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 |
|---|---|---|---|---|---|
a ) 11 , b ) 15 , c ) 20 , d ) 38 , e ) 56 | a | add(add(floor(power(210, const_0_33)), const_1), floor(power(210, const_0_33))) | the product of 3 consecutive numbers is 210 . then the sum of the smallest two numbers is ? | product of three numbers = 210 210 = 2 * 3 * 5 * 7 = 5 * 6 * 7 . so , the three numbers are 5 , 6 and 7 . and sum of smallest of these two = 5 + 6 = 11 . answer : option a | a = 210 ** const_0_33
b = math.floor(a)
c = b + 1
d = 210 ** const_0_33
e = math.floor(d)
f = c + e
|
a ) 3,955 , b ) 3,925 , c ) 3,956 , d ) 3,926 , e ) 3,915 | c | subtract(658,805, add(add(multiply(const_2, const_100), multiply(add(const_3, const_4), const_10)), const_2)) | how many integers between 263,205 and 658,805 have tens digit 1 and units digit 3 ? | "there is one number in hundred with 1 in the tens digit and 3 in the units digit : 13 , 113 , 213 , 313 , . . . the difference between 263,205 and is 658,805 - 263205 = 395,600 - one number per each hundred gives 133,900 / 100 = 3,956 answer : c ." | a = 2 * 100
b = 3 + 4
c = b * 10
d = a + c
e = d + 2
f = 658 - 805
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a ) 1 kmph , b ) 6 kmph , c ) 7 kmph , d ) 14 kmph , e ) 9 kmph | d | divide(subtract(36, 8), const_2) | a man can row his boat with the stream at 36 km / h and against the stream in 8 km / h . the man ' s rate is ? | "explanation : ds = 36 us = 8 s = ? s = ( 36 - 8 ) / 2 = 14 kmph answer : d" | a = 36 - 8
b = a / 2
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a ) 38 , b ) 27 , c ) 99 , d ) 17 , e ) 80 | e | subtract(multiply(75, 6), multiply(74, 5)) | ashok secured average of 75 marks in 6 subjects . if the average of marks in 5 subjects is 74 , how many marks did he secure in the 6 th subject ? | "explanation : number of subjects = 6 average of marks in 6 subjects = 75 therefore total marks in 6 subjects = 75 * 6 = 450 now , no . of subjects = 5 total marks in 5 subjects = 74 * 5 = 370 therefore marks in 6 th subject = 450 – 370 = 80 answer : e" | a = 75 * 6
b = 74 * 5
c = a - b
|
a ) a ) 3820 , b ) b ) 930 , c ) c ) 9309 , d ) d ) 3900 , e ) e ) 5625 | e | multiply(multiply(subtract(add(80, 60), 15), 15), 3) | a rectangular lawn of dimensions 80 m * 60 m has two roads each 15 m wide running in the middle of the lawn , one parallel to the length and the other parallel to the breadth . what is the cost of traveling the two roads at rs . 3 per sq m ? | "explanation : area = ( l + b – d ) d ( 80 + 60 – 15 ) 15 = > 1875 m 2 1875 * 3 = rs . 5625 answer : option e" | a = 80 + 60
b = a - 15
c = b * 15
d = c * 3
|
['a ) 55', 'b ) 70', 'c ) 57', 'd ) 58', 'e ) none of these'] | b | divide(rectangle_perimeter(90, 50), 4) | a rectangular plot measuring 90 metres by 50 metres is to be enclosed by wire fencing . if the poles of the fence are kept 4 metres apart , how many poles will be needed ? | solution perimeter of the plot = 2 ( 90 + 50 ) = 280 m . ∴ number of poles = [ 280 / 4 ] = 70 m answer b | a = rectangle_perimeter / (
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['a ) 10', 'b ) 11', 'c ) 12', 'd ) 13', 'e ) none of them'] | c | divide(1848, circle_area(divide(14, const_2))) | if the capacity of a cylindrical tank is 1848 m 3 and the diameter of its base is 14 m , then find the depth of the tank . | let the depth of the tank be h meters . then , ∏ x 72 x h = 1848 h = ( 1848 x ( 7 / 22 ) x ( 1 / 49 ) = 12 m answer is c | a = 14 / 2
b = 1848 / circle_area
|
a ) 800 , b ) 125 , c ) 288 , d ) 266 , e ) 121 | a | multiply(multiply(160, const_0_2778), 18) | if a train , travelling at a speed of 160 kmph , crosses a pole in 18 sec , then the length of train is ? | "d = 160 * 5 / 18 * 18 = 800 m answer : a" | a = 160 * const_0_2778
b = a * 18
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a ) rs . 234.80 , b ) rs . 334.80 , c ) rs . 434.80 , d ) rs . 534.80 , e ) none of these | b | multiply(divide(45, const_100), add(multiply(25, 12), add(multiply(const_2, multiply(25, 6)), multiply(multiply(12, 6), const_2)))) | a tank is 25 m long 12 m wide and 6 m deep . the cost of plastering its walls and bottom at 45 paise per sq m is | "explanation : area to be plastered = [ 2 ( l + b ) ã — h ] + ( l ã — b ) = [ 2 ( 25 + 12 ) ã — 6 ] + ( 25 ã — 12 ) = 744 sq m cost of plastering = 744 ã — ( 45 / 100 ) = rs . 334.80 answer : b" | a = 45 / 100
b = 25 * 12
c = 25 * 6
d = 2 * c
e = 12 * 6
f = e * 2
g = d + f
h = b + g
i = a * h
|
a ) 6 , b ) 15 , c ) 17 , d ) 18 , e ) 2 | b | divide(subtract(divide(120, 2), divide(60, 2)), const_2) | a man rows his boat 120 km downstream and 60 km upstream , taking 2 hours each time . find the speed of the stream ? | "speed downstream = d / t = 120 / ( 2 ) = 60 kmph speed upstream = d / t = 60 / ( 2 ) = 30 kmph the speed of the stream = ( 60 - 30 ) / 2 = 15 kmph answer : b" | a = 120 / 2
b = 60 / 2
c = a - b
d = c / 2
|
a ) 1 / 5 , b ) 11 / 22 , c ) 81 / 724 , d ) 91 / 946 , e ) 101 / 987 | d | multiply(divide(14, add(add(14, 20), 10)), divide(subtract(14, const_1), subtract(add(add(14, 20), 10), const_1))) | there are 14 slate rocks , 20 pumice rocks , and 10 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 ? | "14 / 44 * 13 / 43 = 91 / 946 the answer is d ." | a = 14 + 20
b = a + 10
c = 14 / b
d = 14 - 1
e = 14 + 20
f = e + 10
g = f - 1
h = d / g
i = c * h
|
a ) 63 years , b ) 60 years , c ) 50 years , d ) 53 years , e ) 46 years | d | multiply(divide(150, add(const_10, const_10)), const_12) | my grandson is about as many days as my son in weeks , and my grandson is as many months as i am in years . my grandson , my son and i together are 150 years . can you tell my son age in years ? | let m be my age in years . if s is my son ' s age in years , then my son is 52 s weeks old . if g is my grandson ' s age in years , then my grandson is 365 g days old . thus , 365 g = 52 s . since my grandson is 12 g months old , 12 g = m . since my grandson , my son and i together are 150 years , g + s + m = 100 . the... | a = 10 + 10
b = 150 / a
c = b * 12
|
a ) 20 % , b ) 40 % , c ) 50 % , d ) 60 % , e ) 75 % | c | subtract(const_100, subtract(subtract(const_100, 20), 20)) | a merchant sells an item at a 20 % discount , but still makes a gross profit of 20 percent of the cost . what percent t of the cost would the gross profit on the item have been if it had been sold without the discount ? | "let the market price of the product is mp . let the original cost price of the product is cp . selling price ( discounted price ) = 100 % of mp - 20 % mp = 80 % of mp . - - - - - - - - - - - - - - - - ( 1 ) profit made by selling at discounted price = 20 % of cp - - - - - - - - - - - - - - ( 2 ) apply the formula : pr... | a = 100 - 20
b = a - 20
c = 100 - b
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a ) 122.9 m , b ) 127.5 m . , c ) 191.25 m , d ) 222.9 m , e ) 12289 m | c | subtract(1000, divide(multiply(subtract(1000, 100), subtract(800, 100)), 800)) | in a race of 1000 m , a can beat by 100 m , in a race of 800 m , b can beat c by 100 m . by how many meters will a beat c in a race of 900 m ? | "when a runs 1000 m , b runs 900 m and when b runs 800 m , c runs 700 m . when b runs 900 m , distance that c runs = ( 900 * 700 ) / 800 = 6300 / 8 = 787.5 m . in a race of 1000 m , a beats c by ( 1000 - 787.5 ) = 212.5 m to c . in a race of 900 m , the number of meters by which a beats c = ( 900 * 212.5 ) / 1000 = 191... | a = 1000 - 100
b = 800 - 100
c = a * b
d = c / 800
e = 1000 - d
|
a ) 3377 , b ) 2688 , c ) 2688 , d ) 8436 , e ) 1268 | d | multiply(7500, multiply(divide(add(const_100, 4), const_100), divide(add(const_100, 4), const_100))) | if rs . 7500 are borrowed at c . i at the rate of 4 % per annum , then after 3 years the amount to be paid is ? | a = 7500 ( 26 / 25 ) ^ 3 = 8436 answer : d | a = 100 + 4
b = a / 100
c = 100 + 4
d = c / 100
e = b * d
f = 7500 * e
|
a ) 54 , b ) 66 , c ) 68 , d ) 60 , e ) 63 | e | multiply(21, divide(divide(36, 2), 6)) | two friends decide to get together ; so they start riding bikes towards each other . they plan to meet halfway . each is riding at 6 mph . they live 36 miles apart . one of them has a pet carrier pigeon and it starts flying the instant the friends start traveling . the pigeon flies back and forth at 21 mph between the ... | "e 63 it takes 3 hours for the friends to meet ; so the pigeon flies for 3 hours at 21 mph = 63 miles" | a = 36 / 2
b = a / 6
c = 21 * b
|
a ) 50 , b ) 40 , c ) 60 , d ) 80 , e ) 70 | d | divide(400, add(divide(400, const_100), const_1)) | the sum of number of boys and girls in a school is 400 . if the number of boys is x , then the number of girls becomes x % of the total number of students . the number of boys is ? | "we have x + x % of 400 = 400 x + x / 100 * 400 = 400 5 * x = 400 x = 80 answer is d" | a = 400 / 100
b = a + 1
c = 400 / b
|
a ) 27 % , b ) 29 % , c ) 31 % , d ) 33 % , e ) 35 % | c | multiply(subtract(const_1, multiply(add(divide(15, const_100), const_1), divide(60, const_100))), const_100) | a customer bought a product at the shop . however , the shopkeeper increased the price of the product by 15 % so that the customer could not buy the required amount of the product . the customer managed to buy only 60 % of the required amount . what is the difference in the amount of money that the customer paid for th... | "let x be the amount of money paid for the first purchase . the second time , the customer paid 0.6 ( 1.15 x ) = 0.69 x . the difference is 31 % . the answer is c ." | a = 15 / 100
b = a + 1
c = 60 / 100
d = b * c
e = 1 - d
f = e * 100
|
a ) 100 , b ) 240 , c ) 120 , d ) 200 , e ) 150 | b | multiply(12, 30) | the h . c . f . of two numbers is 12 and their l . c . m . is 600 . if one of the number is 30 , find the other ? | "other number = 12 * 600 / 30 = 240 answer is b" | a = 12 * 30
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a ) 1 / 2 , b ) 2 , c ) 1 / 3 , d ) 3 , e ) 1 / 6 | e | sqrt(divide(1, 36)) | if xy = 1 , x / y = 36 , for positive numbers x and y , y = ? | "very easy question . 2 variables and 2 easy equations . xy = 1 - - - > x = 1 / y - ( i ) x / y = 36 - - - > replacing ( i ) here - - - > 1 / ( y ^ 2 ) = 36 - - - > y ^ 2 = 1 / 36 - - - > y = 1 / 6 or - 1 / 6 the question states that x and y are positive integers . therefore , y = 1 / 6 is the answer . answer e ." | a = 1 / 36
b = math.sqrt(a)
|
a ) 14 m , b ) 24 m , c ) 28 m , d ) 40 m , e ) none of the above | c | multiply(multiply(divide(divide(multiply(divide(88, 1000), add(const_3, const_4)), const_2), add(multiply(const_10, const_2), const_2)), const_1000), const_2) | for covering 88 km a wheel revolve 1000 times . what is the radius of wheel ? | distance travel in 1 round = 88000 / 1000 m = 88 m perimeter = 88 m , 2 π r = 882 r = [ 88 * 7 / 22 ] = 28 m hence , diameter = 28 m answer c | a = 88 / 1000
b = 3 + 4
c = a * b
d = c / 2
e = 10 * 2
f = e + 2
g = d / f
h = g * 1000
i = h * 2
|
a ) 104 kmph , b ) 176 kmph , c ) 298 kmph , d ) 186 kmph , e ) 107 kmph | e | divide(642, 6) | a car covers a distance of 642 km in 6 ½ hours . find its speed ? | 642 / 6 = 107 kmph answer : e | a = 642 / 6
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a ) 6 , b ) 6.25 , c ) 7 , d ) 7.5 , e ) 10 | e | divide(multiply(18, 80), const_100) | a can complete a certain job in 18 days . b is 80 % more efficient than a . in how many days can b complete the same job ? | "let , total work unit = 180 units a can finish in 18 days = 180 unit work i . e . a can finish in 1 days = 10 unit work i . e . b can finish in 1 days = 10 + ( 80 / 100 ) * 10 = 18 unit work days in which b will complete the work alone = 180 / 18 = 10 days answer : option e" | a = 18 * 80
b = a / 100
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a ) $ 100 , b ) $ 250 , c ) $ 300 , d ) $ 200 , e ) $ 180 | c | divide(multiply(divide(multiply(18, 12), subtract(18, 12)), const_100), 12) | i sold a book at a profit of 12 % . had i sold it for $ 18 more , 18 % would have been gained . find the cost price ? | "118 % of cost - 112 % of cost = $ 18 6 % of cost = $ 18 cost = 18 * 100 / 6 = $ 300 answer is c" | a = 18 * 12
b = 18 - 12
c = a / b
d = c * 100
e = d / 12
|
a ) 9.75 , b ) 5.75 , c ) 8.75 , d ) 6.75 , e ) 5.15 | c | multiply(divide(21, const_60), add(20, 5)) | the speed of a boat in still water is 20 km / hr and the rate of current is 5 km / hr . the distance travelled downstream in 21 minutes is : | "explanation : speed downstream = ( 20 + 5 ) kmph = 25 kmph distance travelled = ( 25 * ( 21 / 60 ) ) km = 8.75 km . answer : c" | a = 21 / const_60
b = 20 + 5
c = a * b
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a ) 20 % , b ) 2 / 8 % , c ) 2 / 1 % , d ) 1 / 3 % , e ) 2 / 7 % | a | multiply(divide(25, add(const_100, 25)), const_100) | if the price of an article went up by 25 % , then by what percent should it be brought down to bring it back to its original price ? | let the price of the article be rs . 100 . 25 % of 100 = 25 . new price = 100 + 25 = rs . 125 required percentage = ( 125 - 100 ) / 125 * 100 = 25 / 125 * 100 = 20 % . answer : a | a = 100 + 25
b = 25 / a
c = b * 100
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a ) 5 , b ) 10 , c ) 15 , d ) 20 , e ) none of them | b | multiply(const_100, divide(subtract(subtract(1, divide(1, const_100)), divide(36, 40)), divide(36, 40))) | a retailer buys 40 pens at the market price of 36 pens from a wholesaler , if he sells these pens giving a discount of 1 % , what is the profit % ? | "let the market price of each pen be rs 1 then , c . p of 40 pens = rs 36 s . p of 40 pens = 99 % of rs 40 = rs 39.60 profit % = ( ( 3.60 * 100 ) / 36 ) % = 10 % answer is b ." | a = 1 / 100
b = 1 - a
c = 36 / 40
d = b - c
e = 36 / 40
f = d / e
g = 100 * f
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a ) 22754.3 , b ) 22254.2 , c ) 25754.2 , d ) 22753.2 , e ) 22254.2 | a | multiply(multiply(multiply(divide(multiply(add(const_10, const_1), const_2), add(const_3, const_4)), const_2), 3.62), const_1000) | given a circular wheel of 3.62 m radius how many revolutions will the will make to travel a distance of 1 km ? | 2 * 22 / 7 * 3.62 * x = 22754.3 x = 1000 answer : a | a = 10 + 1
b = a * 2
c = 3 + 4
d = b / c
e = d * 2
f = e * 3
g = f * 1000
|
a ) 2 , b ) 3 , c ) 5 , d ) 7 , e ) 8 | b | subtract(427398, multiply(floor(divide(427398, 15)), 15)) | find the least number must be subtracted from 427398 so that remaining no . is divisible by 15 ? | "on dividing 427398 by 15 we get the remainder 3 , so 3 should be subtracted b" | a = 427398 / 15
b = math.floor(a)
c = b * 15
d = 427398 - c
|
a ) 77 % , b ) 78 % , c ) 79 % , d ) 80 % , e ) 81 % | c | divide(add(multiply(15, 73), multiply(10, 88)), 25) | if 15 students in a class average 73 % on an exam and 10 students average 88 % on the same exam , what is the average in percent for all 25 students ? | "( 15 * 73 + 10 * 88 ) / 25 = 79 % the answer is c ." | a = 15 * 73
b = 10 * 88
c = a + b
d = c / 25
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a ) 4 % increase , b ) 17 % increase , c ) 10 % decrease , d ) 6 % increase , e ) none of these | b | subtract(divide(multiply(subtract(const_100, 10), add(const_100, 30)), const_100), const_100) | if the price of a tv is first decreased by 10 % and then increased by 30 % , then the net change in the price will be : | "explanation : solution : let the original price be rs . 100 . new final price = 130 % of ( 10 % of 100 ) = rs . 130 / 100 * 90 / 100 * 100 = rs . 117 . . ' . increase = 17 % answer : b" | a = 100 - 10
b = 100 + 30
c = a * b
d = c / 100
e = d - 100
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a ) rs . 768 , b ) rs . 968 , c ) rs . 1960 , d ) rs . 2400 , e ) none | a | add(divide(multiply(const_100, 168), multiply(14, 2)), 168) | if the true discount on a sum due 2 years hence at 14 % per annum be rs . 168 , the sum due is : | solution p . w = 100 xt . d . / r x t = 100 x 168 / 14 x 2 = 600 . ∴ sum = ( p . w . + td . ) = rs . 768 . answer a | a = 100 * 168
b = 14 * 2
c = a / b
d = c + 168
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a ) 30 yr , b ) 25 yr , c ) 45 yr , d ) 40 yr , e ) 50 yr | c | add(subtract(30, subtract(30, add(const_3, const_2))), multiply(subtract(30, add(const_3, const_2)), const_2)) | the difference between the ages of two persons is 30 years . fifteen years ago , the elder one was twice as old as the younger one . the present age of the younger person is ? | "let their ages be x years and ( x + 30 ) years then , ( x + 30 ) - 15 = 2 ( x - 15 ) x + 15 = 2 x - 30 x = 45 answer is c" | a = 3 + 2
b = 30 - a
c = 30 - b
d = 3 + 2
e = 30 - d
f = e * 2
g = c + f
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a ) $ 13,746 , b ) $ 15,325 , c ) $ 16,000 , d ) $ 16,225 , e ) $ 17,155 | a | multiply(divide(const_3, const_4), const_1000) | a store owner estimates that the average price of type a products will increase by 20 % next year and that the price of type b products will increase by 11 % next year . this year , the total amount paid for type a products was $ 3500 and the total price paid for type b products was $ 8600 . according to the store owne... | "cost of type a products next year = 1.20 * 3500 = 4200 cost of type b products next year = 1.11 * 8300 = 9546 total 4200 + 9546 = 13746 answer : a" | a = 3 / 4
b = a * 1000
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a ) 15360 , b ) 13780 , c ) 15060 , d ) 14930 , e ) 16075 | b | subtract(add(6000, 10000), add(multiply(6000, divide(12, const_100)), multiply(divide(15, const_100), 10000))) | a soft drink company had 6000 small and 10000 big bottles in storage . if 12 % of small 15 % of big bottles have been sold , then the total bottles remaining in storage is | "6000 + 10000 - ( 0.12 * 6000 + 0.15 * 10000 ) = 13780 . answer : b ." | a = 6000 + 10000
b = 12 / 100
c = 6000 * b
d = 15 / 100
e = d * 10000
f = c + e
g = a - f
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a ) 1 / 140 , b ) 1 / 180 , c ) 3 / 12 , d ) 3 / 8 , e ) 57 / 120 | d | add(add(divide(1, 8), divide(1, 12)), divide(1, 6)) | in a race where 18 cars are running , the chance that car x will win is 1 / 8 , that y will win is 1 / 12 and that z will win is 1 / 6 . assuming that a dead heat is impossible , find the chance that one of them will win . | "required probability = p ( x ) + p ( y ) + p ( z ) ( all the events are mutually exclusive ) . = 1 / 8 + 1 / 12 + 1 / 6 = 3 / 8 answer : d" | a = 1 / 8
b = 1 / 12
c = a + b
d = 1 / 6
e = c + d
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a ) a ) 78 , b ) b ) 82 , c ) c ) 98 , d ) d ) 91 , e ) e ) 85 | c | divide(add(subtract(multiply(100, 25), 60), 10), 25) | the average marks of 25 students in a class is 100 . but a student mark is wrongly noted as 60 instead of 10 then find the correct average marks ? | "correct avg marks = 100 + ( 10 - 60 ) / 25 avg = 100 - 2 = 98 answer is c" | a = 100 * 25
b = a - 60
c = b + 10
d = c / 25
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a ) 2345 , b ) 4500 , c ) 5000 , d ) 6000 , e ) 7000 | a | add(5, add(add(multiply(2, const_1000), multiply(3, const_100)), multiply(const_10, 4))) | what is the sum of the local values of the digits 2 , 3 , 4 , 5 in the number 2345 ? | 2000 + 300 + 40 + 5 = 2345 answer a | a = 2 * 1000
b = 3 * 100
c = a + b
d = 10 * 4
e = c + d
f = 5 + e
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a ) a ) 44500 , b ) b ) 42000 , c ) c ) 44098 , d ) d ) 43007 , e ) e ) 44098 | b | subtract(91000, multiply(const_60, const_100)) | a started a business with an investment of rs . 70000 and after 6 months b joined him investing rs . 120000 . if the profit at the end of a year is rs . 91000 , then the share of b is ? | "ratio of investments of a and b is ( 70000 * 12 ) : ( 120000 * 6 ) = 7 : 6 total profit = rs . 91000 share of b = 6 / 13 ( 91000 ) = rs . 42000 answer : b" | a = const_60 * 100
b = 91000 - a
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a ) 2449 , b ) 5449 , c ) 6749 , d ) 6725 , e ) 6468 | d | subtract(multiply(divide(54671, const_100), 14456), multiply(divide(const_1, const_3), multiply(divide(54671, const_100), 14456))) | 54671 - 14456 - 33490 = ? | "d if we calculate we will get 6725" | a = 54671 / 100
b = a * 14456
c = 1 / 3
d = 54671 / 100
e = d * 14456
f = c * e
g = b - f
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a ) 36 , b ) 42 , c ) 44 , d ) 43 , e ) none | d | subtract(add(28, 17), const_2) | if p and q are positive integers each greater than 1 , and 17 ( p + 1 ) = 28 ( q + 1 ) , what is the least possible value of p + q ? | "17 ( p + 1 ) = 29 ( q + 1 ) - - > ( p + 1 ) / ( q + 1 ) = 28 / 17 - - > the least positive value of p + 1 is 28 , so the least value of p is 27 and the least positive value of q + 1 is 17 , so the least value of q is 16 - - > the least value of p + q is 27 + 16 = 43 . answer : d" | a = 28 + 17
b = a - 2
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a ) 350 m , b ) 200 m , c ) 400 m , d ) 900 m , e ) none of them | d | divide(multiply(225, 8), subtract(10, 8)) | a thief is spotted by a policeman from a distance of 225 meters . when the policeman starts the chase , the thief also starts running . if the speed of the thief be 8 km / hr and that of the policeman 10 km / hr , how far the thief will have run before he is overtaken ? | "relative speed of the policeman = ( 10 - 8 ) km / hr = 2 km / hr . time taken by police man to cover ( 225 m / 1000 ) x 1 / 2 hr = 9 / 80 hr . in 9 / 80 hrs , the thief covers a distance of 8 x 9 / 80 km = 9 / 10 km = 900 m answer is d ." | a = 225 * 8
b = 10 - 8
c = a / b
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a ) 13 / 8 , b ) 26 / 11 , c ) 24 / 7 , d ) 12 / 13 , e ) 1 / 2 | c | inverse(add(inverse(12), add(inverse(const_3), inverse(add(add(const_4, const_4), const_1))))) | a , b , c can complete a piece of work in 24,6 and 12 days respectively . working together , they will complete the same work in how many days ? | "( a + b + c ) ' s 1 day work = ( 1 / 24 ) + ( 1 / 6 ) + ( 1 / 12 ) = 7 / 24 a , b , c together will complete the work in 24 / 7 days answer is c" | a = 1/(12)
b = 1/(3)
c = 4 + 4
d = c + 1
e = 1/(d)
f = b + e
g = a + f
h = 1/(g)
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a ) 12 , b ) 10 , c ) 9 , d ) 8 , e ) 11 | e | divide(407, add(multiply(9, const_3), multiply(5, const_2))) | mary works 9 hours per day on monday , wednesday and friday , and 5 hours per day on tuesday and thursday . she does not work on saturday and sunday . she earns $ 407 per week . how much does she earn in dollars per hour ? | so , she works 27 hours in 3 days so , she works 10 hours in 2 days so in a week she works 37 hours ( 27 + 10 ) and earns $ 407 so , hourly wage is 407 / 37 = > 11 hence answer will be ( e ) 11 | a = 9 * 3
b = 5 * 2
c = a + b
d = 407 / c
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a ) 3 , b ) 5 , c ) 5.6 , d ) 5.7 , e ) 6.5 | a | multiply(divide(9, 12), 4) | when a number is divided by 4 & then multiply by 12 the answer is 9 what is the no . ? | if $ x $ is the number , x / 4 * 12 = 9 = > 3 x = 9 = > x = 3 a | a = 9 / 12
b = a * 4
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a ) 1 / 4 , b ) 1 / 2 , c ) 2 / 3 , d ) 2 , e ) 4 | d | divide(const_1, divide(multiply(add(divide(3, 4), const_1), divide(3, 5)), const_2)) | a toy store ' s revenue in november was 3 / 5 of its revenue in december and its revenue in january was 3 / 4 of its revenue in november , then the store ' s revenue in december was how many times the average ( arithmetic mean ) of its revenues in november and january ? | let dec rev = 100 then nov rev is 3 / 5 ( 100 ) = > 60 therefore jan rev = 3 / 4 ( nov rev ) = 3 / 4 ( 60 ) = > 45 hence dec rev = x * ( nov rev + jan rev ) / 2 100 = x * ( 60 + 45 ) / 2 x = 100 / 52.5 = > 1.90 = 2 ans ) d | a = 3 / 4
b = a + 1
c = 3 / 5
d = b * c
e = d / 2
f = 1 / e
|
a ) 600 , b ) 700 , c ) 800 , d ) 900 , e ) 1000 | e | divide(divide(divide(120, subtract(const_1, divide(4, 5))), divide(4, 5)), divide(1, 4)) | of the goose eggs laid at a certain pond , 1 / 4 hatched and 4 / 5 of the geese that hatched from those eggs survived the first month . of the geese that survived the first month , 2 / 5 did not survive the first year . if 120 geese survived the first year and if no more than one goose hatched from each egg , how many ... | "let x be the number of eggs that were laid . ( 3 / 5 ) ( 4 / 5 ) ( 1 / 4 ) x = 120 ( 12 / 100 ) x = 120 x = 1000 the answer is e ." | a = 4 / 5
b = 1 - a
c = 120 / b
d = 4 / 5
e = c / d
f = 1 / 4
g = e / f
|
a ) 2 / 7 , b ) 17 / 30 , c ) 1 / 2 , d ) 27 / 40 , e ) 5 / 7 | d | divide(const_10, 30) | in a graduate physics course , 60 percent of the students are male and 30 percent of the students are married . if two - sevenths of the male students are married , what fraction of the female students is single ? | "let assume there are 100 students of which 60 are male and 40 are females if 30 are married then 70 will be single . now its given that two - sevenths of the male students are married that means 2 / 7 of 60 = 17 males are married if 30 is the total number of students who are married and out of that 17 are males then t... | a = 10 / 30
|
a ) 21 , b ) 29 , c ) 19 , d ) 14 , e ) 10 | c | add(18, const_1) | calculate the average of first 18 even numbers is ? | explanation : sum of 10 even numbers = 18 * 19 = 342 average = 342 / 18 = 19 answer : option c | a = 18 + 1
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a ) 160 , b ) 150 , c ) 250 , d ) 80 , e ) 50 | c | divide(subtract(multiply(200, divide(16, const_100)), 22), subtract(divide(16, const_100), divide(12, const_100))) | an empty fuel tank with a capacity of 200 gallons was filled partially with fuel a and then to capacity with fuel b . fuel a contains 12 % ethanol by volume and fuel b contains 16 % ethanol by volume . if the full fuel tank contains 22 gallons of ethanol , how many gallons of fuel a were added ? | "say there are a gallons of fuel a in the tank , then there would be 200 - a gallons of fuel b . the amount of ethanol in a gallons of fuel a is 0.12 a ; the amount of ethanol in 200 - a gallons of fuel b is 0.16 ( 200 - a ) ; since the total amount of ethanol is 22 gallons then 0.12 a + 0.16 ( 200 - a ) = 22 - - > a =... | a = 16 / 100
b = 200 * a
c = b - 22
d = 16 / 100
e = 12 / 100
f = d - e
g = c / f
|
a ) 7 , b ) 8 , c ) 10 , d ) 12 , e ) 14 | a | subtract(36, subtract(add(26, 20), 17)) | in a class of 36 students 26 play football and play 20 long tennis , if 17 play above , many play neither ? | "26 + 20 - 17 = 29 36 - 29 = 7 play neither answer is a" | a = 26 + 20
b = a - 17
c = 36 - b
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a ) 5 , b ) 7 , c ) 9 , d ) 11 , e ) 12 | a | multiply(subtract(divide(power(29, const_2), 56), floor(divide(power(29, const_2), 56))), 56) | on dividing a number by 56 , we get 29 as remainder . on dividing the same number by 8 , what will be the remainder ? | "formula : ( divisor * quotient ) + remainder = dividend . soln : ( 56 * q ) + 29 = d - - - - - - - ( 1 ) d % 8 = r - - - - - - - - - - - - - ( 2 ) from equation ( 2 ) , ( ( 56 * q ) + 29 ) % 8 = r . = > assume q = 1 . = > ( 56 + 29 ) % 8 = r . = > 85 % 8 = r = > 5 = r . a )" | a = 29 ** 2
b = a / 56
c = 29 ** 2
d = c / 56
e = math.floor(d)
f = b - e
g = f * 56
|
a ) 7 , b ) 8 , c ) 9 , d ) 10 , e ) 11 | b | add(add(3, 3), 2) | given that p is a positive even integer with a positive units digit , if the units digit of p ^ 3 minus the units digit of p ^ 2 is equal to 0 , what is the units digit of p + 2 ? | "p is a positiveeveninteger with apositive units digit - - > the units digit of p can be 2 , 4 , 6 , or 8 - - > in order the units digit of p ^ 3 - p ^ 2 to be 0 , the units digit of p ^ 3 and p ^ 2 must be the same . thus the units digit of p can be 0 , 1 , 5 or 6 . intersection of values is 6 , thus the units digit o... | a = 3 + 3
b = a + 2
|
a ) 8 , b ) 10 , c ) 12 , d ) 14 , e ) 16 | c | divide(add(18, multiply(6, 5)), subtract(5, const_1)) | dan ' s age after 18 years will be 5 times his age 6 years ago . what is the present age of dan ? | "let dan ' s present age be x . x + 18 = 5 ( x - 6 ) 4 x = 48 x = 12 the answer is c ." | a = 6 * 5
b = 18 + a
c = 5 - 1
d = b / c
|
a ) 200 π , b ) 450 π , c ) 300 π , d ) 480 π , e ) 1,200 π | b | multiply(multiply(multiply(multiply(divide(10, add(multiply(const_2, const_100), multiply(add(const_2, const_3), const_1000))), const_2), divide(add(const_2, multiply(const_2, 10)), add(const_3, const_4))), 1,980), const_60) | the end of a blade on an airplane propeller is 10 feet from the center . if the propeller spins at the rate of 1,980 revolutions per second , how many miles will the tip of the blade travel in one minute ? ( 1 mile = 5,280 feet ) | "distance traveled in 1 revolution = 2 π r = 2 π 10 / 5280 revolutions in one second = 1980 revolutions in 60 seconds ( one minute ) = 1980 * 60 total distance traveled = total revolutions * distance traveled in one revolution 1980 * 60 * 2 π 10 / 5280 = 450 π b is the answer" | a = 2 * 100
b = 2 + 3
c = b * 1000
d = a + c
e = 10 / d
f = e * 2
g = 2 * 10
h = 2 + g
i = 3 + 4
j = h / i
k = f * j
l = k * 1
m = l * const_60
|
a ) 1 : 4 , b ) 1 : 5 , c ) 3 : 2 , d ) 1 : 2 , e ) 2 : 5 | c | divide(subtract(divide(const_1, 3), divide(const_1, 5)), subtract(divide(const_1, 5), divide(const_1, multiply(const_2, const_4)))) | a grocery store bought some mangoes at a rate of 5 for a dollar . they were separated into two stacks , one of which was sold at a rate of 3 for a dollar and the other at a rate of 9 for a dollar . what was the ratio of the number of mangoes in the two stacks if the store broke even after having sold all of its mangoes... | "the cost price of a mango = 1 / 5 dollars . the selling price of a mango from the first stack = 1 / 3 dollars - - > the profit from one mango = 1 / 3 - 1 / 5 = 2 / 15 = 4 / 30 dollars . the selling price of a mango from the second stack = 1 / 9 dollars - - > the loss from one mango = 1 / 5 - 1 / 9 = 4 / 45 dollars . t... | a = 1 / 3
b = 1 / 5
c = a - b
d = 1 / 5
e = 2 * 4
f = 1 / e
g = d - f
h = c / g
|
a ) 500 , b ) 688 , c ) 200 , d ) 121 , e ) 800 | e | divide(subtract(420, 380), divide(5, const_100)) | if 5 % more is gained by selling an article for rs . 420 than by selling it for rs . 380 , the cost of the article is ? | let c . p . be rs . x . then , 5 % of x = 420 - 380 = 40 x / 20 = 40 = > x = 800 answer : e | a = 420 - 380
b = 5 / 100
c = a / b
|
a ) 7 , b ) 11 , c ) 13 , d ) 14 , e ) 38 | d | divide(multiply(39, divide(72, const_100)), const_2) | each of the 39 points is placed either inside or on the surface of a perfect sphere . if 72 % or fewer of the points touch the surface , what is the maximum number of segments which , if connected from those points to form chords , could be the diameter of the sphere ? | "maximum number of points on the surface is 72 % * 39 = 28.08 . . . or 28 since it has to be an integer now note that if two points form a diameter , they can not be part of any other diameter . so in the best case we can pair up the points we have 28 points , so at best we can form 14 pairs ( 28 ) . so , answer is ( d... | a = 72 / 100
b = 39 * a
c = b / 2
|
a ) 40.9 % , b ) 41.9 % , c ) 42.9 % , d ) 43.9 % , e ) 44.9 % | e | multiply(divide(add(4, 5), add(add(5, 6), add(4, 5))), const_100) | the proportion of water to alcohol in solution a is 5 : 4 and the proportion of water to alcohol in solution b is 6 : 5 . if an equal amount of each solution is mixed together , what is the concentration of alcohol in the new solution ? | "let v be the total volume of the new solution . then a volume of v / 2 was added from each solution a and b . the amount of alcohol added to the new solution was : ( 4 / 9 ) ( v / 2 ) + ( 5 / 11 ) ( v / 2 ) = 2 v / 9 + 5 v / 22 = 89 v / 198 . the concentration of alcohol is 89 / 198 = 44.9 % the answer is e ." | a = 4 + 5
b = 5 + 6
c = 4 + 5
d = b + c
e = a / d
f = e * 100
|
a ) 180 , b ) 196 , c ) 160 , d ) 164 , e ) 172 | b | multiply(multiply(4, 3), multiply(4, 3)) | in the coordinate plane , one of the vertices of a square is the point ( - 4 , - 4 ) . if the diagonals of that square intersect at point ( 3 , 2 ) , what is the area of that square ? | "one point ( - 4 - 4 ) , intersection ( 3,2 ) so the distance from the first point - 4 - 3 = - 7 is the midpoint of the square - - > whole side 14 , 14 * 14 = 196 b" | a = 4 * 3
b = 4 * 3
c = a * b
|
a ) 100 m , b ) 80 m , c ) 130 m , d ) 150 m , e ) none of these | b | subtract(180, multiply(divide(3, const_60), const_1000)) | a policeman noticed a criminal from a distance of 180 km . the criminal starts running and the policeman chases him . the criminal and the policeman run at the rate of 8 km and 10 km per hour respectively . what is the distance between them after 3 minutes ? | "explanation : solution : relative speed = ( 10 - 8 ) = 2 km / hr . distance covered in 3 minutes = ( 2 * 3 / 60 ) km = 1 / 10 km = 100 m . . ' . distance between the criminal and policeman = ( 180 - 100 ) m = 80 m . answer : b" | a = 3 / const_60
b = a * 1000
c = 180 - b
|
a ) 121 , b ) 123 , c ) 119 , d ) 125 , e ) 127 | a | divide(multiply(22, 55), 10) | if 22 men do a work in 55 days , in how many days will 10 men do it ? | "22 * 55 = 10 * x x = 121 days answer : a" | a = 22 * 55
b = a / 10
|
a ) 85 , b ) 94 , c ) 82 , d ) 72 , e ) none | c | add(multiply(divide(add(10, 6), const_2), 10), subtract(10, divide(add(10, 6), const_2))) | the sum of digits of a two digit number is 10 , the difference between the digits is 6 . find the number | description : = > x + y = 10 , x - y = 6 adding these 2 x = 16 = > x = 8 , y = 2 . thus the number is 82 answer c | a = 10 + 6
b = a / 2
c = b * 10
d = 10 + 6
e = d / 2
f = 10 - e
g = c + f
|
a ) $ 350 , b ) $ 400 , c ) $ 365 , d ) $ 385 , e ) $ 375 | c | divide(subtract(multiply(7, 400), add(add(add(add(406, 413), 420), 436), 395)), const_2) | tough and tricky questions : word problems . a salesman ' s income consists of commission and base salary . his weekly income totals over the past 5 weeks have been $ 406 , $ 413 , $ 420 , $ 436 and $ 395 . what must his average ( arithmetic mean ) income over the next two weeks be to decrease his average weekly income... | official solution : ( c ) first , we need to add up the wages over the past 5 weeks : $ 406 + $ 413 + $ 420 + $ 436 + $ 395 = $ 2070 . to average $ 400 over 7 weeks , the salesman would need to earn : $ 400 × 7 = $ 2800 . subtract $ 2070 from $ 2800 to determine how much he would need to earn , in total , over the next... | a = 7 * 400
b = 406 + 413
c = b + 420
d = c + 436
e = d + 395
f = a - e
g = f / 2
|
a ) 258 , b ) 318 , c ) 322 , d ) 324 , e ) 330 | a | add(multiply(6, const_4), multiply(divide(40, 10), const_60)) | a man walks at a rate of 10 mph . after every ten miles , he rests for 6 minutes . how much time does he take to walk 40 miles ? | "to cover 40 miles the man needs ( time ) = ( distance ) / ( rate ) = 40 / 10 = 4 hours = 240 minutes . he will also rest 3 times ( after 10 , 20 , and 30 miles ) , so total resting time = 3 * 6 = 18 minutes . total time = 240 + 18 = 258 minutes . answer : a ." | a = 6 * 4
b = 40 / 10
c = b * const_60
d = a + c
|
a ) 2 / 7 , b ) 3 / 5 , c ) 3 / 11 , d ) 18 / 85 , e ) 7 / 16 | d | divide(multiply(choose(const_4.0, const_2), choose(add(const_3.0, 6), const_1)), choose(add(add(3, 6), 8), 3)) | a bag contains 3 red , 6 yellow and 8 green balls . 3 balls are drawn randomly . what is the probability that the balls drawn contain balls of different colours ? | "total number of balls = 3 + 6 + 8 = 17 n ( s ) = 17 c 3 = 680 n ( e ) = 3 c 1 * 6 c 1 * 8 c 1 = 144 probability = 144 / 680 = 18 / 85 answer is d" | a = math.comb(4, 0)
b = 3 + 0
c = math.comb(b, 1)
d = a * c
e = 3 + 6
f = e + 8
g = math.comb(f, 3)
h = d / g
|
a ) 2 , b ) 2.4 , c ) 2.7 , d ) 3 , e ) 3.5 | d | divide(240, add(divide(240, 12), divide(240, 4))) | while working alone at their constant rates , computer x can process 240 files in 12 hours , and computer y can process 240 files in 4 hours . if all files processed by these computers are the same size , how many hours would it take the two computers , working at the same time at their respective constant rates , to p... | "both computers together process files at a rate of 240 / 12 + 240 / 4 = 20 + 60 = 80 files per hour . the time required to process 240 files is 240 / 80 = 3 hours the answer is d ." | a = 240 / 12
b = 240 / 4
c = a + b
d = 240 / c
|
a ) 573 , b ) 608 , c ) 613 , d ) 616 , e ) 621 | a | add(multiply(subtract(72, const_1), 8), 5) | let s be the set of all positive integers that , when divided by 8 , have a remainder of 5 . what is the 72 th number in this set ? | the set s = { 5 , 13 , 21 , 29 , . . . . . . . . . . . . . . . . . . . . . } 1 st number = 8 * 0 + 5 = 5 2 nd number = 8 * 1 + 5 = 13 3 rd number = 8 * 2 + 5 = 21 72 th number = 8 * ( 72 - 1 ) + 5 = 573 answer = a | a = 72 - 1
b = a * 8
c = b + 5
|
a ) 4 , b ) 6 , c ) 8 , d ) 12 , e ) 16 | c | multiply(multiply(add(const_1, const_1), add(const_1, const_1)), add(const_1, const_1)) | how many positive integers will divide evenly into 190 ? | the question is asking how many factors 190 has . 190 = 2 * 5 * 19 the number of factors is 2 ^ 3 = 8 the answer is c . | a = 1 + 1
b = 1 + 1
c = a * b
d = 1 + 1
e = c * d
|
a ) 150 , b ) 500 / 3 , c ) 400 , d ) 480 , e ) 600 | a | multiply(divide(subtract(25, 10), subtract(30, 25)), 50) | solution x is 10 percent alcohol by volume , and solution y is 30 percent alcohol by volume . how many milliliters of solution y must be added to 50 milliliters of solution x to create a solution that is 25 percent alcohol by volume ? | "we know that x is 10 % , y is 30 % and w . avg = 25 % . what does this mean with respect to w . avg technique ? w . avg is 1 portion away from y and 3 portion away from x so for every 1 portion of x we will have to add 3 portions of y . if x = 50 then y = 150 answer : a" | a = 25 - 10
b = 30 - 25
c = a / b
d = c * 50
|
a ) 14 , b ) 18 , c ) 22 , d ) 26 , e ) 30 | e | add(divide(400, 10), subtract(subtract(10, 4), const_1)) | in a certain quiz that consists of 10 questions , each question after the first is worth 4 points more than the preceding question . if the 10 questions on the quiz are worth a total of 400 points , how many points is the third question worth ? | "x x + 4 x + 8 x + 12 x + 16 x + 20 x + 24 x + 28 x + 32 x + 36 10 x + 180 = 400 10 x = 220 x = 22 3 rd question = x + 8 = 22 + 8 = 30 answer e" | a = 400 / 10
b = 10 - 4
c = b - 1
d = a + c
|
a ) 8 % , b ) 15 % , c ) 45 % , d ) 52 % , e ) 66 % | e | multiply(divide(5, 40), const_100) | a pharmaceutical company received $ 5 million in royalties on the first $ 40 million in sales of and then $ 9 million in royalties on the next $ 210 million in sales . by approximately what percentage did the ratio of royalties to sales decrease from the first $ 40 million in sales to the next $ 210 million in sales ? | "( 9 / 210 ) / ( 5 / 40 ) = 12 / 35 = 34 % it means that 9 / 210 represents only 34 % . therefore a decrease of 66 % . answer e" | a = 5 / 40
b = a * 100
|
a ) 20 % , b ) 80 % , c ) 100 % , d ) 180 % , e ) 200 % | d | multiply(divide(20, subtract(subtract(const_100, 80), 20)), const_100) | jane makes toy bears . when she works with an assistant , she makes 80 percent more bears per week and works 20 percent fewer hours each week . having an assistant increases jane ’ s output of toy bears per hour by what percent ? | "we can use fractional equivalents here to solve the problem 80 % = 4 / 5 ; this means that in 1 st case if she prepares 5 bears , in 2 nd case she prepares 9 bears 10 % = 1 / 10 ; this means that in 1 st case if she needs 10 hours , in 2 nd case she needs 9 hours now we come to productivity based on above fractional v... | a = 100 - 80
b = a - 20
c = 20 / b
d = c * 100
|
a ) 60 m 2 , b ) 64 m 2 , c ) 68 m 2 , d ) 66 m 2 , e ) none of these | d | multiply(5, multiply(multiply(multiply(3, divide(22, 7)), divide(1.4, 3)), 3)) | the diameter of a garden roller is 1.4 m and it is 3 m long . how much area will it cover in 5 revolutions ? ( use ï € = 22 â „ 7 ) | "required area covered in 5 revolutions = 5 ã — 2 ï € rh = 5 ã — 2 ã — 22 â „ 7 ã — 0.7 ã — 3 = 66 m 2 answer d" | a = 22 / 7
b = 3 * a
c = 1 / 4
d = b * c
e = d * 3
f = 5 * e
|
a ) 1 / 20 , b ) 1 / 50 , c ) 1 / 75 , d ) 2 / 25 , e ) none of these | d | divide(circle_area(divide(8, const_2)), const_2) | what will be the fraction of 8 % | "explanation : 8 * 1 / 100 = 2 / 25 . option d" | a = 8 / 2
b = circle_area / (
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a ) 14 , b ) 20 , c ) 22 , d ) 24 , e ) 15 | e | divide(60000, divide(add(add(add(5000, 12000), 15000), 16000), add(add(add(2, 4), 2), 4))) | shipment - - - no . of defective chips / shipment - - - total chips in shipment s 1 - - - - - - - - - - - - - - - - - - - - - - 2 - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 5000 s 2 - - - - - - - - - - - - - - - - - - - - - - 4 - - - - - - - - - - - - - - - - - - - - - - - - - -... | for a total of 51000 chips ( adding s 1 , s 2 , s 3 , s 4 ) total number of defective chips is 17 ( ( adding defective chips of s 1 , s 2 , s 3 , s 4 ) so ratio is 12 / 48000 or 1 every 4000 chips . keeping this ratio constant for 60000 chips number of defective chips will be ( 1 / 4000 ) * 60000 = 15 e | a = 5000 + 12000
b = a + 15000
c = b + 16000
d = 2 + 4
e = d + 2
f = e + 4
g = c / f
h = 60000 / g
|
a ) 392 , b ) 229 , c ) 753 , d ) 493 , e ) 540 | c | multiply(multiply(multiply(divide(3, 4), divide(1, 2)), divide(2, 5)), 5020) | 3 / 4 of 1 / 2 of 2 / 5 of 5020 = ? | "c 753 ? = 5020 * ( 2 / 5 ) * ( 1 / 2 ) * ( 3 / 4 ) = 753" | a = 3 / 4
b = 1 / 2
c = a * b
d = 2 / 5
e = c * d
f = e * 5020
|
a ) 19 , b ) 27 , c ) 29 , d ) 48 , e ) 28 | d | divide(add(360, multiply(multiply(const_0_2778, 36), 12)), multiply(const_0_2778, 36)) | a train running at a speed of 36 kmph crosses an electric pole in 12 seconds . in how much time will it cross a 360 m long platform ? | "let the length of the train be x m . when a train crosses an electric pole , the distance covered is its own length . so , x = 12 * 36 * 5 / 18 m = 120 m . time taken to cross the platform = ( 120 + 360 ) / 36 * 5 / 18 = 48 min . answer : d" | a = const_0_2778 * 36
b = a * 12
c = 360 + b
d = const_0_2778 * 36
e = c / d
|
a ) 120 , b ) 240 , c ) 360 , d ) 480 , e ) 720 | c | multiply(factorial(const_4), divide(divide(factorial(6), factorial(const_4)), factorial(const_2))) | an auto assembly plant performs 6 functions with each frame that arrives : add axles , add wheels to the axles , install the windshield to the frame , install the instrument panel , install the steering wheel , and install the interior seating . once those 6 tasks are performed , each car goes to a separate building fo... | c ) 360 short way : there are 6 c ! ways to do the six tasks . half will have wheels before axles and half will have axles before wheels . so we want t = 6 c ! / 2 - > 720 / 2 = 360 | a = math.factorial(4)
b = math.factorial(6)
c = math.factorial(4)
d = b / c
e = math.factorial(2)
f = d / e
g = a * f
|
a ) 1 , 4,6 , b ) 12 , 24,36 , c ) 10 , 20 , 30 , d ) 12 , 24 , 36 , e ) 9 , 36,54 . | e | add(multiply(multiply(1, 6), const_100), multiply(4, 6)) | three numbers are in the ratio 1 : 4 : 6 and their h . c . f is 9 . the numbers are : | "let the required numbers be x , 4 x and 6 x . then , their h . c . f = x . so , x = 9 . the numbers are 9 , 36,54 . answer : e" | a = 1 * 6
b = a * 100
c = 4 * 6
d = b + c
|
a ) 52.5 , b ) 52.9 , c ) 52.1 , d ) 48.75 , e ) 42.5 | d | divide(add(multiply(30, 30), multiply(50, 60)), add(30, 50)) | the average marks of a class of 30 students is 30 and that of another class of 50 students is 60 . find the average marks of all the students ? | "sum of the marks for the class of 30 students = 30 * 30 = 900 sum of the marks for the class of 50 students = 50 * 60 = 3000 sum of the marks for the class of 80 students = 900 + 3000 = 3900 average marks of all the students = 3900 / 80 = 48.75 answer : d" | a = 30 * 30
b = 50 * 60
c = a + b
d = 30 + 50
e = c / d
|
a ) 25 / 323 , b ) 21 / 969 , c ) 28 / 989 , d ) 74 / 879 , e ) 23 / 589 | a | divide(multiply(choose(6, 2), choose(5, 1)), choose(add(add(5, 6), 8), 3)) | an urn contains 5 red , 6 blue and 8 green balls . 3 balls are randomly selected from the urn , find the probability that the drawn ball are 2 blue and 1 red ? | "sample space = no . of ways 3 balls were drawn from urn = 19 c 3 = 969 no . ways 2 blue balls and 1 red were drawn from bag = 6 c 2 * 5 c 1 = 75 probability = 75 / 969 = 25 / 323 ans - a" | a = math.comb(6, 2)
b = math.comb(5, 1)
c = a * b
d = 5 + 6
e = d + 8
f = math.comb(e, 3)
g = c / f
|
a ) $ 1.63 , b ) $ 1.64 , c ) $ 1.68 , d ) $ 1.70 , e ) $ 1.76 | d | divide(add(multiply(1300, 1.89), multiply(750, 1.38)), add(1300, 750)) | john purchased 1300 large bottles at $ 1.89 per bottle and 750 small bottles at $ 1.38 per bottle . what was the approximate average price paid per bottle ? | "( 1300 * 1.89 + 750 * 1.38 ) / ( 1300 + 750 ) = ~ 1.70 option ( d )" | a = 1300 * 1
b = 750 * 1
c = a + b
d = 1300 + 750
e = c / d
|
a ) 41.4 , b ) 34.1 , c ) 13.4 , d ) 12.4 , e ) 10.8 | a | add(inverse(subtract(divide(const_1, 12.5), divide(const_1, 30))), inverse(subtract(divide(const_1, 7.5), divide(const_1, 12)))) | two consultants can type up a report in 12.5 hours and edit it in 7.5 hours . if mary needs 30 hours to type the report and jim needs 12 hours to edit it alone , how many hours q will it take if jim types the report and mary edits it immediately after he is done ? | break down the problem into two pieces : typing and editing . mary needs 30 hours to type the report - - > mary ' s typing rate = 1 / 30 ( rate reciprocal of time ) ( point 1 in theory below ) ; mary and jim can type up a report in 12.5 and - - > 1 / 30 + 1 / x = 1 / 12.5 = 2 / 25 ( where x is the time needed for jim t... | a = 1 / 12
b = 1 / 30
c = a - b
d = 1/(c)
e = 1 / 7
f = 1 / 12
g = e - f
h = 1/(g)
i = d + h
|
a ) 4 3 / 6 , b ) 4 3 / 9 , c ) 4 3 / 8 , d ) 4 3 / 4 , e ) 4 3 / 1 | c | add(multiply(add(3, divide(const_1, const_2)), subtract(add(5, divide(const_3, 4)), add(4, divide(const_1, const_2)))), const_2) | two men a and b start from place x walking at 4 ½ kmph and 5 ¾ kmph respectively . how many km apart they are at the end of 3 ½ hours if they are walking in the same direction ? | "rs = 5 3 / 4 - 4 1 / 2 = 1 1 / 4 t = 3 1 / 2 h . d = 5 / 4 * 7 / 2 = 35 / 8 = 4 3 / 8 km answer : c" | a = 1 / 2
b = 3 + a
c = 3 / 4
d = 5 + c
e = 1 / 2
f = 4 + e
g = d - f
h = b * g
i = h + 2
|
a ) 198 , b ) 288 , c ) 432 , d ) 396 , e ) 484 | c | multiply(multiply(multiply(power(2, const_2.0), 3), divide(12, 2)), 2) | if 2 ^ 4 , 3 ^ 3 , and 12 ^ 3 are factors of the product of 1,452 and w , where w is a positive integer , what is the smallest possible value of w ? | i will go with c ( pending elements to match is 2 ^ 2 * 3 ^ 2 * 12 ^ 1 = 432 | a = 2 ** 2
b = a * 3
c = 12 / 2
d = b * c
e = d * 2
|
a ) - 10 , b ) - 2 , c ) 8 , d ) 13 , e ) 17 | d | subtract(reminder(reminder(94, 33), 17), reminder(96, reminder(33, 17))) | for all positive integers m and v , the expression m θ v represents the remainder when m is divided by v . what is the value of ( ( 94 θ 33 ) θ 17 ) - ( 96 θ ( 33 θ 17 ) ) ? | "( ( 94 θ 33 ) θ 17 ) the remainder of 98 divided by 33 is 28 ; the remainder of 28 divided by 17 is 11 ; ( 96 θ ( 33 θ 17 ) ) the remainder of 33 divided by 17 is 16 ; the remainder of 96 divided by 16 is 0 . 11 - 0 = 11 . answer : d ." | a = reminder - (
|
a ) 50 , b ) 100 , c ) 490 , d ) 500 , e ) 75 | e | divide(735, 9.8) | a sports equipment store sold ping pong rackets for a total of $ 735 . if the average ( arithmetic mean ) price of a pair of rackets is $ 9.8 , how many pairs were sold ? | "average price for a pair of rackets = $ 9.8 total cost = $ 9.8 * x = $ 735 x = 75 pairs were sold . answer : e" | a = 735 / 9
|
a ) 45 , b ) 67 , c ) 70 , d ) 77 , e ) 98 | b | add(add(add(divide(lcm(lcm(lcm(3, 1), 1), 3), 3), divide(lcm(lcm(lcm(3, 1), 1), 3), 1)), divide(lcm(lcm(lcm(3, 1), 1), 3), 1)), divide(lcm(lcm(lcm(3, 1), 1), 3), 3)) | john distributes his pencil among his 4 friends rose , mary , ranjan , and rohit in the ratio 1 / 3 : 1 / 3 : 1 / 4 : 1 / 5 . what is the minimum no . of pencils that the person should have ? | "rakesh : rahul : ranjan : rohit = 1 / 3 : 1 / 3 : 1 / 4 : 1 / 5 step 1 : at first we need to do is lcm of 3 , 3,4 and 5 is 60 . step 2 : then pencil are distributed in ratio among friends , rakesh = ( 1 / 3 x 60 ) = 20 . rahul = ( 1 / 3 x 60 ) = 20 . ranjan = ( 1 / 4 x 60 ) = 15 . rohit = ( 1 / 5 x 60 ) = 12 . step 3 ... | a = math.lcm(3, 1)
b = math.lcm(a, 1)
c = math.lcm(b, 3)
d = c / 3
e = math.lcm(3, 1)
f = math.lcm(e, 1)
g = math.lcm(f, 3)
h = g / 1
i = d + h
j = math.lcm(3, 1)
k = math.lcm(j, 1)
l = math.lcm(k, 3)
m = l / 1
n = i + m
o = math.lcm(3, 1)
p = math.lcm(o, 1)
q = math.lcm(p, 3)
r = q / 3
s = n + r
|
a ) 6500 , b ) 3250 , c ) 1100 , d ) 1300 , e ) 1200 | d | divide(3250, const_3) | divide rs . 3250 among a , b and c so that a receives 1 / 5 as much as b and c together and b receives 2 / 3 as a and c together . b ' s share is ? | "a + b + c = 3250 a = 1 / 5 ( b + c ) ; b = 2 / 3 ( a + c ) b / ( a + c ) = 2 / 3 b = 1 / 5 * 6500 = > 1300 answer : d" | a = 3250 / 3
|
a ) 150 , b ) 185 , c ) 190 , d ) 210 , e ) 220 | b | subtract(200, 15) | the mean of 50 observations is 200 . but later he found that there is decrements of 15 from each observations . what is the the updated mean is ? | "185 answer is b" | a = 200 - 15
|
a ) 150 m , b ) 899 m , c ) 200 m , d ) 166 m , e ) 187 m | a | subtract(divide(600, const_2), 150) | if the perimeter of a rectangular garden is 600 m , its length when its breadth is 150 m is ? | "2 ( l + 150 ) = 600 = > l = 150 m answer : a" | a = 600 / 2
b = a - 150
|
a ) 4.31 , b ) 6.75 , c ) 7.92 , d ) 5.5 , e ) 6.5 | d | divide(110, multiply(add(60, 12), const_0_2778)) | a train 110 m long is running with a speed of 60 km / hr . in what time will it pass a trolley that is running with a speed of 12 km / hr in the direction opposite to that in which the train is going ? | speed of train relative to trolley = 60 + 12 = 72 km / hr . = 72 * 5 / 18 = 20 m / sec . time taken to pass the trolley = 110 * 1 / 20 = 5.5 sec . answer : d | a = 60 + 12
b = a * const_0_2778
c = 110 / b
|
a ) 75 , b ) 80 , c ) 85 , d ) 90 , e ) 95 | c | divide(subtract(divide(const_3600, const_10), multiply(10, const_2)), const_4) | in a certain parallelogram the degree measure of one angle exceeds that of the other by 10 what is the degree measure of the smaller angle ? | "in a parallelogram opposite angles are equal and the angles at each side are supplementary to each other ( supplementary angles are two angles that add up to 180 ° ) . given : x + ( x + 10 ) = 180 - - > x = 85 . answer : c ." | a = 3600 / 10
b = 10 * 2
c = a - b
d = c / 4
|
a ) 20 , b ) 21 , c ) 22 , d ) 23 , e ) 24 | c | divide(add(multiply(10, 18), subtract(66, 26)), 10) | the average of 10 numbers was calculated as 18 . it is discovered later on that while calculating the average , one number , namely 66 , was incorrectly read as 26 . what is the correct average ? | "10 * 18 - 26 + 66 = 220 220 / 10 = 22 the answer is c ." | a = 10 * 18
b = 66 - 26
c = a + b
d = c / 10
|
a ) 22 , b ) 65 , c ) 12 , d ) 36 , e ) 50 | e | multiply(10, 5) | each child has 5 crayons and 14 apples . if there are 10 children , how many crayons are there in total ? | 5 * 10 = 50 . answer is e . | a = 10 * 5
|
a ) 4 , b ) 5 , c ) 6 , d ) 7 , e ) 3 | e | divide(1050, lcm(lcm(10, 25), 35)) | how many integers between 1 and 1050 are divisible by 10 , 25 , and 35 ? | prime factorization of given numbers 10 = 2 * 5 25 = 5 ^ 2 35 = 5 * 7 lcm of the given numbers = 2 * 5 ^ 2 * 7 = 50 * 7 = 350 therefore , number of integers = 1050 / 350 = 3 answer : option e | a = math.lcm(10, 25)
b = math.lcm(a, 35)
c = 1050 / b
|
a ) - 12 number , b ) - 14 , c ) 2 , d ) 8 , e ) 6 | a | subtract(negate(30), multiply(subtract(64, 48), divide(subtract(64, 48), subtract(78, 64)))) | 78 , 64 , 48 , 30 10 , ( . . . ) | "explanation : 78 - 14 = 64 64 - 16 = 48 48 - 18 = 30 30 - 20 = 10 10 - 22 = - 12 answer : option a" | a = negate - (
|
a ) 39 % , b ) 20 % , c ) 23 % , d ) 74 % , e ) 60 % | e | multiply(divide(subtract(1440, 900), 900), const_100) | a cycle is bought for rs . 900 and sold for rs . 1440 , find the gain percent ? | "900 - - - - 540 100 - - - - ? = > 60 % answer : e" | a = 1440 - 900
b = a / 900
c = b * 100
|
a ) 52 / 7 , b ) 8 , c ) 14 / 2 , d ) 6 , e ) 43 / 6 | a | add(const_1, inverse(divide(divide(const_1, 7), subtract(const_1, divide(const_1, 8))))) | a and b can finish a work in 7 days and 8 days respectively . if both do work one day and leave one day . and a start the work then in how much days work will finish ? | ( a + b ) work in 2 days = [ 1 / 7 + 1 / 8 ] = 15 / 56 ( a + b ) work in 6 days = 45 / 56 now , the turn of a , work of a in 1 day = 1 / 7 . till now completed work = [ 45 / 56 + 1 / 7 ] = 53 / 56 , remaining work = [ 1 - 53 / 56 ] = 3 / 56 now , turn of b , 1 / 8 work b do in 1 day so , 3 / 56 part of work b do = [ 8 ... | a = 1 / 7
b = 1 / 8
c = 1 - b
d = a / c
e = 1/(d)
f = 1 + e
|
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