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 : ( 1 ) 77 x : 1 * 1 * 9 = 9 ( 2 ) x 77 : 8 * 1 * 1 = 8 ( 3 ) 7 x 7 : 1 * 9 * 1 = 9 9 + 8 + 9 = 26 number 777 is missing . so the total becomes 225 + 26 + 1 = 252 d is the correct answer ." | 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 ( 500 / 4000 ) x 100 = 12.5 % in percentage terms . but the question asks ratio between his total land to total cultivated land . hence the answer is 12.5 % x ( 100 / 60 ) = 20.833 % and the answer is not there in the options . the correct answer is ( d ) ." | a = 500 / 4000
b = a * 100
c = b * 100
d = c / 60
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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
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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
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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
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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
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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
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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 total hours of person - work . if instead you wanted the job done in 3 hours , you ' d assign 30 / 3 = 10 employees to do the job , because you want to get a total of 30 hours of work from the employees . we can solve this problem identically . if 15 machines ( identical ones , i assume ) work simultaneously for 36 days , they will do a total of 15 * 36 machine - days of work . so the job requires 15 * 36 days of machine work in total . we instead want the job done in 1 / 4 less time , so in 27 days . so we ' ll need 15 * 36 / 27 = 20 machines , or 5 additional machines . a" | 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 same . the median of the set is ( 3 + 6 ) / 2 = 4.5 , thus the number selected must be 5 or greater . for the range to remain the same , the number must be between 2 and 8 inclusive . to satisfy both conditions , the number selected must be 5 , 6 , 7 , or 8 . the probability is 4 / 10 = 0.4 the answer is c ." | 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
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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
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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 we ' d be adding to that big number ) . eliminate a . with answer e , we ' d have 625 ^ ( - 4 ) , which would create a tiny fraction ( and we ' d add some other fractions to it , so the total would be much too small ) . eliminate e . with answer d , we ' d have 625 ^ ( - 1 / 4 ) , which will also be a fraction ( just not as tiny as the one in answer e ) , but the total would still be too small . eliminate d . with answer c , anything to the ' 0 power ' is 1 , so we ' d have 1 + 1 + 1 = 3 . this is not 15 . eliminate c . c" | 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 for this problem area of the big plate = pi * r ^ 2 , where r = 6 = > pi * 36 area of the small plate = pi * 25 surface not covered by the plate = pi * 36 - pi * 25 = pi * 11 fraction of big plate ' s surface is not covered by small plate = pi * 11 / total area of the big plate = > pi * 11 / pi * 36 answer a | a = 12 / 2
b = circle_area - (
c = 10 / 2
d = b / circle_area
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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 therefore total no . of days of job = 750 man - day / 8 days = 375 / 4 = 94 days ( approx . ) now since this is total and ques . is asking for additional no . of days , so 94 - 20 = 74 days the nearest approx . to answer is 75 ans : c ( 75 days )" | 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
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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(divide(subtract(subtract(31, const_10), const_2), const_4), const_2), const_2))) | 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)
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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
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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
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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 22 percent , what is the discount rate on pony jeans ? | "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
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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
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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 . . . . . . . . translating : 3631 = x / 100 * 6000 - - - > x = 60.51666666 x = 60.5 % . . . . . . . . . . e" | 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 paid by solomon = 403 - 222 = 181 / - for 7 days answer is e | 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 = 5050 - 2550 = 2500 so 101 + 103 + . . . . . . . 199 = 50 * 100 + ( 1 + 3 + 5 + 7 + . . . . . . ) = 5000 + 2500 = 7500 b is the answer ." | 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 ) or 20 + x = ( 100 + x ) 8 / 25 500 + 25 x = 800 + 8 x 17 x = 300 x = 300 / 17 ans : e" | 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 small as possible and the smaller number needs to be as large as possible to be close to each other . the first digit ( hundreds digit ) of both numbers should be consecutive integers now let ' s think about the next digit ( the tens digit ) . to minimize the difference between the numbers , the tens digit of the greater number should be as small as possible and the tens digit of the smaller number should be as large as possible . so let ' s not use 3 and 8 in the hundreds places and reserve them for the tens places . now what are the options ? try and make a pair with ( 4 * * and 5 * * ) . make the 4 * * number as large as possible and make the 5 * * number as small as possible . 487 and 536 ( difference is 49 ) or try and make a pair with ( 6 * * and 7 * * ) . make the 6 * * number as large as possible and make the 7 * * number as small as possible . we get 685 and 734 ( difference is 49 ) b" | 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
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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
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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
|
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
|
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
|
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
|
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)
|
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 cabbages did she produce this year ? | "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 it will be ( 99 + 98 ) * ( 99 - 98 ) . thus x = 99 and y = 98 x ^ 2 = 99 ^ 2 = 9801 the answer is a ." | 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 stocks to purchase them again , this time at $ 6 per stock . if jerome ended up having 3000 webweb . com stocks fewer than the number he had before selling them , how many webweb . com stocks did he have originally ? | "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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