options stringlengths 37 300 | correct stringclasses 5
values | annotated_formula stringlengths 7 727 | problem stringlengths 5 967 | rationale stringlengths 1 2.74k | program stringlengths 10 646 |
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a ) 120 , b ) 150 , c ) 160 , d ) 180 , e ) 200 | c | divide(subtract(multiply(240, 60), multiply(52, 240)), subtract(52, 40)) | how many liters of oil at rs . 40 per liter should be mixed with 240 liters of a second variety of oil at rs . 60 per liter so as to get a mixture whose cost is rs . 52 per liter ? | 8 : 12 = 2 : 3 if 240 lrs of the 2 nd variety taken then the 1 st variety should be taken as 160 lr answer c | a = 240 * 60
b = 52 * 240
c = a - b
d = 52 - 40
e = c / d
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a ) 2 , b ) 4 , c ) 5 , d ) 3 , e ) 7 | d | add(divide(divide(2, 1), divide(3, 3)), const_1) | if w / x = 1 / 3 and w / y = 2 / 3 , then ( x + y ) / y = | "ratio 1 : 3 w = x ratio 2 : 3 w = 2 y x = 2 y ( x + y ) / y = ( 2 y + y ) / y = y ( 2 + 1 ) / y = 3 answer is d" | a = 2 / 1
b = 3 / 3
c = a / b
d = c + 1
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a ) 3 : 1 , b ) 3 : 2 , c ) 3 : 8 , d ) 2 : 5 , e ) 3 : 4 | d | divide(subtract(25, 20), subtract(20, 18)) | two trains running in opposite directions cross a man standing on the platform in 25 seconds and 18 seconds respectively and they cross each other in 20 seconds . the ratio of their speeds is : | "let the speeds of the two trains be x m / sec and y m / sec respectively . then , length of the first train = 25 x meters , and length of the second train = 18 y meters . ( 25 x + 18 y ) / ( x + y ) = 20 = = > 25 x + 18 y = 20 x + 20 y = = > 5 x = 2 y = = > x / y = 2 / 5 answer : option d" | a = 25 - 20
b = 20 - 18
c = a / b
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a ) 900 , b ) 648 , c ) 720 , d ) 252 , e ) 729 | d | divide(divide(1000, 100), 7) | in how many no . between 100 and 1000 at least one of their digits is 7 ? | "let ' s count the number of occurrences with only one 7 : ( 1 ) 7 xx : 1 * 9 * 9 = 81 ( 2 ) x 7 x : 8 * 1 * 9 = 72 ( 3 ) xx 7 : 8 * 9 * 1 = 72 81 + 72 + 72 = 225 at this point we can already see that the answer must be d since the choice are very dispersed . anyways , let ' s count number of occurrences with two 7 s :... | a = 1000 / 100
b = a / 7
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a ) 15 % , b ) 20 % , c ) 40 % , d ) 50 % , e ) 150 % | b | multiply(divide(subtract(const_100, multiply(divide(subtract(const_100, 25), subtract(const_100, 10)), const_100)), multiply(divide(subtract(const_100, 25), subtract(const_100, 10)), const_100)), const_100) | the charge for a single room at hotel p is 25 percent less than the charge for a single room at hotel r and 10 percent less than the charge for a single room at hotel g . the charge for a single room at hotel r is what percent greater than the charge for a single room at hotel g ? | "let rate in r = 100 x then p = 75 x g = 100 y p = 90 y thus 75 x = 90 y or x = 1.20 y ans r = 120 y so increase = 20 % answer : b ." | a = 100 - 25
b = 100 - 10
c = a / b
d = c * 100
e = 100 - d
f = 100 - 25
g = 100 - 10
h = f / g
i = h * 100
j = e / i
k = j * 100
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a ) 15 % , b ) 25 % , c ) 12.5 % , d ) 20.83 % , e ) none | d | divide(multiply(multiply(divide(500, 4000), const_100), const_100), 60) | farm tax is levied on the 60 % of the cultivated land . the tax department collected total $ 4000 through the farm tax from the village of mr . willam . mr . willam paid only $ 500 as farm tax . the percentage of total land of mr . willam over the total taxable land of the village is : | "only trick n this question is to ignore 60 % information as farm tax is levied uniformly in the village and that includes mr william ' s land . what percentage of tax mr william paid ? this will be equal to the percentage of total cultivated land he holds over the total cultivated land in the village . that leads to (... | a = 500 / 4000
b = a * 100
c = b * 100
d = c / 60
|
a ) 2197 , b ) 1267 , c ) 3500 , d ) 2267 , e ) 1262 | c | divide(divide(subtract(multiply(4000, power(add(const_1, divide(10, const_100)), 2)), 4000), 2), multiply(2, divide(6, const_100))) | the s . i . on a certain sum of money for 2 years at 6 % per annum is half the c . i . on rs . 4000 for 2 years at 10 % per annum . the sum placed on s . i . is ? | "explanation : c . i . = [ 4000 * ( 1 + 10 / 100 ) 2 - 4000 ] = ( 4000 * 11 / 10 * 11 / 10 - 4000 ) = rs . 840 . sum = ( 420 * 100 ) / ( 2 * 6 ) = rs . 3500 answer : c" | a = 10 / 100
b = 1 + a
c = b ** 2
d = 4000 * c
e = d - 4000
f = e / 2
g = 6 / 100
h = 2 * g
i = f / h
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a ) 56 , b ) 65 , c ) 75 , d ) 89 , e ) 87 | e | subtract(multiply(65, const_4), subtract(multiply(64, const_4), add(3, subtract(multiply(65, const_4), multiply(60, 3))))) | the avg weight of a , b & c is 60 kg . if d joins the group , the avg weight of the group becomes 65 kg . if another man e who weights is 3 kg more than d replaces a , then the avgof b , c , d & e becomes 64 kg . what is the weight of a ? | "a + b + c = 3 * 60 = 180 a + b + c + d = 4 * 65 = 260 - - - - ( i ) so , d = 80 & e = 80 + 3 = 83 b + c + d + e = 64 * 4 = 256 - - - ( ii ) from eq . ( i ) & ( ii ) a - e = 260 – 256 = 4 a = e + 4 = 83 + 4 = 87 answer : e" | a = 65 * 4
b = 64 * 4
c = 65 * 4
d = 60 * 3
e = c - d
f = 3 + e
g = b - f
h = a - g
|
a ) 1.91 , b ) 2.91 , c ) 4.91 , d ) 3.91 , e ) 5.91 | b | multiply(const_12, divide(multiply(40, divide(40, const_100)), 66)) | a reduction of 40 % in the price of bananas would enable a man to obtain 66 more for rs . 40 , what is reduced price per dozen ? | "40 * ( 40 / 100 ) = 16 - - - 66 ? - - - 12 = > rs . 2.91 answer : b" | a = 40 / 100
b = 40 * a
c = b / 66
d = 12 * c
|
a ) 38 kmph , b ) 33 kmph , c ) 34 kmph , d ) 35 kmph , e ) 36 kmph | a | divide(add(100, 50), add(divide(100, 30), divide(50, 80))) | a car travels uphill at 30 km / hr and downhill at 80 km / hr . it goes 100 km uphill and 50 km downhill . find the average speed of the car ? | "avg speed = total distance / total time . total distance traveled = 100 + 50 = 150 km ; time taken for uphill journey = 100 / 30 = 10 / 3 ; time taken for down hill journey = 50 / 80 = 5 / 8 ; avg speed = 150 / ( 10 / 3 + 5 / 8 ) = 38 kmph answer : a" | a = 100 + 50
b = 100 / 30
c = 50 / 80
d = b + c
e = a / d
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a ) 3.5 kmph . , b ) 2.5 kmph . , c ) 1.2 kmph . , d ) 1.1 kmph . , e ) 1.9 kmph . | d | multiply(const_3_6, divide(8, 26)) | convert the 8 / 26 m / s into kilometers per hour ? | "8 / 26 m / s = 8 / 26 * 18 / 5 = 1 ( 1 / 10 ) = 1.1 kmph . answer : d" | a = 8 / 26
b = const_3_6 * a
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a ) 30 , b ) 45 , c ) 55 , d ) 65 , e ) 70 | a | add(add(choose(7, const_1), choose(7, const_1)), choose(const_4, const_1)) | jane and thomas are among the 7 people from which a committee of 4 people is to be selected . how many different possible committees of 4 people can be selected from these 7 people if at least one of either jane or thomas is to be selected ? | "the total number of ways to choose 4 people from 7 is 7 c 4 = 35 . the number of committees without jane or thomas is 5 c 4 = 5 . there are 35 - 5 = 30 possible committees which include jane and / or thomas . the answer is a ." | a = math.comb(7, 1)
b = math.comb(7, 1)
c = a + b
d = math.comb(4, 1)
e = c + d
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a ) 1 / 8 , b ) 1 / 16 , c ) 1 / 48 , d ) 1 / 96 , e ) 1 / 168 | c | multiply(multiply(divide(1, 7), divide(1, 8)), subtract(1, divide(1, 6))) | jack , jill , and sandy each have one try to make a basket from half court . if their individual probabilities of making the basket are 1 / 6 , 1 / 7 , and 1 / 8 respectively , what is the probability that jack and jill will make a basket but sandy will miss ? | "the probability that jack and jill will make a basket but sandy will miss is 1 / 6 * 1 / 7 * 7 / 8 = 1 / 48 . the answer is c ." | a = 1 / 7
b = 1 / 8
c = a * b
d = 1 / 6
e = 1 - d
f = c * e
|
a ) 38 % , b ) 46 % , c ) 47.68 % , d ) 44.32 % , e ) 36.32 % | e | subtract(42, divide(42, 4)) | you hold some gold in a vault as an investment . over the past year the price of gold increases by 42 % . in order to keep your gold in the vault , you must pay 4 % of the total value of the gold per year . what percentage has the value of your holdings changed by over the past year . | "( 100 % + 42 % ) * ( 100 % - 4 % ) = 1.42 * 0.96 = 136.32 % an increase of 36.32 % your gold holdings have increased in value by 36.32 % . the answer is e" | a = 42 / 4
b = 42 - a
|
a ) 440 , b ) 420 , c ) 410 , d ) 442 , e ) 422 | a | multiply(const_3, multiply(8, multiply(2, 5))) | calculate how many seconds it eill take for 4 bells to toll together again , given that they begin to toll together respectively at the intervals of 2 , 5 , 8 and 11 seconds . ? | "lcm of 2 , 5 , 8 and 11 is 440 lcm = 440 answer : a" | a = 2 * 5
b = 8 * a
c = 3 * b
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a ) 22 , b ) 8 , c ) 10 , d ) 99 , e ) 38 | b | divide(subtract(divide(50, divide(5, 1)), multiply(subtract(5, const_1), 1)), 1) | the sum of the ages of 5 children born at the intervals of 1 year each is 50 years . what is the age of the youngest child ? | "let x = the youngest child . each of the other four children will then be x + 1 , x + 2 , x + 3 , x + 4 . we know that the sum of their ages is 50 . so , x + ( x + 1 ) + ( x + 2 ) + ( x + 3 ) + ( x + 4 ) = 50 therefore the youngest child is 8 years old answer : b" | a = 5 / 1
b = 50 / a
c = 5 - 1
d = c * 1
e = b - d
f = e / 1
|
a ) a . 5 , b ) b . 8 , c ) c . 10 , d ) d . 12 , e ) e . 16 | a | subtract(divide(multiply(15, 36), multiply(divide(const_3, const_4), 36)), 15) | if 15 machine can finish a job in 36 days , then how many more machines would be needed to finish the job in one - fourth less time ? | "you might think of this in a management context - we can use the principle of ' person - hours ' to solve any problem where we have identical workers . so , using simpler numbers , suppose you know that 6 identical employees , working simultaneously , would finish a job in 5 hours . then that job requires 6 * 5 = 30 t... | a = 15 * 36
b = 3 / 4
c = b * 36
d = a / c
e = d - 15
|
a ) 0.2 , b ) 0.3 , c ) 0.4 , d ) 0.5 , e ) 0.6 | c | divide(const_4, const_10) | if a randomly selected non - negative single digit integer is added to { 2 , 3 , 6 , 8 } . what is the probability that the median of the set will increase but the range still remains the same ? | "we are selecting from non - negative single digit integers , so from { 0 , 1 , 2 , 3 , 4 , 5 , 6 , 7 , 8 , 9 } . these 10 digits represent the total number of outcomes . hence , the total number of outcomes is 10 . we need to find the probability that the median of the set will increase but the range still remains the... | a = 4 / 10
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a ) 2.5 , b ) 4.7 , c ) 2.9 , d ) 2.3 , e ) 2.1 | b | divide(140, multiply(108, const_0_2778)) | in what time will a train 140 m long cross an electric pole , it its speed be 108 km / hr ? | "speed = 108 * 5 / 18 = 30 m / sec time taken = 140 / 30 = 4.7 sec . answer : b" | a = 108 * const_0_2778
b = 140 / a
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a ) 3 / 7 , b ) 2 / 7 , c ) 1 / 4 , d ) 2 / 3 , e ) 5 / 7 | b | inverse(add(inverse(2), 3)) | a small water pump would take 2 hours to fill an empty tank . a larger pump would take 1 / 3 hour to fill the same tank . how many hours would it take both pumps , working at their respective constant rates , to fill the empty tank if they began pumping at the same time ? | "rate of the small pump is 1 / 2 tank / hour rate of the larger pump is 1 / ( 1 / 3 ) or 3 tank / hour ; combined rate of the two pumps is 1 / 2 + 3 = 7 / 2 tank / hour , together they will fill the empty tank in 1 / ( 7 / 2 ) = 2 / 7 hours ( time = job / rate ) . answer : b" | a = 1/(2)
b = a + 3
c = 1/(b)
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a ) 31 % , b ) 34 % , c ) 35 % , d ) 36 % , e ) 37 % | a | multiply(add(multiply(divide(45, const_100), divide(20, const_100)), multiply(divide(subtract(const_100, 45), const_100), divide(40, const_100))), const_100) | in a certain company 20 % of the men and 40 % of the women attended the annual company picnic . if 45 % of all the employees are men . what % of all the employee went to the picnic ? | "total men in company 45 % means total women in company 55 % ( assume total people in company 100 % ) no of men employees attended picnic = 45 x ( 20 / 100 ) = 9 no of women employees attend picnic = 55 x ( 40 / 100 ) = 22 total percentage of employees attend the picnic = 9 + 22 = 31 % answer : a" | a = 45 / 100
b = 20 / 100
c = a * b
d = 100 - 45
e = d / 100
f = 40 / 100
g = e * f
h = c + g
i = h * 100
|
a ) 6 , b ) 7 , c ) 8 , d ) 9 , e ) 10 | b | multiply(2, divide(negate(multiply(add(add(5, 4), 2), 7)), subtract(multiply(add(add(5, 4), 2), const_2), multiply(add(add(5, 4), 2), 4)))) | the ratio by weight , measured in pounds , of books to clothes to electronics in a suitcase initially stands at 5 : 4 : 2 . someone removes 7 pounds of clothing from the suitcase , thereby doubling the ratio of books to clothes . how many pounds do the electronics in the suitcase weigh ? | "the weights of the items in the suitcase are 5 k , 4 k , and 2 k . if removing 7 pounds of clothes doubles the ratio of books to clothes , then 7 pounds represents half the weight of the clothes . 2 k = 7 pounds and then k = 3.5 pounds . the electronics weigh 2 ( 3.5 ) = 7 pounds . the answer is b ." | a = 5 + 4
b = a + 2
c = b * 7
d = negate / (
e = 5 + 4
f = e + 2
g = f * 2
h = 5 + 4
i = h + 2
j = i * 4
k = g - j
l = 2 * d
|
a ) 3 , b ) 4 , c ) 5 , d ) 6 , e ) 7 | e | subtract(multiply(10, 2.00), multiply(1.60, 10)) | martin bought 10 concert tickets , some at the full price of $ 2.00 per ticket , and some at a discounted price of $ 1.60 per ticket . if he spent a total of $ 17.20 , how many discounted tickets did he buy ? | "let x be the number of tickets he bought at $ 2 per ticket . then 2 x + ( 10 - x ) 1.6 = 17.2 0.4 x = 1.2 = > x = 3 discounted tickets = 10 - x = 7 ans : e" | a = 10 * 2
b = 1 * 60
c = a - b
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a ) - 4 , b ) - 1 / 4 , c ) 0 , d ) 1 / 4 , e ) 4 | c | divide(const_1, 4) | if 625 ^ ( - x ) + 25 ^ ( - 2 x ) + 5 ^ ( - 4 x ) = 10 , what is the value of x ? | "we ' re told that 625 ^ ( - x ) + 25 ^ ( - 2 x ) + 5 ^ ( - 4 x ) = 15 . we ' re asked for the value of x . since each of the calculated terms must be positive ( regardless of what the exponent is ) , we can use thebasesto our advantage . . . . . with answer a , we ' d have 625 ^ 4 , which is much bigger than 15 ( and ... | a = 1 / 4
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a ) 2 , b ) 8 , c ) 12 , d ) 21 , e ) 35 | c | add(subtract(multiply(2, 3), 3), power(3, 2)) | if a # b = ab – b + b ^ 2 , then 2 # 3 = | "solution - simply substitute 2 and 3 in equation in the place of a and b respectively . 2 # 3 = 2 * 3 - 3 + 3 ^ 2 = 6 - 3 + 9 = 12 . ans c" | a = 2 * 3
b = a - 3
c = 3 ** 2
d = b + c
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a ) 56 , b ) 52 , c ) 51 , d ) 50 , e ) 49 | a | add(subtract(125, 70), const_1) | andy solves problems 70 to 125 inclusive in a math exercise . how many problems does he solve ? | 125 - 70 + 1 = 56 ' a ' is the answer | a = 125 - 70
b = a + 1
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a ) 900 , b ) 980 , c ) 1200 , d ) 1240 , e ) 1400 | e | subtract(divide(4200, 2), divide(4200, 6)) | share rs . 4200 among john , jose & binoy in the ration 2 : 4 : 6 . find the amount received by john ? | "amount received by sanjay . 4 / 12 x 4200 = 1400 = ( related ratio / sum of ratio ) x total amount so , the amount received by sanjay is 1400 . e" | a = 4200 / 2
b = 4200 / 6
c = a - b
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a ) 0 , b ) 1 , c ) 42 , d ) 118 , e ) 242 | b | subtract(power(7, subtract(const_1, const_1)), power(subtract(const_1, const_1), 7)) | if k is a non - negative integer and 21 ^ k is a divisor of 435,961 then 7 ^ k - k ^ 7 = | "4 + 3 + 5 + 9 + 6 + 1 = 28 , so this number is not divisible by 3 and thus not divisible by 21 . therefore , k = 0 7 ^ k - k ^ 7 = 1 - 0 = 1 the answer is b ." | a = 1 - 1
b = 7 ** a
c = 1 - 1
d = c ** 7
e = b - d
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a ) 16 , b ) 36 , c ) 20 , d ) 24 , e ) 30 | b | multiply(4, divide(60, add(4, 6))) | maxwell leaves his home and walks toward brad ' s house at the same time that brad leaves his home and runs toward maxwell ' s house . if the distance between their homes is 60 kilometers , maxwell ' s walking speed is 4 km / h , and brad ' s running speed is 6 km / h , what is the distance traveled by brad ? | "time taken = total distance / relative speed total distance = 60 kms relative speed ( opposite side ) ( as they are moving towards each other speed would be added ) = 6 + 4 = 10 kms / hr time taken = 60 / 10 = 6 hrs distance traveled by brad = brad ' s speed * time taken = 6 * 6 = 36 kms . . . answer - b" | a = 4 + 6
b = 60 / a
c = 4 * b
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a ) 29 , b ) 40 , c ) 25 , d ) 66 , e ) 09 | a | divide(divide(add(90, 200), const_1000), divide(36, const_3600)) | a train 90 meters long completely crosses a 200 meters long bridge in 36 seconds . what is the speed of the train is ? | "s = ( 90 + 200 ) / 36 = 290 / 36 * 18 / 5 = 29 answer : a" | a = 90 + 200
b = a / 1000
c = 36 / 3600
d = b / c
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['a ) 11 / 36', 'b ) 23 / 10', 'c ) 5 / 14', 'd ) 22 / 11', 'e ) 3 / 4'] | a | divide(subtract(circle_area(divide(12, const_2)), circle_area(divide(10, const_2))), circle_area(divide(12, const_2))) | a circular plate with a diameter of 10 inches is kept on another plate of 12 inches diameter . what fraction of the big plate ' s surface is not covered by the small plate ? | the questions asks us to find the surface which is not covered by the plate i . e . , area of the surface not covered . where as circumference is the length along the edge of the circle , 2 * pi * r implies the length of the curve pi * r ^ 2 implies area enclosed by that curve . . hence area of the circle is considered... | a = 12 / 2
b = circle_area - (
c = 10 / 2
d = b / circle_area
|
a ) 60 , b ) 70 , c ) b = 75 , d ) b = 80 , e ) 100 | c | divide(multiply(divide(multiply(10, 20), const_0_25), subtract(const_1, const_0_25)), subtract(10, 2)) | a contractor undertakes to do a job within 100 days and hires 10 people to do it . after 20 days , he realizes that one fourth of the work is done so he fires 2 people . in how many more days b will the work get over ? | "we can also use the concept of man - days here 100 days - - > 10 men so the job includes 100 * 10 = 1000 man - days after 20 days 1 / 4 of job is completed so 1 / 4 x 1000 man - days = 250 man - days job is done now the balance job = 1000 - 250 = 750 man - days worth of job since 2 men are fired so b / l men = 8 there... | a = 10 * 20
b = a / const_0_25
c = 1 - const_0_25
d = b * c
e = 10 - 2
f = d / e
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a ) 238 , b ) 278 , c ) 300 , d ) 166 , e ) 129 | c | multiply(divide(subtract(const_100, 25), 25), const_100) | if the cost price is 25 % of selling price . then what is the profit percent | "explanation : let the s . p = 100 then c . p . = 25 profit = 75 profit % = ( 75 / 25 ) * 100 = 300 % answer : c" | a = 100 - 25
b = a / 25
c = b * 100
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a ) 1.5 kmph , b ) 1.75 kmph , c ) 2 kmph , d ) 3 kmph , e ) none | a | divide(subtract(divide(32, 6), divide(14, 6)), const_2) | a man rows downstream 32 km and 14 km upstream . if he takes 6 hours to cover each distance , then the velocity ( in kmph ) of the current is : | sol . rate downstream = [ 32 / 6 ] kmph ; rate upstream = [ 14 / 6 ] kmph . ∴ velocity of current = 1 / 2 [ 32 / 6 - 14 / 6 ] kmph = 3 / 2 kmph = 1.5 kmph . answer a | a = 32 / 6
b = 14 / 6
c = a - b
d = c / 2
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a ) 85 , b ) 86.5 , c ) 90 , d ) 88.5 , e ) 110 | e | add(multiply(10, 4), 70) | the average weight of 10 person ' s increases by 4 kg when a new person comes in place of one of them weighing 70 kg . what is the weight of the new person ? | "total increase in weight = 10 x 4 = 40 if x is the weight of the new person , total increase in weight = x − 70 = > 40 = x - 70 = > x = 40 + 70 = 110 answer : e" | a = 10 * 4
b = a + 70
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a ) 5 kg , b ) 15 kg , c ) 25 kg , d ) 30 kg , e ) none | c | divide(const_100, divide(subtract(const_100, 20), 20)) | the price of rice falls by 20 % . how much rice can be bought now with the money that was sufficient to buy 20 kg of rice previously ? | "solution : let rs . 100 be spend on rice initially for 20 kg . as the price falls by 20 % , new price for 20 kg rice , = ( 100 - 20 % of 100 ) = 80 new price of rice = 80 / 20 = rs . 4 per kg . rice can bought now at = 100 / 4 = 25 kg . answer : option c" | a = 100 - 20
b = a / 20
c = 100 / b
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a ) 2 mph , b ) 2.5 mph , c ) 3 mph , d ) 4 mph , e ) none | a | divide(subtract(sqrt(add(multiply(power(10, const_2), const_4), power(multiply(divide(36, divide(90, const_60)), const_2), const_2))), multiply(divide(36, divide(90, const_60)), const_2)), const_2) | a boat takes 90 minutes less to travel 36 miles downstream than to travel the same distance upstream . if the speed of the boat in still water is 10 mph , the speed of the stream is | "solution speed downstreams = ( 10 + x ) mph . speed upstreams = ( 10 - x ) mph . = 18 kmph . 36 / ( 10 - x ) - 36 / ( 10 + x ) = 90 / 60 = 72 x × 60 = 90 ( 100 - x ² ) x ² + 48 x + 100 = 0 . x = 2 mph . answer a" | a = 10 ** 2
b = a * 4
c = 90 / const_60
d = 36 / c
e = d * 2
f = e ** 2
g = b + f
h = math.sqrt(g)
i = 90 / const_60
j = 36 / i
k = j * 2
l = h - k
m = l / 2
|
a ) 124 , b ) 129 , c ) 128 , d ) 125 , e ) 120 | b | add(power(2, 2), power(11, 2)) | if 2 + 3 = 10 ; 2 + 5 = 27 ; 2 + 7 = 53 then 2 + 11 = ? | "2 ^ 0 + 3 ^ 2 = 1 + 9 = 10 2 ^ 1 + 5 ^ 2 = 2 + 25 = 27 2 ^ 2 + 7 ^ 2 = 4 + 49 = 53 and 2 ^ 3 + 11 ^ 2 = 8 + 121 = 129 answer : b" | a = 2 ** 2
b = 11 ** 2
c = a + b
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a ) 9 : 4 , b ) 8 : 4 , c ) 7 : 4 , d ) 7 : 3 , e ) 6 : 4 | d | divide(7, 3) | if the sides of a cube are in the ratio 7 : 3 . what is the ratio of their diagonals ? | "explanation : diagonal of a cube = a √ 3 where a is side a 1 : a 2 = 7 : 3 d 1 : d 2 = 7 : 3 where √ 3 cancelled both side answer : d" | a = 7 / 3
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a ) 17 , 18 , b ) 7 , 8 , c ) 15 , 16 , d ) 1 , 2 , e ) 8 , 9 | c | add(add(power(add(add(divide(subtract(subtract(31, const_10), const_2), const_4), const_2), const_2), const_2), power(add(add(add(divide(subtract(subtract(31, const_10), const_2), const_4), const_2), const_2), const_2), const_2)), add(power(divide(subtract(subtract(31, const_10), const_2), const_4), const_2), power(add... | the sum of two consecutive integers is 31 . find the numbers . | "n + ( n + 1 ) = 31 2 n + 1 = 31 2 n = 30 n = 15 answer : c" | a = 31 - 10
b = a - 2
c = b / 4
d = c + 2
e = d + 2
f = e ** 2
g = 31 - 10
h = g - 2
i = h / 4
j = i + 2
k = j + 2
l = k + 2
m = l ** 2
n = f + m
o = 31 - 10
p = o - 2
q = p / 4
r = q ** 2
s = 31 - 10
t = s - 2
u = t / 4
v = u + 2
w = v ** 2
x = r + w
y = n + x
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a ) 25 , b ) 27 , c ) 29 , d ) 31 , e ) 32 | b | add(divide(multiply(4, 24), 4), const_3) | the average of 4 consecutive odd numbers is 24 . find the largest number | explanation : let the numbers are x , x + 2 , x + 4 , x + 6 , then = > x + ( x + 2 ) + ( x + 4 ) + ( x + 6 ) / 4 = 24 = > 4 x + 12 ) / 4 = 24 = > x + 3 = 24 = > x = 21 so largest number is 21 + 6 = 27 option b | a = 4 * 24
b = a / 4
c = b + 3
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a ) 141 , b ) 180 , c ) 130 , d ) 122 , e ) 280 | e | lcm(lcm(multiply(const_2, const_4), add(const_3, const_4)), 20) | what is the smallest integer that is multiple of 8,7 and 20 | correct answer : e it is the lcm of 8,7 and 20 which is 280 | a = 2 * 4
b = 3 + 4
c = math.lcm(a, b)
d = math.lcm(c, 20)
|
a ) 20 kmph , b ) 17 kmph , c ) 15 kmph , d ) 14 kmph , e ) 13 kmph | a | divide(subtract(multiply(40, const_3), divide(multiply(multiply(40, const_3), const_2), const_3)), subtract(const_3, const_1)) | by travelling at 40 kmph , a person reaches his destination on time . he covered two - third the total distance in one - third of the total time . what speed should he maintain for the remaining distance to reach his destination on time ? | "let the time taken to reach the destination be 3 x hours . total distance = 40 * 3 x = 120 x km he covered 2 / 3 * 120 x = 80 x km in 1 / 3 * 3 x = x hours so , the remaining 40 x km , he has to cover in 2 x hours . required speed = 40 x / 2 x = 20 kmph . answer : a" | a = 40 * 3
b = 40 * 3
c = b * 2
d = c / 3
e = a - d
f = 3 - 1
g = e / f
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a ) 100 , b ) 120 , c ) 200 , d ) 226 , e ) 286 | e | add(260, divide(multiply(260, 10), const_100)) | the present population of a town is 260 . population increase rate is 10 % p . a . find the population of town after 1 years ? | "p = 260 r = 10 % required population of town = p * ( 1 + r / 100 ) ^ t = 260 * ( 1 + 10 / 100 ) = 260 * ( 11 / 10 ) = 286 answer is e" | a = 260 * 10
b = a / 100
c = 260 + b
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a ) 55 , b ) 67 , c ) 77 , d ) 87 , e ) 97 | a | sqrt(multiply(3025, const_100)) | a group of students decided to collect as many paise from each member of group as is the number of members . if the total collection amounts to rs . 3025 . , the number of the member is the group is : | "money collected = ( 30.25 x 100 ) paise = 3025 paise . number of members = square root of 3025 = 55 . answer : option a" | a = 3025 * 100
b = math.sqrt(a)
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a ) 1600 , b ) 1800 , c ) 1900 , d ) 2000 , e ) 2500 | b | divide(subtract(2108, 200), add(const_1, divide(6, const_100))) | in 1996 , the property tax of a community is increased by 6 % over the 1995 tax . an additional surcharge of $ 200 is also added for a special project . if the petersons ' 1996 tax totals $ 2108 , find their property tax for the year 1995 | tax for the year 1996 = 2108 surcharge add : 200 ie 2000 - 200 = 1800 1800 * 6 % = 108 + 2000 = 2108 so the answer is b | a = 2108 - 200
b = 6 / 100
c = 1 + b
d = a / c
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a ) 10 % , b ) 25 % , c ) 30 % , d ) 35 % , e ) 40 % | e | multiply(divide(subtract(divide(64, const_100), multiply(divide(76, const_100), divide(2, const_3))), divide(1, const_3)), const_100) | in an election , candidate douglas won 64 percent of the total vote in counties x and y . he won 76 percent of the vote in county x . if the ratio of people who voted in county x to county y is 2 : 1 , what percent of the vote did candidate douglas win in county y ? | "given voters in ratio 2 : 1 let x has 200 votersy has 100 voters for x 76 % voted means 76 * 200 = 152 votes combined for xy has 300 voters and voted 64 % so total votes = 192 balance votes = 192 - 152 = 40 as y has 100 voters so 40 votes means 40 % of votes required ans e" | a = 64 / 100
b = 76 / 100
c = 2 / 3
d = b * c
e = a - d
f = 1 / 3
g = e / f
h = g * 100
|
a ) 287 , b ) 288 , c ) 500 , d ) 400 , e ) 121 | d | multiply(multiply(subtract(divide(900, multiply(subtract(63, 3), const_0_2778)), const_1), const_10), const_2) | how many seconds will a 900 meter long train take to cross a man walking with a speed of 3 km / hr in the direction of the moving train if the speed of the train is 63 km / hr ? | "let length of tunnel is x meter distance = 900 + x meter time = 1 minute = 60 seconds speed = 78 km / hr = 78 * 5 / 18 m / s = 65 / 3 m / s distance = speed * time 900 + x = ( 65 / 3 ) * 60 900 + x = 20 * 65 = 1300 x = 1300 - 900 = 400 meters answer : d" | a = 63 - 3
b = a * const_0_2778
c = 900 / b
d = c - 1
e = d * 10
f = e * 2
|
a ) 8 , b ) 6 , c ) 10 , d ) 4 , e ) 3 | c | max(4, const_10) | 16 * 16 * 16 * 16 * 16 = 4 ^ ? | 4 ^ 2 * 4 ^ 2 * 4 ^ 2 * 4 ^ 2 * 4 ^ 2 = 4 ^ ( 2 + 2 + 2 + 2 + 2 ) = 4 ^ 10 answer : 10 option : c | a = max(4)
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a ) 9 % , b ) 10 % , c ) 11 % , d ) 12 % , e ) 15 % | d | multiply(subtract(divide(22, const_100), divide(subtract(8.82, multiply(divide(22, const_100), multiply(18, 2))), subtract(multiply(15, 3), multiply(18, 2)))), const_100) | fox jeans regularly sell for $ 15 a pair and pony jeans regularly sell for $ 18 a pair . during a sale these regular unit prices are discounted at different rates so that a total of $ 8.82 is saved by purchasing 5 pairs of jeans : 3 pairs of fox jeans and 2 pairs of pony jeans . if the sum of the two discount rates is ... | "let x be the discount on pony jeans . then 0.22 - x is the discount on fox jeans . 3 ( 0.22 - x ) ( 15 ) + 2 x ( 18 ) = 8.82 9.9 - 45 x + 36 x = 8.82 9 x = 1.08 x = 0.12 the answer is d ." | a = 22 / 100
b = 22 / 100
c = 18 * 2
d = b * c
e = 8 - 82
f = 15 * 3
g = 18 * 2
h = f - g
i = e / h
j = a - i
k = j * 100
|
a ) 17 , b ) 24 , c ) 21 , d ) 23 , e ) 25 | b | subtract(25, const_1) | when average age of 25 members are 0 , how many members greater than 0 ? | "average of 25 numbers = 0 . sum of 25 numbers ( 0 x 25 ) = 0 . it is quite possible that 24 of these numbers may be positive and if their sum is a then 25 th number is ( - a ) answer is 24 ( b )" | a = 25 - 1
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a ) 8 , b ) 16 , c ) 18 , d ) 25 , e ) 10 | a | divide(10, add(const_1, divide(25, const_100))) | sakshi can do a piece of work in 10 days . tanya is 25 % more efficient than sakshi . the number of days taken by tanya to do the same piece of work : | "solution ratio of times taken by sakshi and tanya = 125 : 100 = 5 : 4 . suppose tanya taken x days to do the work . 5 : 4 : : 10 : x ⇒ x = ( 10 x 4 / 5 ) ⇒ x = 8 days . hence , tanya takes 8 days is complete the work . answer a" | a = 25 / 100
b = 1 + a
c = 10 / b
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a ) 228 , b ) 744 , c ) 255 , d ) 650 , e ) 231 | d | divide(multiply(divide(300, divide(subtract(65, subtract(const_100, 65)), const_100)), 65), const_100) | there were two candidates in an election . winner candidate received 65 % of votes and won the election by 300 votes . find the number of votes casted to the winning candidate ? | "w = 65 % l = 35 % 65 % - 35 % = 30 % 30 % - - - - - - - - 300 65 % - - - - - - - - ? = > 650 answer : d" | a = 100 - 65
b = 65 - a
c = b / 100
d = 300 / c
e = d * 65
f = e / 100
|
a ) 72 , b ) 60 , c ) 90 , d ) 120 , e ) 240 | a | divide(6.00, subtract(divide(1.00, 4), divide(0.50, 3))) | a grocer purchased a quantity of bananas at 3 pounds for $ 0.50 and sold the entire quantity at 4 pounds for $ 1.00 . how many pounds did the grocer purchase if the profit from selling the bananas was $ 6.00 ? | "cost price of 1 pound of bananas = 0.5 / 3 = 1 / 6 selling price of 1 pound of bananas = 1 / 4 profit per pound = ( 1 / 4 - 1 / 6 ) = ( 1 / 12 ) total profit is given as 6 ( 1 / 12 ) * x = 6 x = 72 answer : a" | a = 1 / 0
b = 0 / 50
c = a - b
d = 6 / 0
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a ) 50 , b ) 54 , c ) 56 , d ) 60 , e ) 60.5 | e | add(divide(const_100, const_2), 1) | in a recent election , geoff received 1 percent of the 6,000 votes cast . to win the election , a candidate needed to receive more than x % of the vote . if geoff needed exactly 3,571 more votes to win the election , what is the value of x ? | "word problems are tricky in somehow more than other problem because you have the additional step to translate . breaking the problem : geoff how many votes he receives ? ? 60 votes he needs 3571 more votes so : 60 + 3571 = 3631 now what ' s the problem wants ? ? a x % . . . . . . . . 3631 is what % of total votes 6000... | a = 100 / 2
b = a + 1
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a ) − 0.3 , b ) 0 , c ) 0.4 , d ) 1.08 , e ) 2.46 | c | subtract(multiply(divide(divide(subtract(power(3, 2), power(1.8, 0.4)), const_1000), const_1000), 3), divide(divide(subtract(power(3, 2), power(1.8, 0.4)), const_1000), const_1000)) | what is the value of 3 x ^ 2 − 1.8 x + 0.4 for x = 0.6 ? | "3 x ^ 2 - 1.8 x + 0.4 for x = 0.6 = 3 ( 0.6 * 0.6 ) - 3 * 0.6 * ( 0.6 ) + 0.4 = 0 + 0.4 = 0.4 answer : c" | 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
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a ) 2984 , b ) 2983 , c ) 2982 , d ) 2450 , e ) none of these | d | subtract(2500, divide(1002, 20.04)) | 2500 - ( 1002 / 20.04 ) = ? | "2500 - 50 = 2450 answer : d" | a = 1002 / 20
b = 2500 - a
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a ) 1 / 10 , b ) 2 / 10 , c ) 3 / 10 , d ) 4 / 10 , e ) 5 / 10 | a | divide(const_2, choose(add(const_3, const_3), const_3)) | what is the probability of getting equilateral triangles from the vertices of regular hexagon ? | total no . of triangles that can b made with the vetices hexagon = 6 c 3 = 20 no . of possible outcomes i . e . no . of equality triangles = 2 . . ' . probability = 2 / 20 = 1 / 10 answer : a | a = 3 + 3
b = math.comb(a, 3)
c = 2 / b
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a ) a ) 165 , b ) b ) 220 , c ) c ) 310 , d ) d ) 185 , e ) e ) 181 | e | subtract(multiply(7, divide(divide(multiply(15000, 11.5), const_100), multiply(const_3, const_10))), multiply(divide(divide(multiply(10000, 9.5), const_100), multiply(const_3, const_10)), 7)) | solomon taken a loan rs . 15000 / - from co - operative society with an interest @ 11.5 % per month . at the same time he deposited rs . 10000 / - as fixed deposit with an interest @ 9.5 % per month . after one week sam asked the manager to calculate the interest to be paid . what is the interest amount for 7 days ? | loan amount : rs . 15000 / - @ 11.5 % interest per month = 15000 / - * 11.5 % = rs . 1725 interest for one day = 1725 / 30 = 57.50 interest for 7 days is = 57.50 * 7 = 403 fd amount is = rs . 10000 / - @ 9.5 % interest per month = 10000 * 9.5 % = 950 / - interest for 7 days = 950 / 30 * 7 = 222 interest amount to be pa... | a = 15000 * 11
b = a / 100
c = 3 * 10
d = b / c
e = 7 * d
f = 10000 * 9
g = f / 100
h = 3 * 10
i = g / h
j = i * 7
k = e - j
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a ) 5,050 , b ) 7,500 , c ) 10,500 , d ) 15,000 , e ) 19,600 | b | multiply(divide(add(200, 101), const_2), add(divide(subtract(200, 101), const_2), const_1)) | the sum of the first 50 positive even integers is 2,550 . what is the sum of the odd integers from 101 to 200 , inclusive ? | "101 + 103 + . . . . . . . 199 if we remove 100 from each of these it will be sum of 1 st 100 odd numbers . so 101 + 103 + . . . . . . . 199 = 50 * 100 + ( 1 + 3 + 5 + 7 + . . . . . . ) sum of 1 st 100 natural numbers = ( 100 * 101 ) / 2 = 5050 sum of 1 st 50 positive even integers = 2550 sum of 1 st 100 odd numbers = ... | a = 200 + 101
b = a / 2
c = 200 - 101
d = c / 2
e = d + 1
f = b * e
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a ) $ 30 , b ) $ 54 , c ) $ 28.50 , d ) $ 12 , e ) $ 11.75 | e | multiply(2.35, 5) | johnny makes $ 2.35 per hour at his work . if he works 5 hours , how much money will he earn ? | 2.35 * 5 = 11.75 . answer is e . | a = 2 * 35
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a ) 10 hours , b ) 20 hours , c ) 30 hours , d ) 40 hours , e ) 50 hours | c | inverse(subtract(inverse(10), inverse(15))) | a and b together can plough a field in 10 hours but by himself a requires 15 hours . how long would b take to plough the same field ? | if a and b together can do a piece of work in x days and a alone can do the same work in y days , then b alone can do the same work in x y / y – x days . therefore , the no . of hours required by b = 10 × 15 / 15 – 10 = 150 / 5 = 30 hours . answer : c | a = 1/(10)
b = 1/(15)
c = a - b
d = 1/(c)
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a ) 38 . , b ) 40 . , c ) 36 . , d ) 44 . , e ) 46 . | c | subtract(multiply(sqrt(divide(576, 4)), 4), sqrt(divide(576, 4))) | the roof of an apartment building is rectangular and its length is 4 times longer than its width . if the area of the roof is 576 feet squared , what is the difference between the length and the width of the roof ? | "let the width = x x * 4 x = 576 x ^ 2 = 144 x = 12 length = 4 * 12 = 48 difference = 48 - 12 = 36 c is the answer" | a = 576 / 4
b = math.sqrt(a)
c = b * 4
d = 576 / 4
e = math.sqrt(d)
f = c - e
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a ) 120 , b ) 121 , c ) 122 , d ) 123 , e ) 124 | a | multiply(add(7, 3), 12) | if two girls starting from same point , walking in the opposite directions with 7 km / hr and 3 km / hr as average speeds respectively . then the distance between them after 12 hours is ? | explanation : total distance = distance traveled by person a + distance traveled by person b = ( 7 ã — 12 ) + ( 3 ã — 12 ) = 84 + 36 = 120 km answer : a | a = 7 + 3
b = a * 12
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a ) 2 / 5 , b ) 7 / 18 , c ) 1 / 4 , d ) 1 / 9 , e ) 2 / 6 | b | multiply(7, add(divide(const_1, 30), divide(const_1, 45))) | two persons a and b can complete a piece of work in 30 days and 45 days respectively . if they work together , what part of the work will be completed in 7 days ? | "a ' s one day ' s work = 1 / 30 b ' s one day ' s work = 1 / 45 ( a + b ) ' s one day ' s work = 1 / 30 + 1 / 45 = 1 / 18 the part of the work completed in 7 days = 7 ( 1 / 18 ) = 7 / 18 . answer b" | a = 1 / 30
b = 1 / 45
c = a + b
d = 7 * c
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a ) 7 / 2 , b ) 5 , c ) 20 / 3 , d ) 8 , e ) 300 / 17 | e | divide(100, add(const_4, const_3)) | how many liters of pure alcohol must be added to a 100 - liter solution that is 20 percent alcohol in order to produce a solution that is 32 percent alcohol ? | "20 % alcohol solution means ; in the 100 liter solution , 20 liters of solution is alcohol and 80 liters other solvents . if we addxliters of alcohol to the solution , the solution becomes 100 + xliters and alcohol , which was 20 liters , becomes 20 + x liters . according to the statement ; 20 + x = 32 % of ( 100 + x ... | a = 4 + 3
b = 100 / a
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a ) 30 , b ) 36 , c ) 34 , d ) 32 , e ) none of these | d | divide(multiply(10, multiply(24, 8)), multiply(10, 6)) | 24 men working 8 hours a day can finish a work in 10 days . working at the rate of 10 hours a day , the number of men required to finish the same work in 6 days is | m 1 × d 1 × t 1 × w 2 = m 2 × d 2 × t 2 × w 1 24 × 10 × 8 × 1 = m 2 × 6 × 10 × 1 ⇒ m 2 = 24 × 10 × 8 / 6 × 10 = 32 men answer d | a = 24 * 8
b = 10 * a
c = 10 * 6
d = b / c
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a ) 59 , b ) 49 , c ) 58 , d ) 113 , e ) 131 | b | subtract(subtract(const_100, multiply(subtract(8, 3,4), const_10)), const_1) | n and m are each 3 - digit integers . each of the numbers 3,4 , 5 , 6 , 7 , and 8 is a digit of either n or m . what is the smallest possible positive difference between n and m ? | "you have 6 digits : 3 , 4 , 5 , 6 , 7 , 8 each digit needs to be used to make two 3 digit numbers . this means that we will use each of the digits only once and in only one of the numbers . the numbers need to be as close to each other as possible . the numbers can not be equal so the greater number needs to be as sma... | a = 8 - 3
b = a * 10
c = 100 - b
d = c - 1
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a ) 88 , b ) 27 , c ) 36 , d ) 31 , e ) 12 | d | divide(add(190, 120), multiply(subtract(45, 9), divide(divide(const_10, const_2), divide(subtract(45, 9), const_2)))) | a jogger running at 9 km / hr along side a railway track is 190 m ahead of the engine of a 120 m long train running at 45 km / hr in the same direction . in how much time will the train pass the jogger ? | "speed of train relative to jogger = 45 - 9 = 36 km / hr . = 36 * 5 / 18 = 10 m / sec . distance to be covered = 190 + 120 = 310 m . time taken = 310 / 10 = 31 sec . answer : d" | a = 190 + 120
b = 45 - 9
c = 10 / 2
d = 45 - 9
e = d / 2
f = c / e
g = b * f
h = a / g
|
a ) rs . 13.44 , b ) rs . 12 , c ) rs . 12.25 , d ) rs . 12.31 , e ) none | a | divide(multiply(11, add(const_100, 10)), subtract(const_100, 10)) | a fruit seller sells mangoes at the rate of rs . 11 per kg and thereby loses 10 % . at what price per kg , he should have sold them to make a profit of 10 % ? | "solution 90 : 11 = 110 : x x = ( 11 ã — 110 / 90 ) = rs . 13.44 hence , s . p per kg = rs . 13.44 answer a" | a = 100 + 10
b = 11 * a
c = 100 - 10
d = b / c
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a ) 50 , b ) 200 , c ) 380 , d ) 598 , e ) 400 | d | multiply(inverse(10), multiply(multiply(const_100, 10), add(const_4, const_4))) | when 1 / 20 % of 6,000 is subtracted from 1 / 10 of 6,000 , the difference is | "1 / 20 % of 6000 = 3 1 / 10 of 6000 = 600 600 - 3 = 598 ans : d" | a = 1/(10)
b = 100 * 10
c = 4 + 4
d = b * c
e = a * d
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a ) 8 , b ) 10 , c ) 15 , d ) 7 , e ) 4 | e | subtract(30, divide(add(multiply(7.50, 30), 620), add(7.50, 25))) | a contractor is engaged for 30 days on the condition thathe receives rs . 25 for each day he works & is fined rs . 7.50 for each day is absent . he gets rs . 620 in all . for how many days was he absent ? | "30 * 25 = 750 620 - - - - - - - - - - - 130 25 + 7.50 = 32.5 130 / 32.5 = 4 e" | a = 7 * 50
b = a + 620
c = 7 + 50
d = b / c
e = 30 - d
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a ) 3 % , b ) 46 1 / 6 % , c ) 25 % , d ) 33 1 / 3 % , e ) 60 % | b | subtract(const_100, divide(multiply(subtract(15.0, 13.0), const_100), subtract(18.8, 15.6))) | in 1982 and 1983 , company b ’ s operating expenses were $ 13.0 million and $ 15.0 million , respectively , and its revenues were $ 15.6 million and $ 18.8 million , respectively . what was the percent increase in company b ’ s profit ( revenues minus operating expenses ) from 1982 to 1983 ? | "profit in 1982 = 15.6 - 13 = 2.6 million $ profit in 1983 = 18.8 - 15 = 3.8 million $ percentage increase in profit = ( 3.8 - 2.6 ) / 2.6 * 100 % = 46 1 / 6 % answer b" | a = 15 - 0
b = a * 100
c = 18 - 8
d = b / c
e = 100 - d
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a ) rs . 1800 , b ) rs . 1450 , c ) rs . 1360 , d ) rs . 6800 , e ) none | c | divide(multiply(85, 80), subtract(85, 80)) | the simple interest and the true discount on a certain sum for a given time and at a given rate are rs . 85 and rs . 80 respectively . the sum is : | "solution sum = s . i xt . d / ( s . i ) - ( t . d ) = 85 x 80 / 85 - 80 = rs . 1360 . answer c" | a = 85 * 80
b = 85 - 80
c = a / b
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a ) 69.55 $ , b ) 50.63 $ , c ) 60.95 $ , d ) 52.15 $ , e ) 53.15 $ | c | divide(75, add(divide(add(7, 15), const_100), const_1)) | a business executive and his client are charging their dinner tab on the executive ' s expense account . the company will only allow them to spend a total of 75 $ for the meal . assuming that they will pay 7 % in sales tax for the meal and leave a 15 % tip , what is the most their food can cost ? | "let x is the cost of the food 1.07 x is the gross bill after including sales tax 1.15 * 1.07 x = 75 x = 60.95 hence , the correct option is c" | a = 7 + 15
b = a / 100
c = b + 1
d = 75 / c
|
a ) 5 : 4 , b ) 7 : 4 , c ) 5 : 2 , d ) 5 : 3 , e ) 7 : 5 | c | divide(add(multiply(4, 5), 5), add(5, 5)) | the age of father 5 years ago was 4 times the age of his son . 5 years hence , father ' s age will be twice that of his son . the ratio of their present ages is : | let the ages of father and son 5 years ago be 4 x and x years respectively . then , ( 4 x + 5 ) + 5 = 2 [ ( x + 5 ) + 5 ] 4 x + 10 = 2 x + 20 x = 5 . required ratio = ( 4 x + 5 ) : ( x + 5 ) = 25 : 10 = 5 : 2 . answer : option c | a = 4 * 5
b = a + 5
c = 5 + 5
d = b / c
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a ) a ) 188 , b ) b ) 65 , c ) c ) 58 , d ) d ) 62 , e ) e ) 48 | a | subtract(add(multiply(6, 58), multiply(6, 65)), multiply(11, 50)) | the average of 11 numbers is 50 . out of 11 numbers the average of first 6 no . is 58 , and last 6 numbers is 65 then find 6 th number ? | "6 th number = sum of 1 st 6 no . s + sum of last 6 no . s - sum of 11 no . s answer = 6 * 58 + 6 * 65 - 11 * 50 = 188 answer is a" | a = 6 * 58
b = 6 * 65
c = a + b
d = 11 * 50
e = c - d
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a ) 23 % , b ) 17 % , c ) 11 % , d ) 10 % , e ) 15 % | d | subtract(const_100, add(add(add(subtract(const_100, 70), subtract(const_100, 75)), subtract(const_100, 80)), subtract(const_100, 80))) | in a urban village of india named ` ` owlna ' ' , 70 % people have refrigerator , 75 % people have television , 80 % people got computers and 80 % got air - conditionor . how many people ( minimum ) got all these luxury . | "d 10 % 100 - [ ( 100 - 85 ) + ( 100 - 80 ) + ( 100 - 75 ) + ( 100 - 70 ) ] = 100 - ( 15 + 20 + 25 + 30 ) = 100 - 90" | a = 100 - 70
b = 100 - 75
c = a + b
d = 100 - 80
e = c + d
f = 100 - 80
g = e + f
h = 100 - g
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a ) 4300 , b ) 4500 , c ) 5120 , d ) 5230 , e ) 12800 | e | subtract(subtract(20000, multiply(20000, divide(20, const_100))), multiply(subtract(20000, multiply(20000, divide(20, const_100))), divide(20, const_100))) | the population of a town is 20000 . it decreases annually at the rate of 20 % p . a . what will be its population after 2 years ? | "20000 × 80 / 100 × 80 / 100 = 12800 answer : e" | a = 20 / 100
b = 20000 * a
c = 20000 - b
d = 20 / 100
e = 20000 * d
f = 20000 - e
g = 20 / 100
h = f * g
i = c - h
|
a ) 12 cm , b ) 16 cm , c ) 18 cm , d ) 20 cm , e ) none of the these | a | add(add(6, 8), 6) | two spherical balls lie on the ground touching . if one of the balls has a radius of 6 cm , and the point of contact is 8 cm above the ground , what is the radius of the other ball ? | "similar triangle properties . . 2 / r + 6 = 6 / r - 6 giving r = 12 . answer : a" | a = 6 + 8
b = a + 6
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a ) 10000 , b ) 25460 , c ) 26709 , d ) 14000 , e ) 14400 | b | multiply(15540, power(add(const_1, divide(28, const_100)), 2)) | the population of a village is 15540 . it increases annually at the rate of 28 % p . a . what will be its population after 2 years ? | "formula : ( after = 100 denominator ago = 100 numerator ) 15540 × 128 / 100 × 128 / 100 = 25460 b" | a = 28 / 100
b = 1 + a
c = b ** 2
d = 15540 * c
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a ) 8 and 9 , b ) 8 and 24 , c ) 17 and 21 , d ) 12 and 29 , e ) 17 and 9 | e | add(multiply(subtract(add(subtract(24, 4), sqrt(subtract(power(subtract(24, 4), const_2), multiply(4, multiply(24, 4))))), 7), const_10), subtract(subtract(subtract(24, 4), sqrt(subtract(power(subtract(24, 4), const_2), multiply(4, multiply(24, 4))))), 7)) | if x / 4 + 24 / x = 5 , what are the values of 2 x - 7 ? | i got the same thing e is the answer 9 or 17 | a = 24 - 4
b = 24 - 4
c = b ** 2
d = 24 * 4
e = 4 * d
f = c - e
g = math.sqrt(f)
h = a + g
i = h - 7
j = i * 10
k = 24 - 4
l = 24 - 4
m = l ** 2
n = 24 * 4
o = 4 * n
p = m - o
q = math.sqrt(p)
r = k - q
s = r - 7
t = j + s
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a ) 45 cm , b ) 25 cm , c ) 4 cm , d ) 5 cm , e ) 50 cm | d | floor(divide(add(multiply(12, const_100), 15), add(multiply(10, const_100), 15))) | which greatest possible length can be used to measure exactly 12 meter 15 cm , 10 meter 15 cm and 10 meter 65 cm | "explanation : convert first all terms into cm . i . e . 1215 cm , 1015 cm , 1065 cm . now whenever we need to calculate this type of question , we need to find the hcf . hcf of above terms is 5 . option d" | a = 12 * 100
b = a + 15
c = 10 * 100
d = c + 15
e = b / d
f = math.floor(e)
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a ) 10 % , b ) 15 % , c ) 20 % , d ) 25 % , e ) 30 % | a | multiply(divide(10, const_100), const_100) | the sum of money will be double itself in 10 years and simple interest find rate of interest ? | t = 10 years p = principle amount = x a = total amount = 2 x si = simple interest = a - p = 2 x - x = x r = 100 si / pt = 100 x / 10 x = 10 % answer is a | a = 10 / 100
b = a * 100
|
a ) 14 , b ) 15 , c ) 18 , d ) 22 , e ) 33 | d | divide(40, divide(divide(40, const_2), 11)) | a runner runs the 40 miles from marathon to athens at a constant speed . halfway through the run she injures her foot , and continues to run at half her previous speed . if the second half takes her 11 hours longer than the first half , how many hours did it take the runner to run the second half ? | "the runner runs the first 20 miles at speed v and the second 20 miles at speed v / 2 . the time t 2 to run the second half must be twice the time t 1 to run the first half . t 2 = 2 * t 1 = t 1 + 11 t 1 = 11 and so t 2 = 22 . the answer is d ." | a = 40 / 2
b = a / 11
c = 40 / b
|
a ) 16 km , b ) 10 km , c ) 12 km , d ) 24 km , e ) 36 km | e | multiply(3, 6) | a man performs 1 / 2 of the total journey by rail , 1 / 3 by bus and the remaining 6 km on foot . his total journey is | "explanation : let the journey be x km then , 1 x / 2 + 1 x / 3 + 6 = x 5 x + 36 = 6 x x = 36 km answer : option e" | a = 3 * 6
|
a ) 28.9 % , b ) 22 % , c ) 28 % , d ) 45 % , e ) 32 % | a | multiply(divide(subtract(4500, 3200), 4500), const_100) | the cost price of a radio is rs . 4500 and it was sold for rs . 3200 , find the loss % ? | "4500 - - - - 1300 100 - - - - ? = > 28.9 % answer : a" | a = 4500 - 3200
b = a / 4500
c = b * 100
|
a ) 22 , b ) 26 , c ) 27 , d ) 29 , e ) 30 | a | sqrt(divide(121, add(power(5, 2), add(power(4, 2), power(2, 2))))) | the ratio of three numbers is 4 : 2 : 5 and their sum is 121 . the second number of the three numbers is ? | "4 : 2 : 5 total parts = 11 11 parts - - > 121 1 part - - - - > 11 the second number of the three numbers is = 2 * 11 = 22 answer : a" | a = 5 ** 2
b = 4 ** 2
c = 2 ** 2
d = b + c
e = a + d
f = 121 / e
g = math.sqrt(f)
|
a ) 9801 , b ) 10,000 , c ) 14,400 , d ) 12,696 , e ) can not be determined | a | power(add(divide(197, const_2), add(const_0_25, const_0_25)), const_2) | a gardener grows cabbages in her garden that is in the shape of a square . each cabbage takes 1 square feet of area in her garden . this year , she has increased her output by 197 cabbages as compared to last year . the shape of the area used for growing the cabbages has remained a square in both these years . how many... | "let the side for growing cabbages this year be x ft . thus the area is x ^ 2 . let the side for growing cabbages last year be y ft . thus , the area was y ^ 2 . the area would have increased by 197 sq ft as each cabbage takes 1 sq ft space . x ^ 2 - y ^ 2 = 197 ( x + y ) ( x - y ) = 197 197 is a prime number and thus ... | a = 197 / 2
b = const_0_25 + const_0_25
c = a + b
d = c ** 2
|
a ) $ 180,000 , b ) $ 202,000 , c ) $ 220,000 , d ) $ 300,000 , e ) $ 2 , 200,000 | d | add(200000, divide(200, divide(0.2, const_100))) | a special municipal payroll tax charges not tax on a payroll less than $ 200000 and only 0.2 % on a company ’ s payroll above $ 200000 . if belfried industries paid $ 200 in this special municipal payroll tax , then they must have had a payroll of ? | answer : d , ( with different approach ) : the 200 paid is 0.2 % of the additional amount above 200,000 . let it be x now 0.2 % of x = 200 therefore x = 100,000 total = 200,000 + x = 300,000 | a = 0 / 2
b = 200 / a
c = 200000 + b
|
a ) 107 , b ) 331 , c ) 511 , d ) 691 , e ) 871 | a | multiply(20, divide(subtract(add(multiply(15, 2), 2), 7), subtract(20, 15))) | when positive integer n is divided by positive integer p , the quotient is 20 , with a remainder of 7 . when n is divided by ( p + 2 ) , the quotient is 15 and the remainder is 2 . what is the value of n ? | "n / p = 10 7 / p = 20 p + 7 n / ( p + 2 ) = 15 2 / ( p + 2 ) = 15 p + 30 + 2 solving these two equations we get p = 5 n = 107 answer is a ." | a = 15 * 2
b = a + 2
c = b - 7
d = 20 - 15
e = c / d
f = 20 * e
|
a ) 344 , b ) 600 , c ) 200 , d ) 800 , e ) 700 | d | multiply(multiply(multiply(5, 4), 10), 4) | a man bought an article and sold it at a gain of 5 % . if he had bought it at 5 % less and sold it for re 4 less , he would have made a profit of 10 % . the c . p . of the article was | explanation : let original cost price is x its selling price = ( 105 / 100 ) * x = 21 x / 20 new cost price = ( 95 / 100 ) * x = 19 x / 20 new selling price = ( 110 / 100 ) * ( 19 x / 20 ) = 209 x / 200 [ ( 21 x / 20 ) - ( 209 x / 200 ) ] = 4 = > x = 800 answer : d ) rs 800 | a = 5 * 4
b = a * 10
c = b * 4
|
a ) 12 , b ) 14 , c ) 16 , d ) 18 , e ) 20 | a | divide(30, divide(40, 16)) | in a group of people , if 30 people were made to stand in each column , 16 columns could be formed . if 40 people were made to stand in a column , how many columns could be formed ? | "16 * 30 = 40 * n n = 12 the answer is a ." | a = 40 / 16
b = 30 / a
|
a ) 1234 , b ) 1345 , c ) 1456 , d ) 1567 , e ) 1499 | e | multiply(divide(subtract(1200, 4), subtract(5, const_1)), 5) | find large number from below question the difference of two numbers is 1200 . on dividing the larger number by the smaller , we get 5 as quotient and the 4 as remainder | "let the smaller number be x . then larger number = ( x + 1200 ) . x + 1200 = 5 x + 4 4 x = 1196 x = 299 large number = 299 + 1200 = 1499 e" | a = 1200 - 4
b = 5 - 1
c = a / b
d = c * 5
|
a ) 5 , b ) 10 , c ) 15 , d ) 20 , e ) 25 | a | divide(subtract(divide(30, const_2), sqrt(subtract(multiply(divide(30, const_2), divide(30, const_2)), multiply(const_4, 50)))), const_2) | the area of a rectangular field is equal to 50 square meters . its perimeter is equal to 30 meters . find the width of this rectangle . | "l * w = 50 : area , l is the length and w is the width . 2 l + 2 w = 30 : perimeter l = 15 - w : solve for l ( 15 - w ) * w = 30 : substitute in the area equation w = 5 and l = 10 correct answer a" | a = 30 / 2
b = 30 / 2
c = 30 / 2
d = b * c
e = 4 * 50
f = d - e
g = math.sqrt(f)
h = a - g
i = h / 2
|
a ) 600 , b ) 887 , c ) 256 , d ) 654 , e ) 675 | e | add(500, multiply(500, divide(35, const_100))) | a person buys an article at rs . 500 . at what price should he sell the article so as to make a profit of 35 % ? | "cost price = rs . 500 profit = 35 % of 500 = rs . 175 selling price = cost price + profit = 500 + 175 = 675 answer : e" | a = 35 / 100
b = 500 * a
c = 500 + b
|
a ) 13,000 , b ) 11,600 , c ) 12,000 , d ) 14,000 , e ) 16,400 | a | add(5, 6) | jerome anticipated that the webweb . com stock price would fall and sold all his webweb . com stocks for $ 5 per stock . he paid $ 10,000 tax on the revenue . a week later , jerome became convinced that the webweb . com stock price would rise , and he used the money that he had gotten from selling the webweb . com stoc... | "let the number of shares be x . 5 * x - 10000 ( money paid in taxes ) = 6 ( x - 3000 ) solving for x , we get the shares as 13000 . ans : ( option a )" | a = 5 + 6
|
a ) 160 , b ) 170 , c ) 180 , d ) 195 , e ) 200 | d | divide(multiply(65, multiply(30, const_2)), 20) | 65 boys can complete a work in 30 days . how many men need to complete twice the work in 20 days | "one man can complete the work in 30 * 65 = 1950 days = one time work to complete the work twice it will be completed in let m be the no . of worker assign for this therefore the eqn becomes m * 20 = 2 * 1950 m = 195 workers answer : d" | a = 30 * 2
b = 65 * a
c = b / 20
|
a ) 901 , b ) 989 , c ) 990 , d ) 991 , e ) 1,001 | d | add(multiply(2000, divide(subtract(50, 0.5), const_100)), const_1) | in a recent election , james received 0.5 percent of the 2000 votes cast . to win the election , a candidate needed to receive more than 50 percent of the vote . how many additional votes would james have needed to win the election ? | james = ( 0.5 / 100 ) * 2000 = 10 votes to win = ( 50 / 100 ) * total votes + 1 = ( 50 / 100 ) * 2000 + 1 = 1001 remaining voted needed to win election = 1001 - 10 = 991 answer : option d | a = 50 - 0
b = a / 100
c = 2000 * b
d = c + 1
|
a ) rs . 420000 , b ) rs . 403200 , c ) rs . 201600 , d ) rs . 504000 , e ) none of these | b | multiply(multiply(multiply(12000, add(const_1, divide(12, const_100))), divide(5, 2)), 12) | the monthly incomes of a and b are in the ratio 5 : 2 . b ' s monthly income is 12 % more than c ' s monthly income . if c ' s monthly income is rs . 12000 , then find the annual income of a ? | "b ' s monthly income = 12000 * 112 / 100 = rs . 13440 b ' s monthly income = 2 parts - - - - > rs . 13440 a ' s monthly income = 5 parts = 5 / 2 * 13440 = rs . 33600 a ' s annual income = rs . 33600 * 12 = rs . 403200 answer : b" | a = 12 / 100
b = 1 + a
c = 12000 * b
d = 5 / 2
e = c * d
f = e * 12
|
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