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 ) 545 , b ) 334 , c ) 555 , d ) 664 , e ) 5598 | a | divide(multiply(divide(multiply(616, const_100), add(const_100, 10)), add(const_100, 10)), add(const_100, 13)) | the sale price of an article including the sales tax is rs . 616 . the rate of sales tax is 10 % . if the shopkeeper has made a profit of 13 % , then the cost price of the article is : | "110 % of s . p . = 616 s . p . = ( 616 * 100 ) / 110 = rs . 560 c . p = ( 110 * 560 ) / 113 = rs . 545 answer : option a" | a = 616 * 100
b = 100 + 10
c = a / b
d = 100 + 10
e = c * d
f = 100 + 13
g = e / f
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a ) 5363 , b ) 6240 , c ) 8700 , d ) 5600 , e ) 2732 | c | multiply(divide(100, 15), 580) | in order to obtain an income of rs . 580 from 15 % stock at rs . 100 , one must make an investment of | "to obtain rs . 10 , investment = rs . 100 . to obtain rs . 580 , investment = = rs . 8700 . answer : c" | a = 100 / 15
b = a * 580
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a ) 25 , b ) 28 , c ) 30 , d ) 32 , e ) 34 | a | subtract(divide(multiply(add(const_100, 20), const_100), subtract(const_100, 4)), const_100) | a shopkeeper sold an article offering a discount of 4 % and earned a profit of 20 % . what would have been the percentage of profit earned if no discount was offered ? | "let c . p . be rs . 100 . then , s . p . = rs . 120 let marked price be rs . x . then , 96 / 100 x = 120 x = 12000 / 96 = rs . 125 now , s . p . = rs . 125 , c . p . = rs . 100 profit % = 25 % . answer : a" | a = 100 + 20
b = a * 100
c = 100 - 4
d = b / c
e = d - 100
|
a ) 14 th , b ) 15 th , c ) 16 th , d ) 17 th , e ) 18 th | b | subtract(divide(multiply(3.2, const_1000), 200), const_1) | apple street begins at peach street and runs directly east for 3.2 kilometers until it ends when it meets cherry street . apple street is intersected every 200 meters by a perpendicular street , and each of those streets other than peach street and cherry street is given a number beginning at 1 st street ( one block east of peach street ) and continuing consecutively ( 2 nd street , 3 rd street , etc . . . ) until the highest - numbered street one block west of cherry street . what is the highest - numbered street that intersects apple street ? | 3.2 km / 200 m = 16 . however , the street at the 3.2 - km mark is not 16 th street ; it is cherry street . therefore , the highest numbered street is 15 th street . the answer is b . | a = 3 * 2
b = a / 200
c = b - 1
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a ) 1 / 13 , b ) 2 / 23 , c ) 5 / 26 , d ) 7 / 30 , e ) 3 / 23 | d | divide(choose(8, 2), choose(add(add(8, 6), 4), 2)) | a bag contains 8 red , 6 blue and 4 green balls . if 2 ballsare picked at random , what is the probability that both are red ? | "p ( both are red ) , = 8 c 216 c 2 = 8 c 216 c 2 = 28 / 120 = 7 / 30 d" | a = math.comb(8, 2)
b = 8 + 6
c = b + 4
d = math.comb(c, 2)
e = a / d
|
a ) $ 100 , b ) $ 150 , c ) $ 125 , d ) $ 134 , e ) $ 243 | a | multiply(5, divide(1480, add(add(multiply(6, 3), multiply(9, 4)), multiply(4, 5)))) | a , b and c completed a piece of work , a worked for 6 days , b for 9 days and c for 4 days . their daily wages were in the ratio of 3 : 4 : 5 . find the daily wages of c , if their total earning was $ 1480 ? | a $ 100 3 x 4 x 5 x 6 9 4 18 x + 36 x + 20 x = 1480 74 x = 1480 = > x = 20 5 x = 100 rs . | a = 6 * 3
b = 9 * 4
c = a + b
d = 4 * 5
e = c + d
f = 1480 / e
g = 5 * f
|
a ) 400 , b ) 420 , c ) 480 , d ) 450 , e ) 510 | c | divide(subtract(multiply(15, 440), multiply(15, 120)), subtract(120, 110)) | the average salary of the employees in a office is rs . 120 / month . the avg salary of officers is rs . 440 and of non officers is rs 110 . if the no . of officers is 15 , then find the no of nonofficers in the office . | "let no . of non - officers be x 15 * 440 + x * 110 = ( x + 15 ) 120 x = 480 c" | a = 15 * 440
b = 15 * 120
c = a - b
d = 120 - 110
e = c / d
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a ) 560 , b ) 780 , c ) 990 , d ) 1008 , e ) 1200 | c | multiply(divide(add(subtract(140, const_3), add(80, const_2)), const_2), add(divide(subtract(subtract(140, const_3), add(80, const_2)), 5), const_1)) | what is the sum of the multiples of 5 from 80 to 140 , inclusive ? | "the formula we want to use in this type of problem is this : average * total numbers = sum first , find the average by taking the sum of the f + l number and divide it by 2 : a = ( f + l ) / 2 second , find the total numbers in our range by dividing our f and l numbers by 5 and add 1 . ( 140 / 5 ) - ( 80 / 5 ) + 1 multiply these together so what we show average * total numbers = sum ( 80 + 140 ) / 2 * ( 140 / 5 ) - ( 80 / 5 ) + 1 = sum 110 * 9 = 990 c" | a = 140 - 3
b = 80 + 2
c = a + b
d = c / 2
e = 140 - 3
f = 80 + 2
g = e - f
h = g / 5
i = h + 1
j = d * i
|
a ) 78 , b ) 40 , c ) 68 , d ) 88 , e ) none | a | add(multiply(divide(720, 30), const_2), 30) | a rectangular field is to be fenced on three sides leaving a side of 30 feet uncovered . if the area of the field is 720 sq . feet , how many feet of fencing will be required ? | "explanation we have : l = 30 ft and lb = 720 sq . ft . so , b = 24 ft . length of fencing = ( l + 2 b ) = ( 30 + 48 ) ft = 78 ft . answer a" | a = 720 / 30
b = a * 2
c = b + 30
|
a ) 14 / 15 , b ) 15 / 14 , c ) 4 / 5 , d ) 21 / 25 , e ) can not be determined | d | divide(divide(42, 5), divide(42, 4.2)) | jack and jill are marathon runners . jack can finish a marathon ( 42 km ) in 5 hours and jill can run a marathon in 4.2 hours . what is the ratio of their average running speed ? ( jack : jill ) | "average speed of jack = distance / time = 42 / 5 average speed of jill = 42 / ( 4.2 ) = 10 ratio of average speed of jack to jill = ( 42 / 5 ) / 10 = 42 / 50 = 21 / 25 answer d" | a = 42 / 5
b = 42 / 4
c = a / b
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a ) 1 : 1 , b ) 2 : 3 , c ) 3 : 2 , d ) 9 : 4 , e ) 27 : 8 | e | divide(multiply(multiply(2, 3), 3), multiply(multiply(2, 2), 2)) | a bottle contains a certain solution . in the bottled solution , the ratio of water to soap is 3 : 2 , and the ratio of soap to salt is three times this ratio . the solution is poured into an open container , and after some time , the ratio of water to soap in the open container is halved by water evaporation . at that time , what is the ratio of water to salt in the solution ? | "water : soap = 3 : 2 soap : salt = 9 : 2 = > for 9 soap , salt = 2 = > for 2 soap , salt = ( 2 / 9 ) * 2 = 4 / 9 so , water : soap : salt = 3 : 2 : 4 / 9 = 27 : 18 : 4 after open container , water : soap : salt = 13.5 : 18 : 4 so , water : salt = 13.5 : 4 = 27 : 8 answer : e" | a = 2 * 3
b = a * 3
c = 2 * 2
d = c * 2
e = b / d
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a ) 5 , b ) 6 , c ) 7 , d ) 8 , e ) 14 | d | divide(subtract(add(13, 14), 11), const_2) | at a party , 13 guests brought wine and 14 guests brought beer . if exactly 11 guests brought only one of the two types of drinks , how many guests brought both types of drinks ? | say x guests brought both drinks . ( 13 - x ) + ( 14 - x ) = 11 - - > x = 8 . answer : d . | a = 13 + 14
b = a - 11
c = b / 2
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a ) 2878 , b ) 279 , c ) 279 , d ) 482 , e ) 661 | d | add(multiply(add(20, const_1), add(20, const_1)), add(20, const_1)) | a sum of money is put out at compound interest for 2 years at 20 % . it would earn rs . 482 more if the interest were paid half - yearly . calculate the sum . | p ( 11 / 10 ) 4 - p ( 6 / 5 ) 2 = 482 p = 2000 answer : d | a = 20 + 1
b = 20 + 1
c = a * b
d = 20 + 1
e = c + d
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a ) − 5 % , b ) 5 % , c ) 15 % , d ) 20 % , e ) 22.5 % | e | multiply(subtract(multiply(add(const_1, divide(75, const_100)), subtract(const_1, divide(30, const_100))), const_1), const_100) | a broker invested her own money in the stock market . during the first year , she increased her stock market wealth by 75 percent . in the second year , largely as a result of a slump in the stock market , she suffered a 30 percent decrease in the value of her stock investments . what was the net increase or decrease on her overall stock investment wealth by the end of the second year ? | "the actual answer is obtained by multiplying 175 % by 70 % and subtracting 100 % from this total . that is : 175 % × 70 % = 122.5 % ; 122.5 % − 100 % = 122.5 % . answer : e" | a = 75 / 100
b = 1 + a
c = 30 / 100
d = 1 - c
e = b * d
f = e - 1
g = f * 100
|
a ) 15 % , b ) 25 % , c ) 0.125 % , d ) 0.2083 % , e ) none | b | divide(multiply(multiply(divide(480, 3840), const_100), const_100), 50) | farm tax is levied on the 50 % of the cultivated land . the tax department collected total $ 3840 through the farm tax from the village of mr . william . mr . william paid only $ 480 as farm tax . the percentage of total land of mr . willam over the total taxable land of the village is : | "this will be equal to the percentage of total cultivated land he holds over the total cultivated land in the village . that leads to ( 480 / 3840 ) 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 / 50 ) = 25 % the correct answer is ( b ) ." | a = 480 / 3840
b = a * 100
c = b * 100
d = c / 50
|
a ) 732 , b ) 990 , c ) 109 , d ) 130 , e ) 690 | e | subtract(subtract(multiply(266, const_3), subtract(const_100, const_1)), subtract(const_10, const_1)) | the total number of digits used in numbering the pages of a book having 266 pages is | "total number of digits = ( no . of digits in 1 - digit page nos . + no . of digits in 2 - digit page nos . + no . of digits in 3 - digit page nos . ) = ( 1 x 9 + 2 x 90 + 3 x 167 ) = ( 9 + 180 + 501 ) = 690 . answer : e" | a = 266 * 3
b = 100 - 1
c = a - b
d = 10 - 1
e = c - d
|
a ) s . 800 , b ) s . 2400 , c ) s . 4000 , d ) s . 3500 , e ) s . 4200 | d | multiply(subtract(multiply(divide(1400, 2), 3), 1400), 5) | the ratio of incomes of two person p 1 and p 2 is 5 : 4 and the ratio of their expenditures is 3 : 2 . if at the end of the year , each saves rs . 1400 , then what is the income of p 1 ? | "let the income of p 1 and p 2 be rs . 5 x and rs . 4 x respectively and let their expenditures be rs . 3 y and 2 y respectively . then , 5 x – 3 y = 1400 … ( i ) and 4 x – 2 y = 1400 … … . . ( ii ) on multiplying ( i ) by 2 , ( ii ) by 3 and subtracting , we get : 2 x = 1400 - > x = 700 p 1 ’ s income = rs 5 * 700 = rs . 3500 answer : d" | a = 1400 / 2
b = a * 3
c = b - 1400
d = c * 5
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a ) rs 16,000 , b ) rs 18,000 , c ) rs 12,000 , d ) rs 14,000 , e ) none of these | c | divide(8,748, subtract(const_1, multiply(divide(10, const_100), 3))) | the value of a machine depreciates at the rate of 10 % every year . it was purchased 3 years ago . if its present value is rs 8,748 , its purchase price was ? | "we have p = 8748 , r = - 10 and n = 3 therefore , the purchase price of the machine = p / ( 1 + ( r / 100 ) ) n = 8748 / ( 1 - ( 10 / 100 ) ) 3 = 8748 x ( 100 / 90 ) x ( 100 / 90 ) x ( 100 / 90 ) = 12,000 . answer : c" | a = 10 / 100
b = a * 3
c = 1 - b
d = 8 / 748
|
a ) $ 1,416 , b ) $ 1,733 , c ) $ 3,466 , d ) $ 13,333 , e ) $ 20,796 | a | subtract(9, multiply(4, const_2)) | a new home buyer pays 4 % annual interest on her first mortgage and 9 % annual interest on her second mortgage . if she borrowed a total of $ 340,000 , 80 % of which was in the first mortgage , what is her approximate monthly interest payment ? | "0.04 x + 0.09 y = 340000 [ 1 ] 0.04 x = 0.80 * 340000 = 272000 [ 2 ] 272000 + 0.09 y = 340000 - - > 0.09 y = 64000 [ 3 ] 272000 / 12 = 22666.67 [ 4 ] 64000 / 12 = 5666.67 [ 5 ] adding [ 4,5 ] we get : 28333.33 [ 6 ] dividing [ 6 ] / 2 to get an average we get 1.416 , ans a" | a = 4 * 2
b = 9 - a
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a ) 10 , b ) 30 , c ) 20 , d ) 15 , e ) 16 | b | divide(subtract(multiply(divide(25, const_100), 150), multiply(divide(10, const_100), 150)), subtract(const_1, divide(25, const_100))) | a mixture of 150 liters of wine and water contains 10 % water . how much more water should be added so that water becomes 25 % of the new mixture ? | "number of liters of water in 150 liters of the mixture = 10 % of 150 = 10 / 100 * 150 = 15 liters . p liters of water added to the mixture to make water 25 % of the new mixture . total amount of water becomes ( 15 + p ) and total volume of mixture is ( 150 + p ) . ( 15 + p ) = 25 / 100 * ( 150 + p ) 60 + 4 p = 150 + p p = 30 liters . answer : b" | a = 25 / 100
b = a * 150
c = 10 / 100
d = c * 150
e = b - d
f = 25 / 100
g = 1 - f
h = e / g
|
a ) 2992 , b ) 7992 , c ) 2877 , d ) 2077 , e ) 6229 | b | subtract(multiply(8, const_1000), 8) | what is the difference between the local values of 8 in the number 58408 ? | explanation : 8000 â € “ 8 = 7992 answer : b | a = 8 * 1000
b = a - 8
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a ) 6 , b ) 12 , c ) 15 , d ) 9 , e ) 7 | d | multiply(2, 4) | three numbers are in the ratio of 2 : 3 : 4 . if the sum of the squares of the extremes is 180 , then the middle number is : | "number be = 2 x , 3 x , 4 x , ( 2 x ) 2 + ( 4 x ) 2 = 180 20 x = 180 ⇒ x = 9 ⇒ x = 3 , midline number = 3 × 3 = 9 answer : d" | a = 2 * 4
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a ) 14 m , b ) 29 m , c ) 49 m , d ) 7 , e ) none | d | sqrt(divide(147, const_2)) | the area of a parallelogram is 147 sq m and its base is thrice the corresponding height . then the length of the base is ? | b * h = 147 b * h = 147 = > b ^ 2 = 49 m . b = 7 answer : ( d ) | a = 147 / 2
b = math.sqrt(a)
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a ) 22 , b ) 27 , c ) 60 , d ) 88 , e ) 12 | b | subtract(120, 60) | a contractor undertakes to complete the construction of a tunnel 720 meters long in 240 days and employs 60 men for the purpose . after 120 days , he finds that only 240 meters of the tunnel is complete . how many more men should be employ in order to complete the work in time ? | in 120 days , only 240 m of the tunnel is constructed by 60 men . the remaining 120 days , 480 m of the tunnel can be constructed by 120 men . additional number of men required = 120 - 60 = 60 men . answer : b | a = 120 - 60
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a ) 30 , b ) 48 , c ) 60 , d ) 80 , e ) 90 | d | multiply(multiply(divide(50, subtract(const_1, divide(2, 3))), divide(2, 3)), divide(4, 5)) | a certain automobile company ’ s best - selling model is the speedster . the speedster , like all of their other models , comes in coupe and convertible styles . 2 / 3 of the current inventory is speedsters , of which 4 / 5 are convertibles . if there are 50 vehicles that are not speedsters , how many speedster convertibles are there ? | "total vehicle = 2 / 3 of speedster + 1 / 3 of others . speedster convertibles = 2 / 3 total vehicle * 4 / 5 given : 1 / 3 constitutes 50 vehicles . hence 2 / 3 constitutes 100 speedster convertibls = 100 * 4 / 5 = 80 d" | a = 2 / 3
b = 1 - a
c = 50 / b
d = 2 / 3
e = c * d
f = 4 / 5
g = e * f
|
a ) 8 , b ) 16 , c ) 10 , d ) 11 , e ) 12 | b | add(4, 12) | if there are 4 peanuts in a box and mary puts 12 more peanuts inside , how many peanuts are in the box ? | "12 + 4 = 16 correct answer is b ) 16" | a = 4 + 12
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a ) 11 / 79 , b ) 10 / 79 , c ) 12 / 79 , d ) 13 / 79 , e ) 14 / 79 | b | divide(10, subtract(multiply(multiply(2, 4), 10), const_1)) | 4 dice are thrown and the sum of the numbers noted is 10 . find the probability that all the numbers lie between 2 and 5 ( both inclusive ) ? | sum of numbers noted on 4 dice ( with six faces ) to be 10 will include combinations : ( 1,1 , 2,6 ) ( 1,1 , 3,5 ) ( 1,1 , 4,4 ) ( 1,1 , 5,3 ) ( 1,1 , 6,2 ) ( 1,2 , 1,6 ) ( 1,2 , 2,5 ) ( 1,2 , 3,4 ) ( 1,2 , 4,3 ) ( 1,2 , 5,2 ) ( 1,2 , 6,1 ) ( 1,3 , 1,5 ) ( 1,3 , 2,4 ) ( 1,3 , 3,3 ) ( 1,3 , 4,2 ) ( 1,3 , 5,1 ) ( 1,4 , 1,4 ) ( 1,4 , 2,3 ) ( 1,4 , 3,2 ) ( 1,4 , 4,1 ) ( 1,5 , 1,3 ) ( 1,5 , 2,2 ) ( 1,5 , 3,1 ) ( 1,6 , 1,2 ) ( 1,6 , 2,1 ) ( 2,1 , 1,6 ) ( 2,1 , 2,5 ) ( 2,1 , 3,4 ) ( 2,1 , 4,3 ) ( 2,1 , 5,2 ) ( 2,1 , 6,1 ) ( 2,2 , 1,5 ) ( 2,2 , 2,4 ) ( 2,2 , 3,3 ) ( 2,2 , 4,2 ) ( 2,2 , 5,1 ) ( 2,3 , 1,4 ) ( 2,3 , 2,3 ) ( 2,3 , 3,2 ) ( 2,3 , 4,1 ) ( 2,4 , 1,3 ) ( 2,4 , 2,2 ) ( 2,4 , 3,1 ) ( 2,5 , 1,2 ) ( 2,5 , 2,1 ) ( 2,6 , 1,1 ) ( 3,1 , 1,5 ) ( 3,1 , 2,4 ) ( 3,1 , 3,3 ) ( 3,1 , 4,2 ) ( 3,1 , 5,1 ) ( 3,2 , 1,4 ) ( 3,2 , 2,3 ) ( 3,2 , 3,2 ) ( 3,2 , 4,1 ) ( 3,3 , 1,3 ) ( 3,3 , 2,2 ) ( 3,3 , 3,1 ) ( 3,4 , 1,2 ) ( 3,4 , 2,1 ) ( 3,5 , 1,1 ) ( 4,1 , 1,4 ) ( 4,1 , 2,3 ) ( 4,1 , 3,2 ) ( 4,1 , 4,1 ) ( 4,2 , 1,3 ) ( 4,2 , 2,2 ) ( 4,2 , 3,1 ) ( 4,3 , 1,2 ) ( 4,3 , 2,1 ) ( 4,4 , 1,1 ) ( 5,1 , 1,3 ) ( 5,1 , 2,2 ) ( 5,1 , 3,1 ) ( 5,2 , 1,2 ) ( 5,2 , 2,1 ) ( 5,3 , 1,1 ) ( 6,1 , 1,2 ) ( 6,1 , 2,1 ) - - - - - - - total 79 combinations with all the numbers lie between 2 and 5 are ( 2,2 , 2,4 ) ( 2,2 , 3,3 ) ( 2,2 , 4,2 ) ( 2,3 , 2,3 ) ( 2,3 , 3,2 ) ( 2,4 , 2,2 ) ( 3,2 , 2,3 ) ( 3,2 , 3,2 ) ( 3,3 , 2,2 ) ( 4,2 , 2,2 ) - - - - - - total 10 so probability = 10 / 79 answer : b | a = 2 * 4
b = a * 10
c = b - 1
d = 10 / c
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a ) 2 : 3 , b ) ratio 1 : 5 , c ) ratio 1 : 10 , d ) ratio 9 : 13 , e ) ratio 7 : 15 | c | divide(200, multiply(divide(100, 50), const_1000)) | a truck covers a distance of 200 metres in 1 minute whereas a bus covers a distance of 100 kms in 50 minutes . the ratio of their speeds is ? | "ratio of speeds = ( 200 / 60 ) 18 / 5 : 60 * 100 / 50 = 12 : 120 = 1 : 10 answer is c" | a = 100 / 50
b = a * 1000
c = 200 / b
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a ) 72 , b ) 27 , c ) 40 , d ) 30 , e ) 20 | d | divide(divide(multiply(900, 30), const_100), 9) | a reduction of 30 % in the price of oil enables a house wife to obtain 9 kgs more for rs . 900 , what is the reduced price for kg ? | "900 * ( 30 / 100 ) = 270 - - - - 9 ? - - - - 1 = > rs . 30 answer : d" | a = 900 * 30
b = a / 100
c = b / 9
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a ) 14420 , b ) 12620 , c ) 17280 , d ) 21200 , e ) 24560 | c | multiply(factorial(6), factorial(4)) | in how many ways 6 boys and 4 girls can be seated in a row so that they are alternative ? | "6 boys can be seated in 6 ! 4 girls can be seated in 4 ! required number = 6 ! 4 ! = 17280 answer is c" | a = math.factorial(6)
b = math.factorial(4)
c = a * b
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a ) 21.84 , b ) 22.84 , c ) 23.84 , d ) 24.84 , e ) 25.84 | a | divide(multiply(139.00, add(divide(const_1, 10), const_1)), 7) | total dinning bill of 7 people was $ 139.00 and 10 % tip divided the bill evenly ? what is the bill amount each person shared . | "dinner bill of 7 person = 139 + 10 % tip so , 10 % of 139 = ( 139 * 10 ) / 100 = 13.9 so , the actual total amount = 139 + 13.9 = $ 152.9 so per head bill = 152.9 / 7 = $ 21.84 answer : a" | a = 1 / 10
b = a + 1
c = 139 * 0
d = c / 7
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a ) 1 : 8 , b ) 1 : 4 , c ) 2 : 1 , d ) 6 : 1 , e ) 8 : 1 | d | multiply(3, const_2) | city x has a population 3 times as great as the population of city y , which has a population twice as great as the population of city z . what is the ratio of the population of city x to the population of city z ? | "x = 3 y , y = 2 * z x : y , y : z 3 : 1 , 2 : 1 6 : 2 , 2 : 1 so , x : z = 6 : 1 ( d )" | a = 3 * 2
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a ) 6623 , b ) 43036 , c ) 51515 , d ) 474232 , e ) 2025 | d | subtract(multiply(800, 594), 968) | what is the dividend ? the divisor is 800 , the quotient is 594 , and the remainder is - 968 . | dividend = ? ? = d * q + r ? = 800 * 594 + - 968 ? = 475,200 + - 968 ? = 474,232 | a = 800 * 594
b = a - 968
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a ) 2 / 3 , b ) 3 / 4 , c ) 1 , d ) 2 , e ) 3 | e | divide(9, divide(12, subtract(12, 8))) | working independently , tina can do a certain job in 12 hours . working independently , ann can do the same job in 9 hours . if tina works independently at the job for 8 hours and then ann works independently , how many hours will it take ann to complete the remainder of the jobs ? | work done by tina in 1 hr = 1 / 12 work done by tina in 8 hr = 1 / 12 * 8 which is 2 / 3 now , the remaining work is 1 / 3 which is completed by ann in 1 / 3 * 9 which is 3 hr answer : e | a = 12 - 8
b = 12 / a
c = 9 / b
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a ) 572 , b ) 573 , c ) 574 , d ) 575 , e ) 576 | e | multiply(multiply(24, const_2), divide(24, const_2)) | sum of 24 odd numbers is ? | "sum of 1 st n odd no . s = 1 + 3 + 5 + 7 + . . . = n ^ 2 so , sum of 1 st 24 odd numbers = 24 ^ 2 = 576 answer : e" | a = 24 * 2
b = 24 / 2
c = a * b
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a ) 84 , b ) 89 , c ) 90 , d ) 92 , e ) 95 | c | subtract(subtract(100, const_3), 9) | set x consists of all two - digit primes and set y consists of all positive odd multiples of 9 less than 100 . if the two sets are combined into one , what will be the range of the new set ? | "set x = { 11 , 13 , 17 , . . . . . . . . . . . . . , 83 , 89 , 97 } set y = { 9 , 27 , 45 , . . . . . . . . . . . . . . . , 63 , 81 , 99 } combining two sets , say set z set z = { 9 , 11 , 13 , 17 , 27 , . . . . . . . . . . . . . . . . . . . , 63 , 81 , 83 , 89 , 97,99 } range = max value - min value range ( z ) = 99 - 9 = 90 oa c is the answer ." | a = 100 - 3
b = a - 9
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a ) 1 : 2 , b ) 9 : 4 , c ) 1 : 8 , d ) 1 : 18 , e ) 1 : 13 | b | divide(power(6, const_2), power(4, const_2)) | the duplicate ratio of 6 : 4 is ? | "36 ^ 2 : 4 ^ 2 = 36 : 16 = 9 : 4 answer : b" | a = 6 ** 2
b = 4 ** 2
c = a / b
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a ) 650 , b ) 640 , c ) 630 , d ) 620 , e ) 610 | a | add(add(multiply(20, 16), multiply(13, 10)), multiply(const_10, subtract(multiply(7, 4), subtract(10, const_2)))) | find 4 + 7 + 10 + 13 + 16 + . . . up to 20 terms | a = 4 d = 7 – 4 = 3 sum of first 20 terms , s 20 answer is a | a = 20 * 16
b = 13 * 10
c = a + b
d = 7 * 4
e = 10 - 2
f = d - e
g = 10 * f
h = c + g
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a ) 3 / 20 , b ) 5 / 26 , c ) 7 / 34 , d ) 9 / 37 , e ) 11 / 49 | a | multiply(divide(10, add(add(10, 11), 4)), divide(subtract(10, const_1), subtract(add(add(10, 11), 4), const_1))) | there are 10 slate rocks , 11 pumice rocks , and 4 granite rocks randomly distributed in a certain field . if 2 rocks are chosen at random and without replacement , what is the probability that both rocks will be slate rocks ? | "10 / 25 * 9 / 24 = 3 / 20 the answer is a ." | a = 10 + 11
b = a + 4
c = 10 / b
d = 10 - 1
e = 10 + 11
f = e + 4
g = f - 1
h = d / g
i = c * h
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a ) 0.35 , b ) 3.5 , c ) 350 , d ) 35 , e ) 3500 | c | multiply(divide(multiply(divide(multiply(multiply(100, 150), 125), multiply(multiply(25, 50), 75)), 20), 200), const_100) | if 100 % of j is equal to 25 % of k , 150 % of k is equal to 50 % of l , and 125 % of l is equal to 75 % of m , then 20 % of m is equal to what percent of 200 % of j ? | "imo answer should be 350 . . . consider j = 10 , then k = 50 , l = 150 and m = 350 . . . . 20 % of 350 , comes out to be 70 . . . . 200 % of 10 is 20 . . . . ( 70 * 100 ) / 20 = 350 . . . . ans : c" | a = 100 * 150
b = a * 125
c = 25 * 50
d = c * 75
e = b / d
f = e * 20
g = f / 200
h = g * 100
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a ) 233 , b ) 877 , c ) 279 , d ) 176 , e ) 291 | d | divide(multiply(add(multiply(5, const_100), 44), add(multiply(3, const_100), 74)), power(divide(add(multiply(5, const_100), 44), power(const_2, const_4)), const_2)) | a room of 5 m 44 cm long and 3 m 74 cm broad is to be paved with squre tiles . find the least number of squre tiles required to cover the floor . | "explanation : area of the room = 544 * 374 sq cm size of largest square tile = h . c . f of 544 cm and 374 cm = 34 cm area of 1 tile = 34 * 34 sq cm no . of tiles required = ( 544 * 374 ) / ( 34 * 34 ) = 176 answer : d ) 176" | a = 5 * 100
b = a + 44
c = 3 * 100
d = c + 74
e = b * d
f = 5 * 100
g = f + 44
h = 2 ** 4
i = g / h
j = i ** 2
k = e / j
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a ) 0 % , b ) 1 % , c ) 2 % , d ) 3 % , e ) 4 % | a | add(multiply(multiply(const_0_25, const_100), divide(4, const_100)), multiply(multiply(divide(3, 4), const_100), divide(5, const_100))) | 5 % of men have unlisted phone numbers and 4 % of women have unlisted phone numbers . population ratio of men : women in the city of gpuzzles is 4 : 3 . if we select randomly 100 people from the phone directory , can you tell us how many people selected will definitely have unlisted phone numbers ? | solution : 0 % explanation : in the number is in the phone directory , it means the number is listed and therefore if we pick any number from phone directory than number is surely listed . answer a | a = const_0_25 * 100
b = 4 / 100
c = a * b
d = 3 / 4
e = d * 100
f = 5 / 100
g = e * f
h = c + g
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a ) 0 , b ) 2 , c ) 3 , d ) 8 , e ) 16 | b | add(7, 7) | how many different values of positive integer x , for which | x + 7 | < x , are there ? | "answer a i opted to put the random value option . i used 0 , 7 , - 7 and the the extreme of 30 and - 30 . . i was able to solve it in 1 : 09 b" | a = 7 + 7
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a ) 28 , b ) 29 , c ) 10 , d ) 31 , e ) 32 | c | sqrt(100) | you buy a piece of land with an area of â ˆ š 100 , how long is one side of the land plot ? | "try filling the numbers into the answer y x y = find the closest to 100 . answer c" | a = math.sqrt(100)
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a ) 288 , b ) 110 , c ) 772 , d ) 592 , e ) 261 | b | multiply(circumface(divide(14, const_2)), 2.50) | find the cost of fencing around a circular field of diameter 14 m at the rate of rs . 2.50 a meter ? | "2 * 22 / 7 * 7 = 44 44 * 2.5 = rs . 110 answer : b" | a = 14 / 2
b = circumface * (
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a ) 188 , b ) 258 , c ) 376 , d ) 470 , e ) 517 | c | multiply(divide(add(multiply(const_1000, const_1), add(multiply(const_10, const_3), 4)), add(add(5, 2), 4)), 4) | a farmer used 1,034 acres of land for beans , wheat , and corn in the ratio of 5 : 2 : 4 , respectively . how many y acres were used for corn ? | "consider 5 x acres of land used for bean consider 2 x acres of land used for wheat consider 4 x acres of land used for corn total given is 1034 acres 11 x = 1034 x = 94 land used for corn y = 4 * 94 = 376 correct option - c" | a = 1000 * 1
b = 10 * 3
c = b + 4
d = a + c
e = 5 + 2
f = e + 4
g = d / f
h = g * 4
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a ) 25 , b ) 35 , c ) 38 , d ) 40 , e ) 45 | a | subtract(add(10, add(15, 5)), 5) | 10 play kabadi , 15 play kho kho only , 5 play both gmaes . then how many in total ? | "10 play kabadi = > n ( a ) = 10 , 5 play both gmaes . = > n ( anb ) = 5 15 play kho kho only , = > n ( b ) = n ( b only ) + n ( anb ) = 15 + 5 = 20 total = > n ( aub ) = n ( a ) + n ( b ) - n ( anb ) = 10 + 20 - 5 = 25 answer : a" | a = 15 + 5
b = 10 + a
c = b - 5
|
a ) 13 , b ) 15 , c ) 17 , d ) 19 , e ) 21 | d | divide(add(add(multiply(const_2, 7), multiply(const_2, const_3.0)), sqrt(add(multiply(7, subtract(45, multiply(multiply(const_2, 5), multiply(const_2, 7)))), power(add(multiply(const_2, 7), multiply(const_2, 5)), const_2)))), const_2) | a tailor trims 7 feet from opposite edges of a square piece of cloth , and 5 feet from the other two edges . if 45 square feet of cloth remain , what was the length of a side of the original piece of cloth ? | "let the original side of the square be x . ( x - 14 ) * ( x - 10 ) = 45 = 5 * 9 x = 19 the answer is d ." | a = 2 * 7
b = 2 * 3
c = a + b
d = 2 * 5
e = 2 * 7
f = d * e
g = 45 - f
h = 7 * g
i = 2 * 7
j = 2 * 5
k = i + j
l = k ** 2
m = h + l
n = math.sqrt(m)
o = c + n
p = o / 2
|
a ) 10 % , b ) 20 % , c ) 25 % , d ) 30 % , e ) 50 % | b | divide(subtract(1000, 500), multiply(500, divide(5, const_100))) | $ 500 will become $ 1000 in 5 years find the rate of interest ? | si = simple interest = a - p = 1000 - 500 = $ 500 r = 100 si / pt = 100 * 500 / 500 * 5 = 20 % answer is b | a = 1000 - 500
b = 5 / 100
c = 500 * b
d = a / c
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a ) - 0.71 , b ) 1.0 , c ) 1.07 , d ) - 1.42 , e ) 2.71 | d | divide(subtract(negate(multiply(1.9, 0.6)), multiply(2.6, 1.2)), 3.0) | ( ( - 1.9 ) ( 0.6 ) – ( 2.6 ) ( 1.2 ) ) / 3.0 = ? | "dove straight into calculation ( ( - 1.9 ) ( 0.6 ) – ( 2.6 ) ( 1.2 ) ) / 3.0 = - 1.42 answer d" | a = 1 * 9
b = negate - (
c = 2 * 6
d = b / c
|
a ) 504 , b ) 532 , c ) 210 , d ) 180 , e ) 280 | d | multiply(multiply(multiply(const_3, const_2), add(const_2, const_3)), multiply(const_3, const_2)) | the number 523 rbc is divisible by 7 , 89 . then what is the value of r * b * c | lcm of 7 , 8 and 9 is 504 , thus 523 rbc must be divisible by 504 . 523 rbc = 523000 + rbc 523000 divided by 504 gives a remainder of 352 . hence , 352 + rbc = k * 504 . k = 1 rbc = 152 - - > r * b * c = 10 k = 2 rbc = 656 - - > r * b * c = 180 as rbc is three digit number k can not be more than 2 . two answers ? well only one is listed in answer choices , so d . answer : d . | a = 3 * 2
b = 2 + 3
c = a * b
d = 3 * 2
e = c * d
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a ) rs . 12 , b ) rs . 18 , c ) rs . 15 , d ) rs . 21 , e ) rs . 25 | c | multiply(divide(const_100, 12), multiply(divide(9, const_100), 20)) | a man buys rs . 20 shares paying 9 % dividend . the man wants to have an interest of 12 % on his money . what is the market value of each share ? | "explanation : face value of each share = rs . 20 dividend per share = 9 % of 20 = 9 × 20 / 100 = 9 / 5 he needs to have an interest of 12 % on his money ie , money paid for a share 9 × 12 / 100 = 9 / 5 money paid for a share = 9 / 5 × 100 / 12 = 15 ie , market value of the share = rs . 15 answer : option c" | a = 100 / 12
b = 9 / 100
c = b * 20
d = a * c
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a ) 7 , b ) 2 , c ) 9 , d ) 4 , e ) 6 | a | divide(multiply(27452, 9), 27452) | what is the smallest no . which must be added to 27452 so as to obtain a sum which is divisible by 9 ? | "for 27452 , 2 + 7 + 4 + 5 + 2 = 20 . 7 must be added to 27452 to make it divisible by 9 . now , 2 + 7 + 4 + 5 + 9 = 27 = > 27 is a multiple of 9 and hence 27452 is also divisible by 9 a" | a = 27452 * 9
b = a / 27452
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a ) 10 , b ) 15 , c ) 12.5 , d ) 13 , e ) 21 | c | divide(add(add(add(4, const_1), add(add(4, const_1), const_2)), add(subtract(5, 4), subtract(5, const_2))), 4) | find the average of first 4 multiples of 5 ? | "average = ( 5 + 10 + 15 + 20 ) / 4 = 12.5 answer is c" | a = 4 + 1
b = 4 + 1
c = b + 2
d = a + c
e = 5 - 4
f = 5 - 2
g = e + f
h = d + g
i = h / 4
|
a ) 338 , b ) 277 , c ) 331.2 , d ) 882 , e ) 212 | c | subtract(subtract(400, divide(multiply(400, 10), const_100)), divide(multiply(subtract(400, divide(multiply(400, 10), const_100)), 8), const_100)) | the sale price sarees listed for rs . 400 after successive discount is 10 % and 8 % is ? | "400 * ( 90 / 100 ) * ( 92 / 100 ) = 331.2 answer : c" | a = 400 * 10
b = a / 100
c = 400 - b
d = 400 * 10
e = d / 100
f = 400 - e
g = f * 8
h = g / 100
i = c - h
|
a ) 344 , b ) 387 , c ) 308 , d ) 299 , e ) 882 | c | multiply(11, 275) | the h . c . f of two numbers is 11 and their l . c . m is 7700 . if one of the numbers is 275 , then the other is | "explanation : other number = \ inline \ fn _ jvn \ left ( \ frac { 11 \ times 7700 } { 275 } \ right ) = 308 answer : c ) 308" | a = 11 * 275
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a ) 100 , b ) 6 , c ) 8 , d ) 12 , e ) 18 | a | add(const_3, const_4) | what is the smallest positive integer x , such that 2160 x is a perfect cube ? | "take out the factors of 2160 that will come 6 ^ 3 * 10 . for perfect cube you need every no . raise to the power 3 . for 2160 to be a perfect cube , you need two 2 and two 5 that means 100 a is the answer ." | a = 3 + 4
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a ) 15 / 2 , b ) 9 / 4 , c ) 5 / 9 , d ) 5 / 7 , e ) 9 / 7 | d | add(subtract(const_1, divide(2, 3)), subtract(divide(2, 3), divide(1, 4))) | a batch of cookies was divided amomg 6 tins : 2 / 3 of all the cookies were placed in either the blue or the green tin , and the rest were placed in the red tin . if 1 / 4 of all the cookies were placed in the blue tin , what fraction of the cookies that were placed in the other tins were placed in the green tin | this will help reduce the number of variables you have to deal with : g + b = 2 / 3 r = 1 / 6 b = 1 / 4 we can solve for g which is 5 / 12 what fraction ( let it equal x ) of the cookies that were placed in the other tins were placed in the green tin ? so . . x * ( g + r ) = g x * ( 5 / 12 + 1 / 6 ) = 5 / 12 x = 5 / 7 answer : d | a = 2 / 3
b = 1 - a
c = 2 / 3
d = 1 / 4
e = c - d
f = b + e
|
a ) 1 , b ) 2 , c ) 3 , d ) 4 , e ) 5 | c | subtract(5, const_2) | in a certain game , a large bag is filled with blue , green , purple and red chips worth 1 , 5 , x and 11 points each , respectively . the purple chips are worth more than the green chips , but less than the red chips . a certain number of chips are then selected from the bag . if the product of the point values of the selected chips is 28160 , how many purple chips were selected ? | "28160 = 1 * 5 * 8 ^ 3 * 11 the factors of 8 must come from the purple point value , so there are 3 purple chips . the answer is c ." | a = 5 - 2
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a ) 140 , b ) 150 , c ) 205 , d ) 170 , e ) 180 | c | divide(2460, 12) | two numbers have a h . c . f of 12 and a product of two numbers is 2460 . find the l . c . m of the two numbers ? | "l . c . m of two numbers is given by ( product of the two numbers ) / ( h . c . f of the two numbers ) = 2460 / 12 = 205 . answer : c" | a = 2460 / 12
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a ) 100 , b ) 12 , c ) 15 , d ) 18 , e ) 19 | a | multiply(multiply(add(9, divide(subtract(sqrt(281), 9), 2)), divide(subtract(sqrt(281), 9), 2)), 2) | if a - b = 9 and a ^ 2 + b ^ 2 = 281 , find the value of ab | "2 ab = ( a ^ 2 + b ^ 2 ) - ( a - b ) ^ 2 = 281 - 81 = 200 = > ab = 100 answer : a" | a = math.sqrt(281)
b = a - 9
c = b / 2
d = 9 + c
e = math.sqrt(281)
f = e - 9
g = f / 2
h = d * g
i = h * 2
|
a ) 6 , b ) 16 , c ) 22 , d ) 30 , e ) 174 | c | add(subtract(18, 6), subtract(16, 6)) | if x and y are sets of integers , x # y denotes the set of integers that belong to set x or set y , but not both . if x consists of 16 integers , y consists of 18 integers , and 6 of the integers are in both x and y , then x # y consists of how many integers ? | "the number of integers that belong to set x only is 16 - 6 = 10 ; the number of integers that belong to set y only is 18 - 6 = 12 ; the number of integers that belong to set x or set y , but not both is 10 + 12 = 22 . answer : c" | a = 18 - 6
b = 16 - 6
c = a + b
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a ) 1 , b ) 1.5 , c ) 2 , d ) 2.5 , e ) 3 | b | divide(multiply(multiply(15, divide(6, 7)), inverse(subtract(const_1, divide(6, 7)))), const_60) | a train is moving at 6 / 7 of its usual speed . the train is 15 minutes too late . what is the usual time ( in hours ) for the train to complete the journey ? | "new time = d / ( 6 v / 7 ) = 7 / 6 * usual time 15 minutes represents 1 / 6 of the usual time . the usual time is 1.5 hours . the answer is b ." | a = 6 / 7
b = 15 * a
c = 6 / 7
d = 1 - c
e = 1/(d)
f = b * e
g = f / const_60
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a ) 21 , b ) 35 , c ) 39 , d ) 60 , e ) 42 | e | divide(multiply(multiply(5, 13), 3), 5) | exactly 3 / 5 of the people in the room are under the age of 21 , and exactly 5 / 13 of the people in the room are over the age of 65 . if the total number of the people in the room is greater than 50 and less than 100 , how many people in the room are under the age of 21 ? | "the total number of the people in the room must be a multiple of both 5 and 14 ( in order 3 / 5 and 5 / 14 of the number to be an integer ) , thus the total number of the people must be a multiple of lcm of 5 and 14 , which is 70 . since , the total number of the people in the room is greater than 50 and less than 100 , then there are 70 people in the room . therefore there are 3 / 5 * 70 = 42 people in the room under the age of 21 . answer : e ." | a = 5 * 13
b = a * 3
c = b / 5
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a ) 50.78 kg , b ) 49.32 kg , c ) 70.76 kg , d ) 69.15 kg , e ) 70.89 kg | c | divide(add(multiply(60, 60), multiply(70, 80)), add(60, 70)) | there are 2 sections a and b in a class , consisting of 60 and 70 students respectively . if the average weight of section a is 60 kg and that of section b is 80 kg , find the average of the whole class ? | "total weight of 60 + 70 students = 60 * 60 + 70 * 80 = 3600 + 5600 average weight of the class is = 9200 / 130 = 70.76 kg answer is c" | a = 60 * 60
b = 70 * 80
c = a + b
d = 60 + 70
e = c / d
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a ) 10 % , b ) 15 % , c ) 20 % , d ) 25 % , e ) 44 % | e | subtract(multiply(multiply(subtract(const_1, divide(20, const_100)), add(const_1, divide(80, const_100))), const_100), const_100) | a furniture store owner decided to drop the price of her recliners by 20 % to spur business . by the end of the week she had sold 80 % more recliners . what is the percentage increase of the gross ? | "say a recliner is actually worth $ 100 if she sells 100 recliners then she earns $ 10000 after the discount of 20 % , she will earn $ 80 per recliner and she sells 80 % more ie . , 180 recliners hence her sales tields 180 * 80 = $ 14400 increase in sales = 14400 - 10000 = $ 4400 so % increase = 4400 * 100 / 10000 = 44 % e is the answer" | a = 20 / 100
b = 1 - a
c = 80 / 100
d = 1 + c
e = b * d
f = e * 100
g = f - 100
|
a ) 20 , b ) 31 , c ) 9 , d ) 31 , e ) 21 | b | add(19, 12) | in a family 19 people eat only vegetarian , 9 people eat only non veg . , 12 people eat both veg and non veg . . how many people eat veg in the family ? | "total people eat veg = only veg + both veg and non veg total = 19 + 12 = 31 answer = b" | a = 19 + 12
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a ) 19 , b ) 20 , c ) 21 , d ) 22 , e ) 23 | b | multiply(divide(36, add(add(divide(25, const_100), const_1), const_1)), add(divide(25, const_100), const_1)) | two friends plan to walk along a 36 - km trail , starting at opposite ends of the trail at the same time . if friend p ' s rate is 25 % faster than friend q ' s , how many kilometers will friend p have walked when they pass each other ? | if q complete x kilometers , then p completes 1.25 x kilometers . x + 1.25 x = 36 2.25 x = 36 x = 16 then p will have have walked 1.25 * 16 = 20 km . the answer is b . | a = 25 / 100
b = a + 1
c = b + 1
d = 36 / c
e = 25 / 100
f = e + 1
g = d * f
|
a ) 12 , b ) 14 , c ) 15 , d ) 21 , e ) 25 | b | divide(divide(divide(3,675, const_3), const_3), add(1, const_4)) | for any integer k greater than 1 , the symbol k * denotes the product of all integers between 1 and k , inclusive . if k * is a multiple of 3,675 , what is the least possible value of k ? | "we basically need 5,5 , 3,7 and 7 in the number . 14 ! , has 3 , 5 , 7 , 10 , 14 now 10 = 2 x 5 14 = 2 x 7 cross check : k ! = 3675 * m ( m is a positive integer ) k ! = 3 * 5 * 5 * 7 * 7 14 ! has all the numbers above . . therefore b . . ! answer : b" | a = 3 / 675
b = a / 3
c = 1 + 4
d = b / c
|
a ) 32 , b ) 64 , c ) 48 , d ) 68 , e ) 78 | b | divide(multiply(192, 16), 48) | l . c . m of two numbers is 192 and there h . c . f is 16 . if one of them is 48 . find the other | explanation : product of two numbers = product of their l . c . m and h . c . f 48 x a = 192 x 16 a = ( 192 x 16 ) / 48 = 64 answer : option b | a = 192 * 16
b = a / 48
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a ) 378 , b ) 277 , c ) 297 , d ) 267 , e ) 130 | e | subtract(multiply(const_10, multiply(const_3, power(const_2, const_3))), multiply(subtract(subtract(multiply(3.4, add(const_4, const_1)), add(const_4, const_1)), const_1), const_10)) | at 3.40 , the hour hand and the minute hand of a clock form an angle of | sol : use formula θ = ∣ ∣ ∣ 30 h − 112 m ∣ ∣ ∣ θ = | 30 h − 112 m | angle = 30 × 3 – 11 / 2 × 40 = 90 – 220 = 130 ° answer : e | a = 2 ** 3
b = 3 * a
c = 10 * b
d = 4 + 1
e = 3 * 4
f = 4 + 1
g = e - f
h = g - 1
i = h * 10
j = c - i
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a ) 3 , b ) 4 , c ) 6 , d ) 9 , e ) 5 | e | subtract(const_12, divide(divide(multiply(divide(14000, 50000), multiply(add(20000, 25000), const_12)), subtract(const_1, divide(14000, 50000))), 30000)) | x and y started a business with capitals rs . 20000 and rs . 25000 . after few months z joined them with a capital of rs . 30000 . if the share of z in the annual profit of rs . 50000 is rs . 14000 , then after how many months from the beginning did z join ? | investments of x , y and z respectively are rs . 20000 , rs . 25000 and rs . 30000 let investment period of z be x months . ratio of annual investments of x , y and z is ( 20000 * 12 ) : ( 25000 * 12 ) : ( 30000 * x ) = 240 : 300 : 30 x = 8 : 10 : x the share of z in the annual profit of rs . 50000 is rs . 14000 . = > [ x / ( 18 + x ) ] 50000 = 14000 = > [ x / ( 18 + x ) ] 25 = 7 = > 25 x = 7 x + ( 18 * 7 ) = > x = 7 months . z joined the business after ( 12 - 7 ) months . i . e . , 5 months . answer : e | a = 14000 / 50000
b = 20000 + 25000
c = b * 12
d = a * c
e = 14000 / 50000
f = 1 - e
g = d / f
h = g / 30000
i = 12 - h
|
a ) 10 , b ) 11 , c ) 12 , d ) 13 , e ) 14 | a | divide(multiply(18, 15), 24) | if 18 men take 15 days to to complete a job , in how many days can 24 men finish that work ? | ans . 10 days | a = 18 * 15
b = a / 24
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a ) 22 1 / 9 kmph , b ) 22 8 / 2 kmph , c ) 22 1 / 8 kmph , d ) 22 1 / 2 kmph , e ) 22 1 / 4 kmph | d | divide(subtract(divide(100, 10), divide(75, 15)), const_2) | a boat goes 100 km downstream in 10 hours , and 75 m upstream in 15 hours . the speed of the stream is ? | 100 - - - 10 ds = 10 ? - - - - 1 75 - - - - 15 us = 5 ? - - - - - 1 s = ( 10 - 5 ) / 2 = 2 21 / 2 kmph answer : d | a = 100 / 10
b = 75 / 15
c = a - b
d = c / 2
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a ) 3 , b ) 4 , c ) 5 , d ) 6 , e ) 8 | d | multiply(subtract(subtract(sqrt(225), sqrt(121)), const_1), const_2) | if k is an integer and 121 < k ^ 2 < 225 , then k can have at most how many values ? | given k is an integer 121 < k ^ 2 < 225 11 < | k | < 15 k = - 12 , - 13 , - 1412 , 1314 answer : d | a = math.sqrt(225)
b = math.sqrt(121)
c = a - b
d = c - 1
e = d * 2
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a ) 5 , 500,000 , b ) 2 , 800,000 , c ) 55,000 , d ) 28,000 , e ) 280 | b | subtract(add(multiply(multiply(divide(volume_cube(100), const_10), 2.5), 2.5), multiply(multiply(divide(volume_cube(100), const_10), multiply(const_2, 3)), 3)), volume_cube(100)) | a specialized type of sand consists of 40 % mineral x by volume and 60 % mineral y by volume . if mineral x weighs 2.5 grams per cubic centimeter and mineral y weighs 3 grams per cubic centimeter , how many grams does a cubic meter of specialized sand combination weigh ? ( 1 meter = 100 centimeters ) | "let the volume be 1 m ^ 3 = 1 m * 1 m * 1 m = 100 cm * 100 cm * 100 cm = 1 , 000,000 cm ^ 3 by volume 40 % is x = 400,000 cm ^ 3 60 % is y = 600,000 cm ^ 3 by weight , in 1 cm ^ 3 , x is 2.5 gms in 400,000 cm ^ 3 , x = 2.5 * 400,000 = 1 , 000,000 grams in 1 cm ^ 3 , y is 3 gms in 600,000 cm ^ 3 , y = 3 * 600,000 = 1 , 800,000 gms total gms in 1 m ^ 3 = 1 , 000,000 + 1 , 800,000 = 2 , 800,000 answer : b" | a = volume_cube / (
b = a * 10
c = b * 2
d = c + 2
e = volume_cube / (
f = e * 10
g = 2 * 3
h = f * g
i = d - h
|
a ) rs . 120 , b ) rs . 160 , c ) rs . 240 , d ) rs . 360 , e ) none | d | subtract(subtract(multiply(divide(2040, const_10), const_2), const_12), const_12) | a sum of rs . 2040 has been divided among a , b and c such that a gets of what b gets and b gets of what c gets . b ’ s share is : | "explanation let c ’ s share = rs . x then , b ’ s share = rs . x / 4 , a ’ s share = rs . ( 2 / 3 x x / 4 ) = rs . x / 6 = x / 6 + x / 4 + x = 2040 = > 17 x / 12 = 2040 = > 2040 x 12 / 17 = rs . 1440 hence , b ’ s share = rs . ( 1440 / 4 ) = rs . 360 . answer d" | a = 2040 / 10
b = a * 2
c = b - 12
d = c - 12
|
a ) 1 hr , b ) 2 hrs , c ) 3 hrs , d ) 4 hrs , e ) 5 hrs | a | divide(45, add(40, 5)) | a boat can travel with a speed of 40 km / hr in still water . if the speed of the stream is 5 km / hr , find the time taken by the boat to go 45 km downstream . | "speed downstream = ( 40 + 5 ) km / hr = 45 km / hr . time taken to travel 45 km downstream = 45 / 45 hrs = 1 hrs . answer : a" | a = 40 + 5
b = 45 / a
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a ) 40 % , b ) 55 % , c ) 57 % , d ) 60 % , e ) 67.2 % | e | multiply(divide(11628, add(add(1036, 4636), 11628)), const_100) | 3 candidates in an election and received 1036 , 4636 and 11628 votes respectively . what % of the total votes did the winning candidate gotin that election ? | total number of votes polled = ( 1036 + 4636 + 11628 ) = 17300 so , required percentage = 11628 / 17300 * 100 = 67.2 % e | a = 1036 + 4636
b = a + 11628
c = 11628 / b
d = c * 100
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a ) 3377 , b ) 2678 , c ) 5460 , d ) 1976 , e ) 5253 | e | divide(multiply(divide(multiply(5000, add(const_100, 2)), const_100), add(const_100, 3)), const_100) | find the amount on rs . 5000 in 2 years , the rate of interest being 2 % per first year and 3 % for the second year ? | "5000 * 102 / 100 * 103 / 100 = > 5253 answer : e" | a = 100 + 2
b = 5000 * a
c = b / 100
d = 100 + 3
e = c * d
f = e / 100
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a ) $ 80,000 , b ) $ 130,000 , c ) $ 260,000 , d ) $ 290,000 , e ) $ 320,000 | c | divide(subtract(subtract(multiply(multiply(add(60, 30), const_1000), const_100), multiply(30, multiply(add(60, 30), const_1000))), multiply(multiply(multiply(divide(30, const_2), 30), const_1000), 60)), 30) | in plutarch enterprises , 60 % of the employees are marketers , 30 % are engineers , and the rest are managers . marketers make an average salary of $ 50,000 a year , and engineers make an average of $ 80,000 . what is the average salary for managers if the average for all employees is also $ 80,000 ? | "for sake of ease , let ' s say there are 10 employees : 6 marketers , 3 engineers , and 1 manager . average company salary * number of employees = total company salary > > > $ 80,000 * 10 = $ 800,000 subtract the combined salaries for the marketers ( 6 * $ 50,000 ) and the engineers ( 3 * $ 80,000 ) > > > $ 800,000 - $ 300,000 - $ 240,000 = $ 260,000 . the correct answer is c ." | a = 60 + 30
b = a * 1000
c = b * 100
d = 60 + 30
e = d * 1000
f = 30 * e
g = c - f
h = 30 / 2
i = h * 30
j = i * 1000
k = j * 60
l = g - k
m = l / 30
|
a ) 16 , b ) 20 , c ) 17 , d ) 12 , e ) 18 | a | divide(0.04, divide(0.25, const_100)) | find the missing figures : 0.25 % of ? = 0.04 | "let 0.25 % of x = 0.04 . then , 0.25 * x / 100 = 0.04 x = [ ( 0.04 * 100 ) / 0.25 ] = 16 . answer is a ." | a = 0 / 25
b = 0 / 4
|
a ) 317608 , b ) 327608 , c ) 337608 , d ) 427608 , e ) 357608 | d | add(subtract(subtract(const_1000, const_10), multiply(multiply(const_10, multiply(6, 6)), multiply(const_4, const_2))), const_10) | how many 6 digit number contain number 4 ? | "total 6 digit no . = 9 * 10 * 10 * 10 * 10 * 10 = 900000 not containing 4 = 8 * 9 * 9 * 9 * 9 * 9 = 472392 total 6 digit number contain 4 = 900000 - 472392 = 427608 answer : d" | a = 1000 - 10
b = 6 * 6
c = 10 * b
d = 4 * 2
e = c * d
f = a - e
g = f + 10
|
a ) 6 , b ) 6.25 , c ) 5.75 , d ) 7.5 , e ) 8 | c | divide(subtract(262, multiply(3.2, 10)), 40) | cricket match is conducted in us . the run rate of a cricket game was only 3.2 in first 10 over . what should be the run rate in the remaining 40 overs to reach the target of 262 runs ? | "required run rate = 262 - ( 3.2 x 10 ) = 230 = 5.75 40 40 c" | a = 3 * 2
b = 262 - a
c = b / 40
|
a ) 76.55 , b ) 36.35 , c ) 46.15 , d ) 16.05 , e ) 20 | b | divide(add(multiply(36, 40), subtract(subtract(40, const_2), 20)), 40) | the mean of 40 observations was 36 . it was found later that an observation 34 was wrongly taken as 20 . the corrected new mean is | "explanation : correct sum = ( 36 * 40 + 34 - 20 ) = 1454 correct mean = = 1454 / 40 = 36.35 answer : b" | a = 36 * 40
b = 40 - 2
c = b - 20
d = a + c
e = d / 40
|
a ) 1000 , b ) 1312.5 , c ) 1400 , d ) 1600 , e ) 1625 | b | divide(add(divide(multiply(300, const_100), 40), 300), divide(80, const_100)) | a small pool filled only with water will require an additional 300 gallons of water in order to be filled to 80 % of its capacity . if pumping in these additional 300 gallons of water will increase the amount of water in the pool by 40 % , what is the total capacity of the pool in gallons ? | "300 gallons of water increases capacity by 40 % that means 40 % is 300 gallons , so 100 % would be = 300 * 100 / 40 = 750 gallons now 750 + 300 gallons is 80 % capacity of tank . so 100 % capacity would be = 1050 * 100 / 80 = 1312.5 b is the answer" | a = 300 * 100
b = a / 40
c = b + 300
d = 80 / 100
e = c / d
|
a ) 25 kmph , b ) 30 kmph , c ) 50 kmph , d ) 36 kmph , e ) 37 kmph | d | multiply(10, const_3_6) | the speed of a car is 10 m / s . what is the its speed in kmph . | explanation : m / sec to km / hr conversion : x m / sec = [ x x ( 18 / 5 ) ] km / hr 10 x ( 18 / 5 ) 36 kmph answer : option d | a = 10 * const_3_6
|
a ) 32.84 , b ) 22.84 , c ) 30.58 , d ) 24.84 , e ) 30.84 | c | divide(multiply(139.00, add(divide(const_1, 10), const_1)), 5) | total dinning bill of 5 people was $ 139.00 and 10 % tip divided the bill evenly ? what is the bill amount each person shared . | "dinner bill of 5 person = 139 + 10 % tip so , 10 % of 139 = ( 139 * 10 ) / 100 = 13.9 so , the actual total amount = 139 + 13.9 = $ 152.9 so per head bill = 152.9 / 5 = $ 30.58 answer : c" | a = 1 / 10
b = a + 1
c = 139 * 0
d = c / 5
|
a ) 6 / 25 , b ) 11 / 50 , c ) 14 / 75 , d ) 23 / 100 , e ) 31 / 150 | c | add(multiply(subtract(const_1, divide(5, 6)), subtract(const_1, divide(3, 5))), multiply(subtract(const_1, divide(4, 5)), divide(3, 5))) | at a monthly meeting , 3 / 5 of the attendees were males and 4 / 5 of the male attendees arrived on time . if 5 / 6 of the female attendees arrived on time , what fraction of the attendees at the monthly meeting did not arrive on time ? | "males who did not arrive on time are 1 / 5 * 3 / 5 = 3 / 25 of the attendees . females who did not arrive on time are 1 / 6 * 2 / 5 = 1 / 15 of the attendees . the fraction of all attendees who did not arrive on time is 3 / 25 + 1 / 15 = 14 / 75 the answer is c ." | a = 5 / 6
b = 1 - a
c = 3 / 5
d = 1 - c
e = b * d
f = 4 / 5
g = 1 - f
h = 3 / 5
i = g * h
j = e + i
|
a ) 0 , b ) 1 , c ) 2 , d ) 3 , e ) 4 | c | subtract(subtract(const_10, add(add(const_1, const_2), const_3)), const_2) | the sum of 7 consecutive integers is 980 . how many of them are prime ? | the middle number is 140 and the seven numbers are 137 , 138 , 139 , · · · , 143 . now 138 , 140 , and 142 are even , 141 is divisible by 3 , and 143 - by 11 . the remaining numbers 137 and 139 are prime ( it is easy to check that they are not divisible by 23 , 57 and 11 ) . correct answer c | a = 1 + 2
b = a + 3
c = 10 - b
d = c - 2
|
a ) 0 , b ) 1 , c ) 2 , d ) 7 , e ) 4 | d | divide(log(7), log(power(8, 8))) | if n = 8 ^ 8 – 7 , what is the units digit of n ? | "8 ^ 8 - 8 = 8 ( 8 ^ 7 - 1 ) = = > 8 ( 2 ^ 21 - 1 ) last digit of 2 ^ 21 is 2 based on what explanation livestronger is saying . 2 ^ 24 - 1 yields 2 - 1 = 1 as the unit digit . now on multiply this with 7 , we get unit digit as 7 answer : d" | a = math.log(7)
b = 8 ** 8
c = math.log(b)
d = a / c
|
a ) 5 , b ) 4 , c ) 3 , d ) 2 , e ) 1 | b | multiply(const_4, const_1) | how many prime numbers between 1 and 100 are factors of 210 ? | factor of 210 = 2 * 3 * 5 * 7 - - - 4 prime numbers b | a = 4 * 1
|
a ) 80 % , b ) 105 % , c ) 96 % , d ) 124.2 % , e ) 138 % | c | multiply(divide(multiply(subtract(const_1, divide(20, const_100)), divide(12, const_100)), divide(10, const_100)), const_100) | in 1998 the profits of company n were 10 percent of revenues . in 1999 , the revenues of company n fell by 20 percent , but profits were 12 percent of revenues . the profits in 1999 were what percent of the profits in 1998 ? | "0,096 r = x / 100 * 0.1 r answer c" | a = 20 / 100
b = 1 - a
c = 12 / 100
d = b * c
e = 10 / 100
f = d / e
g = f * 100
|
a ) 4 , b ) 3 , c ) 2 , d ) 1 , e ) 0 | d | subtract(multiply(11, divide(subtract(multiply(2, 3), 2), subtract(multiply(6, 3), multiply(2, 7)))), add(multiply(7, divide(subtract(multiply(2, 3), 2), subtract(multiply(6, 3), multiply(2, 7)))), 3)) | when positive integer x is divided by 7 , the quotient is y and the remainder is 3 . when 2 x is divided by 6 , the quotient is 3 y and the remainder is 2 . what is the value of 11 y – x ? | "( 1 ) x = 7 y + 3 ( 2 ) 2 x = 18 y + 2 ( 2 ) - ( 1 ) : x = 11 y - 1 11 y - x = 1 the answer is d ." | a = 2 * 3
b = a - 2
c = 6 * 3
d = 2 * 7
e = c - d
f = b / e
g = 11 * f
h = 2 * 3
i = h - 2
j = 6 * 3
k = 2 * 7
l = j - k
m = i / l
n = 7 * m
o = n + 3
p = g - o
|
a ) 0 , b ) 5 , c ) 4 , d ) 3 , e ) 2 | a | divide(9, add(1, 9)) | n is a positive integer . when n + 1 is divided by 9 , the remainder is 1 . what is the remainder when n is divided by 9 ? | "n + 1 = 9 a + 1 i . e . n + 1 = 10 , 19 , 28 , 37 , . . . etc . i . e . n = 9 , 18 , 27 , 36 , . . . etc . when n is divided by 9 remainder is always 0 answer : a" | a = 1 + 9
b = 9 / a
|
a ) 17 , b ) 25 , c ) 24 , d ) 22 , e ) 20 | a | subtract(subtract(subtract(23, 2), const_1), const_1) | how many positive integers less than 23 are prime numbers , odd multiples of 5 , or the sum of a positive multiple of 2 and a positive multiple of 4 ? | "8 prime numbers less than 28 : { 2 , 3 , 5 , 7 , 11 , 13 , 17 , 19 } 2 odd multiples of 5 : { 5 , 15 } 9 numbers which are the sum of a positive multiple of 2 and a positive multiple of 4 : { 6 , 8 , 10 , 12 , 14 , 16 , 18 , 20 , 22 } notice , that 5 is in two sets , thus total # of integers satisfying the given conditions is 8 + 1 + 9 - 1 = 17 . answer : a ." | a = 23 - 2
b = a - 1
c = b - 1
|
['a ) 8', 'b ) 9', 'c ) 10', 'd ) 11', 'e ) 12'] | e | multiply(const_3, subtract(power(125, const_0_33), const_1)) | we need to carve out 125 identical cubes from a cube . what is the minimum number of cuts needed ? | total no . of cubes = n ^ 3 here n ^ 3 = 125 which makes n = 5 , also minimum no . of cuts required = 3 ( n - 1 ) hence , 3 ( 5 - 1 ) = 12 cuts . answer : e | a = 125 ** const_0_33
b = a - 1
c = 3 * b
|
a ) 57 : 11 , b ) - 57 : 11 , c ) 11 : 10 , d ) - 11 : 10 , e ) - 1 : 10 | b | divide(add(multiply(5, 3), multiply(7, 6)), subtract(3, multiply(2, 7))) | if a : b : : 3 : 7 , then what is ( 5 a + 6 b ) : ( a - 2 b ) ? | a / b = 3 / 7 dividing numerator & denominator of ' ( 5 a + 6 b ) / ( a - 2 b ) ' by b , [ 5 ( a / b ) + 6 ] / [ ( a / b ) - 2 ] = [ 5 * ( 3 / 7 ) + 6 ] / [ ( 3 / 7 ) - 2 ] = - 57 / 11 answer : b | a = 5 * 3
b = 7 * 6
c = a + b
d = 2 * 7
e = 3 - d
f = c / e
|
a ) 5.5 % , b ) 8.3 % , c ) 11.6 % , d ) 14.2 % , e ) 17.5 % | b | multiply(divide(const_100, add(add(multiply(multiply(const_4, const_100), const_4), const_100), const_100)), const_100) | a block of wood has dimensions 10 cm x 10 cm x 50 cm . the block is painted red and then cut evenly at the 25 cm mark , parallel to the sides , to form two rectangular solids of equal volume . what percentage of the surface area of each of the new solids is not painted red ? | "the area of each half is 100 + 4 ( 250 ) + 100 = 1200 the area that is not painted is 100 . the fraction that is not painted is 100 / 1200 = 1 / 12 = 8.3 % the answer is b ." | a = 4 * 100
b = a * 4
c = b + 100
d = c + 100
e = 100 / d
f = e * 100
|
a ) 145 , b ) 90 , c ) 175 , d ) 160 , e ) 130 | b | multiply(divide(30, 20), const_60) | a mobile battery in 1 hour charges to 20 percent . how much time ( in minute ) will it require more to charge to 30 percent . | 1 hr = 20 percent . thus 15 min = 5 percent . now to charge 30 percent 90 min . answer : b | a = 30 / 20
b = a * const_60
|
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