2225 , b ) 2325 , c ) 2425 , d ) 2625 , e ) 2525 | d | multiply(subtract(12, 7), divide(2500, subtract(7, 3))) | an amount of money is to be divided between p , q and r in the ratio of 3 : 7 : 12 . if the difference between the shares of p and q is rs . 2500 , what will be the difference between q and r ' s share ? | "4 - - - 2100 5 - - - ? = > 2625 answer : d" | a = 12 - 7
b = 7 - 3
c = 2500 / b
d = a * c
|
a ) 114 , b ) 115 , c ) 116 , d ) 117 , e ) 118 | a | divide(15, 0.132) | a certain industrial loom weaves 0.132 meters of cloth every second . approximately how many seconds will it take for the loom to weave 15 meters of cloth ? | "let the required number of seconds be x more cloth , more time , ( direct proportion ) hence we can write as ( cloth ) 0.132 : 15 : : 1 : x = > 0.132 * x = 15 = > x = 15 / 0.132 = > x = 114 answer : a" | a = 15 / 0
|
a ) 1 , b ) - 4 , c ) 4 , d ) - 5 , e ) 5 | d | multiply(4, 4) | if x is a number such that x ^ 2 + 4 x - 5 = 0 and x ^ 2 + x - 20 = 0 , then x = | x ^ 2 + 4 x - 5 = ( x + 5 ) ( x - 1 ) = 0 then x = - 5 or x = 1 . x ^ 2 + x - 20 = ( x - 4 ) ( x + 5 ) = 0 then x = 4 or x = - 5 . thus x = - 5 . the answer is d . | a = 4 * 4
|
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