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 ) 8 , b ) 10 , c ) 2 , d ) 16 , e ) 24 | c | subtract(divide(power(negate(4), 2), 2), 2) | find the value of a / b + b / a , if a and b are the roots of the quadratic equation x 2 + 4 x + 2 = 0 ? | "a / b + b / a = ( a 2 + b 2 ) / ab = ( a 2 + b 2 + a + b ) / ab = [ ( a + b ) 2 - 2 ab ] / ab a + b = - 4 / 1 = - 4 ab = 2 / 1 = 2 hence a / b + b / a = [ ( - 4 ) 2 - 2 ( 2 ) ] / 2 = 4 / 2 = 2 . c )" | a = negate ** (
b = a / 2
c = b - 2
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a ) 3 , b ) 2 , c ) 4 , d ) 8 , e ) 6 | d | subtract(50248, multiply(floor(divide(50248, 20)), 20)) | what least no . must be subtracted from 50248 so that remaining no . is divisible by 20 ? | "explanation : on dividing 50248 by 20 we get the remainder 8 , so 8 should be subtracted option d" | a = 50248 / 20
b = math.floor(a)
c = b * 20
d = 50248 - c
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a ) 200 , b ) 384 , c ) 345 , d ) 480 , e ) 242 | d | multiply(32, 15) | find the area of a parallelogram with base 32 cm and height 15 cm . | "area of a parallelogram = base * height = 32 * 15 = 480 cm 2 answer : option d" | a = 32 * 15
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a ) 30 min , b ) 35 min , c ) 45 min , d ) 50 min , e ) 55 min | a | multiply(add(const_3, 4), 5) | a clock shows the time as 10 a . m . if the minute hand gains 5 minutes every hour , how many minutes will the clock gain by 4 p . m . ? | "there are 6 hours in between 10 a . m . to 4 p . m . 6 * 5 = 30 minutes . answer : a" | a = 3 + 4
b = a * 5
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a ) 480 , b ) 2,880 , c ) 21,600 , d ) 28,800 , e ) 48,000 | c | multiply(6, const_3600) | a space shuttle orbits the earth at about 6 kilometers per second . this speed is equal to how many kilometers per hour ? | seconds in 1 hours : 60 s in 1 min 60 min in 1 hr 60 * 60 = 3600 sec in 1 hr 6 * 3600 = 21,600 answer : c | a = 6 * 3600
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a ) 1 / 3 , b ) 2 / 3 , c ) 1 / 2 , d ) 3 / 4 , e ) 3 / 7 | a | divide(choose(const_2, const_1), factorial(const_3)) | a father purchased dress for his 3 daughters . the dresses are of same color but diff size and they are kept in dark room . what is probability that all the 3 will not choose there own dress ? | explanation : let 1 st girl come and she choose wrong dress so probability of that girl to choose wrong dress out of 3 is = 2 / 3 . now 2 nd girl come nd she choose wrong dress so probability of that girl to choose wrong dress out of 2 is 1 / 2 . now for 3 rd girl probability is 1 to choose wrong dress . so probability tht all the 3 wil not choose der own dress is = 2 / 3 * 1 / 2 * 1 = 1 / 3 . hence ( a ) is the correct answer . answer : a | a = math.comb(2, 1)
b = math.factorial(3)
c = a / b
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a ) 22 , b ) 23 , c ) 24 , d ) 26 , e ) 28 | c | divide(subtract(multiply(48, const_4), 144), const_2) | a man has some hens and cows . if the number of heads be 48 and the number of feet equals 144 , then the number of hens will be : | "let hens be x and cows be y now , feet : x * 2 + y * 4 = 144 heads : x * 1 + y * 1 = 48 implies , 2 x + 4 y = 144 and x + y = 48 solving these two equations , we get x = 24 and y = 24 therefore , hens are 26 . answer : c" | a = 48 * 4
b = a - 144
c = b / 2
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a ) 47 , b ) 37 , c ) 39 , d ) 43 , e ) 33 | e | add(subtract(60, multiply(3, 10)), 3) | a batsman in his 10 th innings makes a score of 60 , and thereby increases his average by 3 . what is his average after the 10 th innings ? he had never been ’ not out ’ . | "average score before 10 th innings = 60 - 3 × 10 = 30 average score after 10 th innings = > 30 + 3 = 33 answer : e" | a = 3 * 10
b = 60 - a
c = b + 3
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a ) 2200 , b ) 5500 , c ) 3300 , d ) 1100 , e ) 4400 | e | multiply(circumface(10), 14) | the radius of a cylinder is 10 m , height 14 m . the volume of the cylinder is : | "cylinder volume = π r ( power 2 ) h = 22 / 7 × 10 × 10 × 14 = 4400 m ( power 3 ) answer is e ." | a = circumface * (
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a ) 62.5 , b ) 62.3 , c ) 65 , d ) 62.2 , e ) 62.9 | c | divide(multiply(add(47.50, divide(multiply(47.50, 30), const_100)), const_100), subtract(const_100, 5)) | at what price must an article costing rs . 47.50 be marked in order that after deducting 5 % from the list price . it may be sold at a profit of 30 % on the cost price ? | "cp = 47.50 sp = 47.50 * ( 130 / 100 ) = 61.75 mp * ( 95 / 100 ) = 61.75 mp = 65 answer : c" | a = 47 * 50
b = a / 100
c = 47 + 50
d = c * 100
e = 100 - 5
f = d / e
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a ) rs . 4000 , b ) rs . 3603 , c ) rs . 3639 , d ) rs . 3632 , e ) rs . 3602 | a | subtract(10000, multiply(divide(3, 5), 10000)) | income and expenditure of a person are in the ratio 5 : 3 . if the income of the person is rs . 10000 , then find his savings ? | "let the income and the expenditure of the person be rs . 5 x and rs . 3 x respectively . income , 5 x = 10000 = > x = 2000 savings = income - expenditure = 5 x - 3 x = 2 x so , savings = rs . 2 * 2000 = rs . 4000 answer : a" | a = 3 / 5
b = a * 10000
c = 10000 - b
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['a ) 22 .', 'b ) 25 .', 'c ) 30 .', 'd ) 32 .', 'e ) 34 .'] | a | subtract(triangle_perimeter(6, 8, sqrt(add(power(6, const_2), power(8, const_2)))), const_2) | in a triangle , one side is 6 cm and another side is 8 cm . which of the following can be the perimeter of the triangle ? | given : one side is 6 cm and another side is 8 cm . so the 3 rd side will be > 3 and < 15 . thus the perimeter will be : 18 < perimeter < 30 . only option satisfying this condition is 22 . hence a . | a = 6 ** 2
b = 8 ** 2
c = a + b
d = math.sqrt(c)
e = triangle_perimeter - (
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a ) 100 , b ) 120 , c ) 90 , d ) 80 , e ) 70 | a | subtract(multiply(multiply(divide(50, add(3, 1)), 3), 3), multiply(divide(50, add(3, 1)), 1)) | in 50 l can , milk and water in the ratio of 3 : 1 . if the ratio has made 1 : 3 then the quantity of water that has to be added further is ? | 100 litre water is to be added . let ' x ' liter water is to be added more . then 1 / 3 = 37.5 / ( 12.5 + x ) x = 100 answer : a | a = 3 + 1
b = 50 / a
c = b * 3
d = c * 3
e = 3 + 1
f = 50 / e
g = f * 1
h = d - g
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a ) 93324 , b ) 92324 , c ) 93424 , d ) 93424 , e ) 93824 | a | multiply(add(add(const_100, const_4), subtract(multiply(const_100, const_10), 1,2)), divide(add(divide(subtract(subtract(multiply(const_100, const_10), 1,2), add(const_100, const_4)), 1,2), const_1), const_2)) | find the sum of all 4 digit numbers formed using digits 1,2 , 5,6 . | "( n - 1 ) ! * ( 111 . . . n ) * ( sum of the digits ) = ( 4 - 1 ) ! * 1111 * ( 1 + 2 + 5 + 6 ) = 93324 answer : a" | a = 100 + 4
b = 100 * 10
c = b - 1
d = a + c
e = 100 * 10
f = e - 1
g = 100 + 4
h = f - g
i = h / 1
j = i + 1
k = j / 2
l = d * k
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a ) 200.9 , b ) 2.06 , c ) 20.06 , d ) 100.9 , e ) 200.6 | a | divide(8.036, 0.04) | 8.036 divided by 0.04 gives : | "= 8.036 / 0.04 = 803.6 / 4 = 200.9 answer is a ." | a = 8 / 36
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a ) 1.2 , b ) 1.4 , c ) 6 , d ) 7 , e ) none | c | divide(multiply(multiply(20, 6), 5), const_100) | the simple interest on rs . 20 for 6 months at the rate of 5 paise per rupeeper month is | "sol . s . i . = rs . [ 20 * 5 / 100 * 6 ] = rs . 6 answer c" | a = 20 * 6
b = a * 5
c = b / 100
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a ) $ 1 , b ) $ 1.84 , c ) $ 1.98 , d ) $ 2.34 , e ) $ 2.56 | b | divide(add(add(multiply(add(7, const_1), const_10), const_4), const_100), const_100) | tom has travelling to 7 cities . gasoline prices varied from city to city . what is the median gasoline price ? | ordering the data from least to greatest , we get : $ 1.61 , $ 1.75 , $ 1.79 , $ 1.84 , $ 1.96 , $ 2.09 , $ 2.11 the median gasoline price is $ 1.84 . ( there were 3 states with higher gasoline prices and 3 with lower prices . ) b | a = 7 + 1
b = a * 10
c = b + 4
d = c + 100
e = d / 100
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a ) 7 , b ) 8 , c ) 9 , d ) 10 , e ) 11 | b | floor(sqrt(divide(8100, 102))) | if n is an integer and 102 n ^ 2 is less than or equal to 8100 , what is the greatest possible value of n ? | "102 * n ^ 2 < = 8100 n ^ 2 < = 8100 / 102 which will be less than 81 since 8100 / 100 = 81 which is the square of 9 next closest value of n where n ^ 2 < = 81 is 8 ans b" | a = 8100 / 102
b = math.sqrt(a)
c = math.floor(b)
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a ) 25 , b ) 19 , c ) 39 , d ) 61 , e ) 36 | e | multiply(multiply(4, divide(12, 4)), divide(12, 4)) | 4 mat - weavers can weave 4 mats in 4 days . at the same rate , how many mats would be woven by 12 mat - weavers in 12 days ? | "let the required number of bottles be x . more weavers , more mats ( direct proportion ) more days , more mats ( direct proportion ) wavers 4 : 12 : : 4 : x days 4 : 12 4 * 4 * x = 12 * 12 * 4 x = ( 12 * 12 * 4 ) / ( 4 x 4 ) x = 36 . answer is e ." | a = 12 / 4
b = 4 * a
c = 12 / 4
d = b * c
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a ) 1 , b ) 2 , c ) 3 , d ) 6 , e ) 9 | c | multiply(3, divide(6, 6)) | if 3 people can do 3 times of a particular work in 3 days , then how many days would it take 6 people to do 6 times of that particular work ? | "3 people can do the work one time in one day . 1 person can do 1 / 3 of the work in one day . 6 people can do 6 / 3 of the work in one day . 6 people can do 6 times the work in 3 days . the answer is c ." | a = 6 / 6
b = 3 * a
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a ) 9 . , b ) 12 . , c ) 35 . , d ) 16 . , e ) 18 . | c | add(4, multiply(14, 2)) | if 4 xz + yw = 7 and xw + yz = 14 , what is the value of the expression ( 2 x + y ) ( 2 z + w ) ? | "( 2 x + y ) * ( 2 z + w ) = 7 + 2 ( 14 ) = 35 answer : c" | a = 14 * 2
b = 4 + a
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a ) 3 , b ) 4 , c ) 6 , d ) 8 , e ) 10 | c | subtract(40, 30) | a , b , k start from the same place and travel in the same direction at speeds of 30 km / hr , 40 km / hr , 120 km / hr respectively . b starts two hours after a . if b and k overtake a at the same instant , how many hours after a did k start ? | "in 2 hours , a travels 60 km . b can catch a at a rate of 10 km / hr , so b catches a 6 hours after b starts . so a and b both travel a distance of 240 km . c needs 2 hours to travel 240 km , so c leaves 6 hours after a . the answer is c ." | a = 40 - 30
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a ) 2338.9 , b ) 2748.9 , c ) 2148.9 , d ) 2745.9 , e ) 2718.9 | b | divide(multiply(multiply(3, 55), multiply(1, const_1000)), multiply(const_1, const_60)) | a river 3 m deep and 55 m wide is flowing at the rate of 1 kmph the amount of water that runs into the sea per minute is ? | "rate of water flow - 1 kmph - - 1000 / 60 - - 16.66 m / min depth of river - - 3 m width of river - - 55 m vol of water per min - - 16.66 * 3 * 55 - - - 2748.9 answer b" | a = 3 * 55
b = 1 * 1000
c = a * b
d = 1 * const_60
e = c / d
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a ) 12 , b ) 18 , c ) 24 , d ) 28 , e ) 80 | e | multiply(4, divide(100, sqrt(add(power(4, const_2), power(3, const_2))))) | in x - y plane , there is a right triangle abc ( ∠ b = 90 o ) . if the length of ac is 100 and the slope of line segment ac is 4 / 3 , what is the length of ab ? | slope = change in vertical direction / change in horizontal direction = 4 / 3 change in vertical direction = 4 x = ab change in horizontal direction = 3 x = bc ab ^ 2 + bc ^ 2 = 100 ^ 2 16 x ^ 2 + 9 x ^ 2 = 10000 25 x ^ 2 = 400 x ^ 2 = 400 x = 20 therefore ab = 20 * 4 = 80 answer : e | a = 4 ** 2
b = 3 ** 2
c = a + b
d = math.sqrt(c)
e = 100 / d
f = 4 * e
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a ) 25 % , b ) 17 % , c ) 29 % , d ) 55 % , e ) 45 % | b | subtract(multiply(divide(const_100, 850), multiply(const_100, multiply(add(const_3, const_2), const_2))), const_100) | a dishonest dealer professes to sell goods at the cost price but uses a weight of 850 grams per kg , what is his percent ? | "850 - - - 150 100 - - - ? = > 17.64 % answer : b" | a = 100 / 850
b = 3 + 2
c = b * 2
d = 100 * c
e = a * d
f = e - 100
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a ) 2 / 21 , b ) 3 / 41 , c ) 5 / 26 , d ) 1 / 38 , e ) 5 / 32 | d | divide(choose(7, 3), choose(add(add(7, 9), 5), 3)) | a bag contains 7 red , 9 blue and 5 green balls . if 3 balls are picked at random , what is the probability that both are red ? | "p ( both are red ) , = 7 c 3 / 21 c 3 = ( 7 * 6 * 5 ) / 21 * 20 * 19 = 1 / 38 d" | a = math.comb(7, 3)
b = 7 + 9
c = b + 5
d = math.comb(c, 3)
e = a / d
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a ) 13.2 , b ) 17.5 , c ) 12.8 , d ) 34.25 , e ) 31.25 | b | divide(multiply(divide(add(const_4, const_3), add(add(const_4, const_3), const_2)), 40), const_2) | 40 is divided into two parts in such a way that seventh part of first and ninth part of second are equal . find the smallest part ? | "x / 7 = y / 9 = > x : y = 7 : 9 7 / 16 * 40 = 17.5 answer : b" | a = 4 + 3
b = 4 + 3
c = b + 2
d = a / c
e = d * 40
f = e / 2
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a ) 1 / 2 , b ) 2 / 5 , c ) 1 , d ) 3 / 2 , e ) 2 | b | divide(subtract(8, multiply(const_3, const_2)), subtract(multiply(const_3, const_2), 4)) | hammers and wrenches are manufactured at a uniform weight per hammer and a uniform weight per wrench . if the total weight of two hammers and three wrenches is one - third that of 8 hammers and 4 wrenches , then the total weight of one wrench is how many times that of one hammer ? | "x b é the weight of a hammer and y be the weight of a wrench . ( 2 x + 3 y ) = 1 / 3 * ( 8 x + 4 y ) 3 ( 2 x + 3 y ) = ( 8 x + 4 y ) 6 x + 9 y = 8 x + 4 y 5 y = 2 x y = 2 x / 5 ans - b" | a = 3 * 2
b = 8 - a
c = 3 * 2
d = c - 4
e = b / d
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a ) . 4 km , b ) 1.4 km , c ) 2.4 km , d ) 3.4 km , e ) none of these | c | divide(multiply(subtract(5, 1), const_3), 5) | a man can row at 5 kmph in still water . if the velocity of the current is 1 kmph and it takes him 1 hour to row to a place and come back . how far is that place . | "explanation : let the distance is x km rate downstream = 5 + 1 = 6 kmph rate upstream = 5 - 1 = 4 kmph then x / 6 + x / 4 = 1 [ because distance / speed = time ] = > 2 x + 3 x = 12 = > x = 12 / 5 = 2.4 km option c" | a = 5 - 1
b = a * 3
c = b / 5
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a ) 27 , b ) 36 , c ) 45 , d ) 50 , e ) 117 | d | subtract(divide(80, subtract(const_1, divide(5, 13))), 80) | in a certain school , the ratio of boys to girls is 5 to 13 . if there are 80 more girls than boys , how many boys are there ? | "the ratio of b to g is 5 : 13 and the other data point is g are more than boys by 80 . . . looking at the ratio we can say that the 8 ( 13 - 5 ) extra parts caused this diff of 80 . so 1 part corresponds to 80 / 8 = 10 and so 5 parts correspond to 5 * 10 = 50 . d" | a = 5 / 13
b = 1 - a
c = 80 / b
d = c - 80
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a ) $ 11 , b ) $ 5 , c ) $ 45 , d ) $ 400 , e ) $ 6.6 | e | divide(subtract(300, multiply(subtract(const_1, divide(10, const_100)), 300)), subtract(5, divide(const_1, const_2))) | a reduction in the price of petrol by 10 % enables a motorist to buy 5 gallons more for $ 300 . find the original price of petrol ? | "price decreased by 10 % , so 9 / 10 times , which means that original gallons bought increased 10 / 9 times . since this increase equals to 5 gallons then 45 gallons were bought originally ( 45 * 10 / 9 = 50 - - > increase 5 gallons ) . hence original price was 300 / 45 = $ 6.6 answer : e ." | a = 10 / 100
b = 1 - a
c = b * 300
d = 300 - c
e = 1 / 2
f = 5 - e
g = d / f
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a ) 100 , b ) 1000 , c ) 10000 , d ) 100000 , e ) none | c | divide(50000, subtract(9, 4)) | it costs a publishing company 50000 dollars to make books . the 50000 is a fixed cost or a cost that can not change . to help the publishing company sell the books , a marketing company charges 4 dollars for each book sold . if the company charges 9 dollars per book , how many books should they sell to break even ? | let c be the cost of producing and selling x books let r be the revenue made for selling x books r = selling price of 1 book × number of books sold r = 9 x c = fixed cost + variable cost variable cost = fee charged for 1 book × number of books sold variable cost = 4 x c = 50000 + 4 x r = c 9 x = 50000 + 4 x 9 x - 4 x = 50000 + 4 x - 4 x 5 x = 50000 x = 10000 since 5 × 10000 = 50000 the break even point is to sell 10000 books . answer c | a = 9 - 4
b = 50000 / a
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a ) 16 % , b ) 32 % , c ) 48 % , d ) 84 % , e ) 92 % | d | subtract(const_100, divide(subtract(const_100, 68), const_2)) | a certain characteristic in a large population has a distribution that is symmetric about the mean m . if 68 % of the distribution lies one standard deviation s of the mean , what percent of the distribution is less than m + s ? | "16 % ________________________________________________ m + s 34 % ________________________________________________ m 34 % ________________________________________________ m - s 16 % since 68 % lies one standard deviation from mean m , = > 50 % of 68 % lies on either side as it is symmetric about m . thus 16 % lie below m - s and 16 % lie above m + s now below m + s = 16 + 34 + 34 = 84 % hence d" | a = 100 - 68
b = a / 2
c = 100 - b
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a ) 5300.0 , b ) 24580.0 , c ) 16537.5 , d ) 7120.0 , e ) 6615.0 | e | multiply(power(add(divide(divide(10, const_2), const_100), const_1), const_2), 6000) | sam invested rs . 6000 @ 10 % per annum for one year . if the interest is compounded half - yearly , then the amount received by sam at the end of the year will be ? | p = rs . 6000 ; r = 10 % p . a . = 5 % per half - year ; t = 1 year = 2 half - year amount = [ 6000 * ( 1 + 5 / 100 ) 2 ] = ( 6000 * 21 / 20 * 21 / 20 ) = rs . 6615.00 answer : e | a = 10 / 2
b = a / 100
c = b + 1
d = c ** 2
e = d * 6000
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a ) 22 days , b ) 10 days , c ) 77 days , d ) 88 days , e ) 55 days | b | divide(subtract(multiply(30, 40), multiply(40, 20)), 40) | 30 men can do a work in 40 days . when should 20 men leave the work so that the entire work is completed in 40 days after they leave the work ? | "total work to be done = 30 * 40 = 1200 let 20 men leave the work after ' p ' days , so that the remaining work is completed in 40 days after they leave the work . 40 p + ( 20 * 40 ) = 1200 40 p = 400 = > p = 10 days answer : b" | a = 30 * 40
b = 40 * 20
c = a - b
d = c / 40
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a ) 189 cm 2 , b ) 150 cm 2 , c ) 127 cm 2 , d ) 450 cm 2 , e ) 187 cm 2 | d | multiply(multiply(divide(const_1, const_2), add(8, 10)), 50) | find the area of the quadrilateral of one of its diagonals is 50 cm and its off sets 10 cm and 8 cm ? | "1 / 2 * 50 ( 10 + 8 ) = 450 cm 2 answer : d" | a = 1 / 2
b = 8 + 10
c = a * b
d = c * 50
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a ) 110.5 , b ) 111.5 , c ) 112.5 , d ) 113.5 , e ) none of these | c | subtract(p_after_gain(divide(25, 4), 5000), p_after_gain(4, 5000)) | sachin borrows rs . 5000 for 2 years at 4 % p . a . simple interest . he immediately lends money to rahul at 25 / 4 % p . a . for 2 years . find the gain of one year by sachin . | explanation : two things need to give attention in this question , first we need to calculate gain for 1 year only . gain in 2 year = [ ( 5000 × 254 × 2100 ) − ( 5000 × 4 × 2100 ) ] = ( 625 − 400 ) = 225 so gain for 1 year = 2252 = 112.50 answer : c | a = 25 / 4
b = p_after_gain - (
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a ) 98.5 % , b ) 101.2 % , c ) 102.8 % , d ) 104.5 % , e ) 105.0 % | b | divide(multiply(add(const_100, multiply(const_100, 10)), add(subtract(const_100, 8), const_4)), multiply(const_100, 10)) | this year , mbb consulting fired 8 % of its employees and left remaining employee salaries unchanged . sally , a first - year post - mba consultant , noticed that that the average ( arithmetic mean ) of employee salaries at mbb was 10 % more after the employee headcount reduction than before . the total salary pool allocated to employees after headcount reduction is what percent of that before the headcount reduction ? | "100 employees getting 1000 $ avg , so total salary for 100 ppl = 100000 8 % reduction in employees lead to 92 employees and a salary increase of 10 % of previous avg salary thus the new avg salary is = 10 % ( 1000 ) + 1000 = 1100 so total salary of 92 employees is 92 * 1100 = 101200 now the new salary is more than previous salary by x % . x = ( 101200 / 100000 ) * 100 = 101.2 % so the answer is b" | a = 100 * 10
b = 100 + a
c = 100 - 8
d = c + 4
e = b * d
f = 100 * 10
g = e / f
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a ) 25 % , b ) 50 % , c ) 75 % , d ) 100 % , e ) 150 % | e | multiply(divide(subtract(6, 3), const_2), const_100) | on average , the bottle - nosed dolphin comes up for air once every 3 minutes ; the beluga whale , a close relative , comes up for air on average once every 6 minutes . the number of times a bottle - nosed dolphin would come up for air in a 24 hour period is approximately what percent greater than the number of times a beluga whale would come up for air in that same period ? | dolphin once in 3 min ; beluga once in 6 min ; so , dolphin comes up 2 times frequently than beluga , which is 150 % ( 6 - 3 ) / 2 * 100 . answer : e . | a = 6 - 3
b = a / 2
c = b * 100
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['a ) 35', 'b ) 36', 'c ) 37', 'd ) 38', 'e ) 39'] | b | divide(72, const_2) | the circumference of a circle is equal to 72 pi . find the radius of this circle . | the circumference of a circle is given by c = 2 pi r , where r is the radius of the circle . substitute c by 72 pi to obtain the equation 72 pi = 2 pi r simplify and solve for r to obtain r = 36 answer b | a = 72 / 2
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a ) 741 , b ) 752 , c ) 878 , d ) 785 , e ) 458 | c | subtract(subtract(multiply(25, 50), multiply(12, 17)), multiply(12, 14)) | the average of 25 results is 50 . the average of first 12 of those is 14 and the average of last 12 is 17 . what is the 13 th result ? | "solution : sum of 1 st 12 results = 12 * 14 sum of last 12 results = 12 * 17 13 th result = x ( let ) now , 12 * 14 + 12 * 17 + x = 25 * 50 or , x = 878 . answer : option c" | a = 25 * 50
b = 12 * 17
c = a - b
d = 12 * 14
e = c - d
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a ) 77 sec , b ) 66 sec , c ) 48 sec , d ) 36 sec , e ) 45 sec | d | multiply(divide(multiply(divide(475, const_1000), const_2), add(55, 40)), const_3600) | two trains each 475 m long are running in opposite directions on parallel tracks . their speeds are 55 km / hr and 40 km / hr respectively . find the time taken by the slower train to pass the driver of the faster one ? | relative speed = 55 + 40 = 95 km / hr . 95 * 5 / 18 = 475 / 18 m / sec . distance covered = 475 + 475 = 950 m . required time = 950 * 18 / 475 = 36 sec . answer : d | a = 475 / 1000
b = a * 2
c = 55 + 40
d = b / c
e = d * 3600
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a ) 20 , b ) 30 , c ) 40 , d ) 60 , e ) 65 | d | divide(divide(multiply(150, const_4), const_10), const_2) | mr . loyd wants to fence his square shaped land of 150 sqft each side . if a pole is laid every 10 ft how many poles do he need ? | "if each side is 120 feet . . then total perimeter is 150 * 4 = 600 poles every 10 feet hence no of poles = 600 / 10 = 60 answer : d" | a = 150 * 4
b = a / 10
c = b / 2
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a ) 1 / 42 , b ) 1 / 21 , c ) 1 / 7 , d ) 1 / 3 , e ) 1 / 2 | c | divide(3, multiply(7, 3)) | in a city where all streets run east - to - west , all avenues run north - to - south , and all intersections are right angles as shown below , jenn needs to walk from the corner of 1 st street and 1 st avenue to the corner of 6 th street and 3 rd avenue . if her friend amanda is sitting on a bench on 4 th street halfway between 1 st and 2 nd avenues , and jenn chooses her path randomly from any route that will allow her to walk exactly 7 blocks to her destination , what is the probability that jenn will walk down 4 th st . past amanda ? | all routes between ( 1,1 ) to ( 3,6 ) = 7 ! / ( 2 ! * 5 ! ) = 21 routes which pass 4 th st . between 1 st and 2 nd avenue = routs between ( 1,1 ) to ( 1,4 ) * routs between ( 2,4 ) to ( 3,6 ) = 1 * ( 3 ! / ( 2 ! * 1 ! ) ) = 3 the probability that jenn will walk down 4 th st . past amanda = 3 / 21 = 1 / 7 c is correct . | a = 7 * 3
b = 3 / a
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a ) 46 m , b ) 60 m , c ) 58 m , d ) 75 m , e ) 80 m | d | divide(add(divide(5300, 26.50), multiply(const_2, 50)), const_4) | length of a rectangular plot is 50 mtr more than its breadth . if the cost of fencin g the plot at 26.50 per meter is rs . 5300 , what is the length of the plot in mtr ? | "let breadth = x metres . then , length = ( x + 50 ) metres . perimeter = 5300 / 26.5 m = 200 m . 2 [ ( x + 50 ) + x ] = 200 2 x + 50 = 100 2 x = 50 x = 25 . hence , length = x + 50 = 75 m d" | a = 5300 / 26
b = 2 * 50
c = a + b
d = c / 4
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a ) s . 9800 , b ) s . 3800 , c ) s . 9800 , d ) s . 4400 , e ) s . 6880 | d | divide(multiply(multiply(multiply(24, 4), 4), 110000), multiply(multiply(multiply(10, 16), 6), 10)) | 10 camels cost as much as 24 horses , 16 horses cost as much as 4 oxen and 6 oxen as much as 4 elephants . if the cost of 10 elephants is rs . 110000 , find the cost of a camel ? | "cost of the camel = p 10 camels = 24 horses 16 horses = 4 oxen 6 oxen = 4 elephants 10 elephants = rs . 110000 p = rs . [ ( 24 * 4 * 4 * 110000 ) / ( 10 * 16 * 6 * 10 ) ] p = rs . ( 42240000 / 9600 ) = > p = rs . 4400 answer : d" | a = 24 * 4
b = a * 4
c = b * 110000
d = 10 * 16
e = d * 6
f = e * 10
g = c / f
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a ) 35 / 189 , b ) 33 / 129 , c ) 25 / 189 , d ) 24 / 113 , e ) 20 / 189 | c | divide(multiply(5, 5), add(multiply(const_60, const_3), multiply(const_3, const_3))) | kyle , david , and catherine each try independently to solve a problem . if their individual probabilities for success are 1 / 3 , 2 / 7 and 5 / 9 , respectively , what is the probability that kyle and catherine , but not david will solve the problem ? | p ( kyle will solve ) = 1 / 3 p ( david will not solve ) = 1 - 2 / 7 = 5 / 7 p ( catherine will solve ) = 5 / 9 p = ( 1 / 3 ) * ( 5 / 7 ) * ( 5 / 9 ) = 25 / 189 answer : c | a = 5 * 5
b = const_60 * 3
c = 3 * 3
d = b + c
e = a / d
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a ) 32 kmph , b ) 33 kmph , c ) 34 kmph , d ) 35 kmph , e ) 36 kmph | e | divide(add(100, 50), add(divide(100, 30), divide(50, 60))) | a car travels uphill at 30 km / hr and downhill at 60 km / hr . it goes 100 km uphill and 50 km downhill . find the average speed of the car ? | "avg speed = total distance / total time . total distance traveled = 100 + 50 = 150 km ; time taken for uphill journey = 100 / 30 = 10 / 3 ; time taken for down hill journey = 50 / 60 = 5 / 6 ; avg speed = 150 / ( 10 / 3 + 5 / 6 ) = 36 kmph answer : e" | a = 100 + 50
b = 100 / 30
c = 50 / 60
d = b + c
e = a / d
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a ) 22 , b ) 20 , c ) 88 , d ) 71 , e ) 12 | e | divide(multiply(multiply(3, const_2), 10), subtract(11, multiply(3, const_2))) | a work which could be finished in 11 days was finished 3 days earlier after 10 more men joined . the number of men employed was ? | "x - - - - - - - 11 ( x + 10 ) - - - - 6 x * 11 = ( x + 10 ) 6 x = 12 \ answer : e" | a = 3 * 2
b = a * 10
c = 3 * 2
d = 11 - c
e = b / d
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a ) 12 , b ) 16 , c ) 24 , d ) 60 , e ) 98 | d | lcm(multiply(3, 5), multiply(4, 5)) | the ratio of numbers is 3 : 4 and their h . c . f is 5 . their l . c . m is : | "let the numbers be 3 x and 4 x . then their h . c . f = x . so , x = 5 . so , the numbers are 15 and 20 . l . c . m of 15 and 20 = 60 . answer : d" | a = 3 * 5
b = 4 * 5
c = math.lcm(a, b)
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a ) 40 , b ) 50 , c ) 90 , d ) 140 , e ) it can not be determined from the information given . | a | subtract(multiply(70, const_2), multiply(50, const_2)) | if the average ( arithmetic mean ) of a and b is 50 and the average of b and c is 70 , what is the value of c − a ? | "- ( a + b = 100 ) b + c = 140 c - a = 40 a . 40" | a = 70 * 2
b = 50 * 2
c = a - b
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a ) $ 10000 , b ) $ 12000 , c ) $ 5000 , d ) $ 6000 , e ) $ 7500 | d | multiply(16000, subtract(const_1, divide(divide(18000, const_2), add(15000, divide(18000, const_2))))) | a invested $ 15000 in a business after 6 months b invested $ 18000 in the business . end of the year if they got $ 16000 as profit . find b shares ? | "a : b = 15000 * 12 : 18000 * 6 a : b = 5 : 3 a ' s share = 16000 * 5 / 8 = 10000 b ' s share = 16000 * 3 / 8 = 6000 answer is d" | a = 18000 / 2
b = 18000 / 2
c = 15000 + b
d = a / c
e = 1 - d
f = 16000 * e
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a ) 60 % , b ) 65 % , c ) 70 % , d ) 75 % , e ) 80 % | a | subtract(add(add(85, 70), 5), const_100) | if 85 percent of the test takers taking an old paper and pencil gmat exam answered the first question on a given math section correctly , and 70 percent of the test takers answered the second question correctly , and 5 percent of the test takers answered neither question correctly , what percent answered both correctly ? | "{ total } = { first correctly } + { second correctly } - { both correctly } + { neither correctly } 100 = 85 + 70 - { both correctly } + 5 { both correctly } = 60 . answer : a ." | a = 85 + 70
b = a + 5
c = b - 100
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a ) a ) 30 , b ) b ) 3 , c ) c ) 4 , d ) d ) 6 , e ) e ) 7 | a | divide(multiply(44, 400), 35) | a number when divided by 44 , gives 400 as quotient and 0 as remainder . what will be the remainder when dividing the same number by 35 | "explanation : p ÷ 44 = 400 = > p = 400 * 44 = 17600 p / 35 = 17600 / 35 = 502 , remainder = 30 answer : option a" | a = 44 * 400
b = a / 35
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a ) 300 sq m , b ) 220 sq m , c ) 200 sq m , d ) 400 sq m , e ) 800 sq m | b | divide(square_area(22), const_2) | what is the area of a square field whose diagonal of length 22 m ? | "d 2 / 2 = ( 22 * 22 ) / 2 = 220 answer : b" | a = square_area / (
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a ) 0.28 , b ) 0.36 , c ) 0.45 , d ) 0.56 , e ) 0.7 | b | multiply(multiply(0.18, 0.2), const_10) | if p ( a ) = 0.18 , p ( b ) = 0.5 and p ( b | a ) = 0.2 , find p ( a n b ) ? | p ( b | a ) = p ( a n b ) / p ( a ) p ( a n b ) = p ( b | a ) × p ( a ) p ( a n b ) = 0.2 × 0.18 p ( a n b ) = 0.36 b ) | a = 0 * 18
b = a * 10
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a ) 50 , b ) 100 , c ) 150 , d ) 200 , e ) 250 | d | divide(subtract(multiply(100, divide(60, const_100)), multiply(100, divide(55, const_100))), subtract(divide(55, const_100), divide(50, const_100))) | a survey of n people in the town of eros found that 50 % of them preferred brand a . another surveyof 100 people in the town of angie found that 60 % preferred brand a . in total , 55 % of all the people surveyed together preferred brand a . what is the total number of people surveyed ? | "50 % of n people from eros prefer brand a . 50 % of n is 50 / 100 x n = n / 2 . 60 % of 100 people from angie prefer brand a . 60 % of 100 is 60 / 100 x 100 = 60 . of the total n + 100 people surveyed , n / 2 + 60 prefer brand a . given that this is 55 % , we have ( n / 2 + 60 ) / ( n + 100 ) x 100 = 55 solving the equation ( n / 2 + 60 ) / ( n + 100 ) x 100 = 55 ( n / 2 + 60 ) = 55 / 100 x ( n + 100 ) ( n / 2 + 60 ) = 11 / 20 n + 55 0 = 11 n / 20 – n / 2 + 55 - 60 now subtracting n / 2 and 60 from both sides 0 = n / 20 - 5 adding 5 on both sides 5 = n / 20 n = 100 hence , the total number of people surveyed is n + 100 = 100 + 100 = 200 . answer : d" | a = 60 / 100
b = 100 * a
c = 55 / 100
d = 100 * c
e = b - d
f = 55 / 100
g = 50 / 100
h = f - g
i = e / h
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a ) 1430.08 , b ) 1420.06 , c ) 781.189 , d ) 656.112 , e ) 456.512 | a | multiply(325.124, power(12.98, 3.001)) | 325.124 x 12.98 ã · 3.001 + 21.21 = ? | "explanation : ? = 325.124 x 12.98 ã · 3.001 + 21.21 = ? â ‰ ˆ ( 325.124 x 13 / 3 ) + 21.21 â ‰ ˆ 1408.87 + 21.21 â ‰ ˆ 1430.080 answer : option a" | a = 12 ** 98
b = 325 * 124
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a ) 2 : 3 , b ) 3 : 2 , c ) 1 : 3 , d ) 2 : 1 , e ) none of these | b | divide(subtract(15, 9), subtract(19, 15)) | gold is 19 times as heavy as water and copper is 9 times heavy . in what ratio must these metals be mixed so that the mixture may be 15 times as heavy as water ? | "? required ratio = 6 ? 4 = 3 : 2 answer b" | a = 15 - 9
b = 19 - 15
c = a / b
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['a ) 5.6 cm', 'b ) 2.4 cm', 'c ) 4.8 cm', 'd ) 2.16 cm', 'e ) 3.2 cm'] | a | divide(multiply(7, 8), const_10) | in triangle pqr , the angle q = 90 degree , pq = 7 cm , qr = 8 cm . x is a variable point on pq . the line through x parallel to qr , intersects pr at y and the line through y , parallel to pq , intersects qr at z . find the least possible length of xz | look at the diagram below : now , in case when qy is perpendicular to pr , two right triangles pqr and pqy are similar : qy : qp = qr : pr - - > qy : 7 = 8 : 10 - - > qy = 5.6 . answer : a . | a = 7 * 8
b = a / 10
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a ) 20 , b ) 11 , c ) 23 , d ) 26 , e ) 21 | d | add(15, 11) | in a family 15 people eat only vegetarian , 8 people eat only non veg . , 11 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 = 15 + 11 = 26 answer = d" | a = 15 + 11
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a ) 10 s , b ) 11 s , c ) 4 s , d ) 8 s , e ) 12 s | b | divide(add(125, 150), add(divide(multiply(54, const_1000), const_3600), divide(multiply(36, const_1000), const_3600))) | two trains a and b are 125 m and 150 m long and are moving at one another at 54 km / hr and 36 km / hr respectively . arun is sitting on coach b 1 of train a . calculate the time taken by arun to completely cross train b . | "detailed solution speed of a = 54 ∗ 1000 / 60 ∗ 60 = 15 m / s speed of b = 36 ∗ 1000 / 60 ∗ 60 = 10 m / s relative speed = s 1 + s 2 = 15 + 10 m / s = 25 m / s the length that needs to be crossed = length of train b = 150 m . therefore time taken = 150 / 25 = 6 s . what is the time taken for trains to completely cross each other ? the length that needs to be crossed = 125 + 150 = 275 m . time taken = 275 / 25 = 11 s . correct answer b ." | a = 125 + 150
b = 54 * 1000
c = b / 3600
d = 36 * 1000
e = d / 3600
f = c + e
g = a / f
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a ) 22 hours , b ) 30 hours , c ) 44 hours , d ) 60 hours , e ) it can not be determined from the information above . | c | divide(const_1, divide(add(divide(const_1, 4), divide(const_1, 11)), 15)) | together , 15 type a machines and 7 type b machines can complete a certain job in 4 hours . together 8 type b machines and 15 type c machines can complete the same job in 11 hours . how many hours t would it take one type a machine , one type b machine , and one type c machine working together to complete the job ( assuming constant rates for each machine ) ? | "say the rates of machines a , b and c are a , b , and c , respectively . together 15 type a machines and 7 type b machines can complete a certain job in 4 hours - - > 15 a + 7 b = 1 / 4 ; together 8 type b machines and 15 type c machines can complete the same job in 11 hours - - > 8 b + 15 c = 1 / 11 . sum the above : 15 a + 15 b + 15 c = 1 / 4 + 1 / 11 = 15 / 44 - - > reduce by 15 : a + b + c = 1 / 44 - - > so , the combined rate of the three machines is 1 / 44 job / hour - - > time is reciprocal of the rate , thus machines a , b and c can do the t job in 44 hours . answer : c ." | a = 1 / 4
b = 1 / 11
c = a + b
d = c / 15
e = 1 / d
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a ) 44 min , b ) 55 min , c ) 47 min , d ) 67 min , e ) 45 min | a | divide(add(320, 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 320 m long platform ? | "a 44 min 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 + 320 ) / 36 * 5 / 18 = 44 min ." | a = const_0_2778 * 36
b = a * 12
c = 320 + b
d = const_0_2778 * 36
e = c / d
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a ) 10 % , b ) 20 % , c ) 40 % , d ) 50 % , e ) 60 % | d | multiply(divide(subtract(450, 300), 300), const_100) | the price of a book is increased from $ 300 to $ 450 . what is the % of increase in its price ? | "explanation : change in the price = rs 450 â € “ rs 300 = rs 150 percentage of increase = change in the price initial price * 100 . percentage increase in price = ( 150 300 ) * 100 = 50 % d" | a = 450 - 300
b = a / 300
c = b * 100
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a ) 24 , 2 , b ) 12 , 6 , c ) 15 , 3 , d ) 14 , 4 , e ) none of these | a | divide(divide(add(26, 22), const_2), const_2) | a man can row downstream at 26 kmph and upstream at 22 kmph . find the speed of the man in still water and the speed of stream respectively ? | "explanation : let the speed of the man in still water and speed of stream be x kmph and y kmph respectively . given x + y = 26 - - - ( 1 ) and x - y = 22 - - - ( 2 ) from ( 1 ) & ( 2 ) 2 x = 48 = > x = 24 , y = 2 . answer : option a" | a = 26 + 22
b = a / 2
c = b / 2
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a ) 1 hour , b ) 30 min , c ) 3 hours 20 min , d ) 2 hours 30 min , e ) 2 hours | e | divide(divide(multiply(divide(6, 7), 20), subtract(const_1, divide(6, 7))), const_60) | a train is walking at 6 / 7 of its usual speed , the train is 20 minutes too late . find its usual time to cover the journey . | new speed = 6 / 7 of the usual speed new time taken = 7 / 6 of the usual time taken so , ( 7 / 6 of the usual time ) - ( usual time ) = 20 min 1 / 6 of the usual time = 20 min usual time = 20 * 6 = 120 min = 2 hours correct option is e | a = 6 / 7
b = a * 20
c = 6 / 7
d = 1 - c
e = b / d
f = e / const_60
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a ) 2 , b ) 4 , c ) 10 , d ) 15 , e ) 17 | b | subtract(multiply(80, divide(30, const_100)), multiply(divide(4, const_100), 5)) | by how much is 30 % of 80 greater than 4 / 5 th of 25 ? | "answer it is ( 30 x 80 ) / 100 - ( 4 x 25 ) / 5 = 24 - 20 = 4 correct option : b" | a = 30 / 100
b = 80 * a
c = 4 / 100
d = c * 5
e = b - d
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a ) 79 , b ) 81 , c ) 83 , d ) 85 , e ) 87 | c | add(divide(subtract(multiply(77, 4), add(6, add(4, 6))), 4), add(4, 6)) | there are 4 people of different heights standing in order of increasing height . the difference is 2 inches between the first person and the second person , and also between the second person and the third person . the difference between the third person and the fourth person is 6 inches and the average height is 77 . how tall is the fourth person ? | "let x be the height of the first person . then the heights are x , x + 2 , x + 4 , and x + 10 . 4 x + 16 = 4 ( 77 ) = 308 x = 73 and the fourth person has a height of 73 + 10 = 83 inches the answer is c ." | a = 77 * 4
b = 4 + 6
c = 6 + b
d = a - c
e = d / 4
f = 4 + 6
g = e + f
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a ) 0.15 , b ) 0.20 , c ) 0.25 , d ) 0.30 , e ) 0.33 | b | divide(add(add(5, 6), 9), const_100) | t = { 2 , 3 , 4 , 5 } b = { 4 , 5 , 6 , 7 , 8 } two integers will be randomly selected from the sets above , one integer from set t and one integer from set b . what is the probability that the sum of the two integers will equal 9 ? | the total number of pairs t , b possible is 4 * 5 = 20 . out of these 20 pairs only 4 sum up to 9 : ( 2 , 7 ) ; ( 3 , 6 ) , ( 4 , 5 ) and ( 5 , 4 ) . the probability thus is 4 / 20 = 0.2 . answer : b . | a = 5 + 6
b = a + 9
c = b / 100
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a ) 6.7 , b ) 4 , c ) 6 , d ) 9 , e ) 3 | a | divide(add(7, subtract(7, 1.5)), const_2) | a man whose speed is 7 kmph in still water rows to a certain upstream point and back to the starting point in a river which flows at 1.5 kmph , find his average speed for the total journey ? | "m = 7.0 s = 1.5 ds = 8.5 us = 5.5 as = ( 2 * 8.5 * 5.5 ) / 14 = 6.7 answer : a" | a = 7 - 1
b = 7 + a
c = b / 2
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a ) 3000 , b ) 6000 , c ) 2000 , d ) 4000 , e ) none of them | b | divide(360, multiply(divide(2, const_100), 3)) | a sum was put at simple interest at a certain rate for 3 years . had it been put at 2 % higher rate , it would have fetched rs . 360 more . find the sum . | "let sum = p and original rate = r . then , [ ( p * ( r + 2 ) * 3 ) / 100 ] – [ ( p * r * 3 ) / 100 ] = 360 . = 3 pr + 6 p - 3 pr = 36000 6 p = 36000 p = 6000 hence , sum = rs . 6000 . answer is b ." | a = 2 / 100
b = a * 3
c = 360 / b
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a ) 6 ^ 5 , b ) 5 ^ 6 , c ) ( 30 / 7 ) ^ 5 , d ) 6 ^ 3 , e ) 15 ^ 3 | c | divide(power(30, 10), power(30, 5)) | 30 ^ 10 / 210 ^ 5 = ? | "30 ^ 10 / 210 ^ 5 = ? a . 6 ^ 5 b . 5 ^ 6 c . ( 30 / 7 ) ^ 5 d . 6 ^ 3 e . 15 ^ 3 - > 30 ^ 10 / 210 ^ 5 = ( 30 ^ 10 ) / ( 7 ^ 5 ) ( 30 ^ 5 ) = ( 30 ^ 5 ) / ( 7 ^ 5 ) = ( 30 / 7 ) ^ 5 . thus , c is the answer ." | a = 30 ** 10
b = 30 ** 5
c = a / b
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a ) 400 , b ) 420 , c ) 430 , d ) 450 , e ) 510 | d | divide(subtract(multiply(15, 420), 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 . 420 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 * 420 + x * 110 = ( x + 15 ) 120 x = 450 d" | a = 15 * 420
b = 15 * 120
c = a - b
d = 120 - 110
e = c / d
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a ) 4 . , b ) 8 . , c ) 12 . , d ) 16 . , e ) 64 . | a | power(subtract(9, divide(add(13, 9), 2)), 2) | if ( a - b - c + d = 13 ) and ( a + b - c - d = 9 ) , what is the value of ( b - d ) ^ 2 ? | "eq 1 : a - b - c + d = 13 eq 2 : a + b - c - d = 9 ( 1 ) subtract eq 1 from eq 2 a - b - c + d = 13 - a + b - c - d = 9 - - - - - - - - - - - - - - - - - - - - - - - - - 2 b + 2 d = 4 ( 2 ) simplify - b + d = 2 b - d = - 2 ( b - d ) ^ 2 = ( - 2 ) ^ 2 = 4 my answer : a" | a = 13 + 9
b = a / 2
c = 9 - b
d = c ** 2
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a ) 2 % , b ) 4 % , c ) 8 % , d ) 10 % , e ) 15 % | b | multiply(divide(subtract(add(multiply(divide(25, const_100), 2), multiply(divide(70, const_100), 3)), add(subtract(3, multiply(divide(70, const_100), 3)), subtract(2, multiply(divide(25, const_100), 2)))), add(3, 2)), const_100) | in a certain state , the ratio of registered republicans to registered democrats is 3 to 2 , and every registered voter is either a republican or a democrat . if 70 percent of the republicans and 25 percent of the democrats are expected to vote for candidate x , and everyone else is expected to vote for candidate y , by what percent is candidate x expected to win the election ? | since we were expected to find a percentage figure - it thought that it might be easier to pick a ' smart number ' to represent the total number of voters ( republicans and democrats ) . therefore , i picked 100 ( as the total number of voters ) and thus 60 : 40 represents the number ratio of republicans : democrats . if 70 % of republicans ( which is ( 60 * 0.7 ) = 42 ) and 25 % of democrats ( 40 * 0.25 = 10 ) voted for candidate x , means that out of total of 100 voters ; 52 ( 42 + 10 ) voters voted for candidate x and 48 voted for candidate y . thus we can infer that candidate x is expected to win the election by 4 ( 52 - 48 ) votes . therefore candidate x is expected to win the election by ( 4 / 100 ) votes which is equivalent to 4 % . i think the answer is b . | a = 25 / 100
b = a * 2
c = 70 / 100
d = c * 3
e = b + d
f = 70 / 100
g = f * 3
h = 3 - g
i = 25 / 100
j = i * 2
k = 2 - j
l = h + k
m = e - l
n = 3 + 2
o = m / n
p = o * 100
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a ) $ 1,100 , b ) $ 1,200 , c ) $ 1,400 , d ) $ 1,800 , e ) $ 2,200 | a | subtract(1,000, 800) | a family pays $ 800 per year for an insurance plan that pays 85 percent of the first $ 1,000 in expenses and 100 percent of all medical expenses thereafter . in any given year , the total amount paid by the family will equal the amount paid by the plan when the family ' s medical expenses total . | "upfront payment for insurance plan = 800 $ family needs to pay 15 % of first 1000 $ in expense = 150 $ total amount paid by family when medical expenses are equal to or greater than 1000 $ = 800 + 150 = 950 $ total amount paid by insurance plan for first 1000 $ = 800 $ total amount paid by family will equal amount paid by plan when medical expense = 1100 $ ( since insurance plan will pay 100 % of amount that exceeds 950 $ ) answer a" | a = 1 - 0
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a ) 7 , b ) 6 , c ) 5 , d ) 9 , e ) 8 | c | multiply(6, add(const_1, divide(20, const_100))) | a vendor bought toffees at 6 for a dollar . how many for a dollar must he sell to gain 20 % ? | "c 5 c . p . of 6 toffees = $ 1 s . p . of 6 toffees = 120 % of $ 1 = $ 6 / 5 for $ 6 / 5 , toffees sold = 6 . for $ 1 . toffees sold = 6 * 5 / 6 = 5" | a = 20 / 100
b = 1 + a
c = 6 * b
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a ) 1 , b ) 4 , c ) 5 , d ) 6 , e ) 7 | a | add(const_4, const_4) | if each year the population of the country grows by 100 % , how many years will elapse before the population of the country doubles ? | "till year 2010 , population is 100 . year 2001 : population becomes 200 . . . . . . . . . . . . . 1 year elapsed answer : a" | a = 4 + 4
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a ) 50 , b ) 100 , c ) 200 , d ) 140 , e ) 2,000 | d | multiply(multiply(divide(50, 50), divide(50, 50)), const_1000) | positive integer y is 50 percent of 50 percent of positive integer x , and y percent of x equals 50 . what is the value of x ? | "y = 50 % of 50 % 0 f x = x / 4 and y / 100 of x = 50 y / 100 * 4 y = 50 y = 35 and x = 140 answer - d" | a = 50 / 50
b = 50 / 50
c = a * b
d = c * 1000
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a ) 19 , b ) 16 , c ) 15 , d ) 14 , e ) 13 | a | add(add(add(const_4, 3), add(3, const_2)), 3) | the number 149 can be written as the sum of the squares of 3 different positive integers . what is the sum of these 3 integers ? | "2 ^ 2 + 8 ^ 2 + 9 ^ 2 = 149 - - > 2 + 9 + 8 = 19 . a" | a = 4 + 3
b = 3 + 2
c = a + b
d = c + 3
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a ) 10780 , b ) 127600 , c ) 125000 , d ) 152000 , e ) 10000 | c | divide(power(power(8, const_2), const_3), power(8, const_3)) | a cube of side 8 meter length is cut into small cubes of side 16 cm each . how many such small cubes can be obtained ? | "along one edge , the number of small cubes that can be cut = 800 / 16 = 50 along each edge 50 cubes can be cut . ( along length , breadth and height ) . total number of small cubes that can be cut = 50 * 50 * 50 = 125000 answer : c" | a = 8 ** 2
b = a ** 3
c = 8 ** 3
d = b / c
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a ) 7 , b ) 6 , c ) 8 , d ) 4 , e ) 3 | a | subtract(28, add(7, 10)) | in a group of 28 junior high school students , 7 take french , 10 take spanish , and 4 take both languages . the students taking both french and spanish are not counted with the 7 taking french or the 10 taking spanish . how many students are not taking either french or spanish ? | "a 7 seven students are not taking a language . add 7 + 10 + 4 to get 21 . then subtract 21 from the total students : 28 - 21 = 7 ." | a = 7 + 10
b = 28 - a
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a ) 20 , b ) 30 , c ) 40 , d ) 50 , e ) 60 | e | divide(720, subtract(17, 5)) | on selling 17 balls at rs . 720 , there is a loss equal to the cost price of 5 balls . the cost price of a ball is | "( c . p . of 17 balls ) - ( s . p . of 17 balls ) = ( c . p . of 5 balls ) c . p . of 12 balls = s . p . of 17 balls = rs . 720 . c . p . of 1 ball = rs . 720 / 12 = rs . 60 . answer : e" | a = 17 - 5
b = 720 / a
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a ) 20 , b ) 21 , c ) 22 , d ) 23 , e ) 24 | e | divide(384, const_10) | the ratio between the perimeter and the width of a rectangle is 5 : 1 . if the area of the rectangle is 384 square centimeters , what is the length of the rectangle in centimeters ? | "perimeter = 2 ( w + l ) = 5 w 3 w = 2 l w = 2 l / 3 wl = 384 2 l ^ 2 / 3 = 384 l ^ 2 = 576 l = 24 cm the answer is e ." | a = 384 / 10
|
a ) $ 960 , b ) $ 1,500 , c ) $ 1,725 , d ) $ 2,050 , e ) $ 2,250 | b | divide(multiply(divide(multiply(add(add(multiply(const_3, const_100), multiply(8, 10)), const_4), const_1000), multiply(multiply(8, 10), 12)), 5.0), const_1000) | a hat company ships its hats , individually wrapped , in 8 - inch by 10 - inch by 12 - inch boxes . each hat is valued at $ 5.0 . if the company ’ s latest order required a truck with at least 288,000 cubic inches of storage space in which to ship the hats in their boxes , what was the minimum value of the order ? | "total volume is 288000 given lbh = 8 * 10 * 12 . the number of hats inside it = 288000 / 10 * 8 * 12 = 300 . price of each hat is 5 $ then total value is 300 * 5.0 = 1500 . imo option b is correct answer . ." | a = 3 * 100
b = 8 * 10
c = a + b
d = c + 4
e = d * 1000
f = 8 * 10
g = f * 12
h = e / g
i = h * 5
j = i / 1000
|
a ) 12880 , b ) 12789 , c ) 27108 , d ) 17600 , e ) 18291 | d | divide(multiply(add(const_100, 10), add(divide(multiply(12500, const_100), subtract(const_100, 20)), add(125, 250))), const_100) | ramesh purchased a refrigerator for rs . 12500 after getting a discount of 20 % on the labelled price . he spent rs . 125 on transport and rs . 250 on installation . at what price should it be sold so that the profit earned would be 10 % if no discount was offered ? | "explanation : price at which the tv set is bought = rs . 12,500 discount offered = 20 % marked price = 12500 * 100 / 80 = rs . 15625 the total amount spent on transport and installation = 125 + 250 = rs . 375 \ total price of tv set = 15625 + 375 = rs . 16000 the price at which the tv should be sold to get a profit of 10 % if no discount was offered = 16000 * 110 / 100 = rs . 17600" | a = 100 + 10
b = 12500 * 100
c = 100 - 20
d = b / c
e = 125 + 250
f = d + e
g = a * f
h = g / 100
|
a ) 3327 , b ) 3237 , c ) 3337 , d ) 2337 , e ) none of these | a | subtract(13200, 9873) | 9873 + x = 13200 , then x is ? | "answer x = 13200 - 9873 = 3327 option : a" | a = 13200 - 9873
|
a ) 1215 , b ) 1314 , c ) 2900 , d ) 1710 , e ) 2750 | d | divide(add(multiply(add(floor(divide(5, add(const_3, const_4))), const_1), 510), multiply(subtract(5, add(floor(divide(5, add(const_3, const_4))), const_1)), 240)), 5) | a library has an average of 510 visitors on sundays and 240 on other day . the average number of visitors in a month of 5 days starting with sunday is | "explanation : as the month begin with sunday , so there will be five sundays in the month . so result will be : = ( 510 × 5 + 240 × 25 / 30 ) = ( 8550 / 5 ) = 1710 answer : option d" | a = 3 + 4
b = 5 / a
c = math.floor(b)
d = c + 1
e = d * 510
f = 3 + 4
g = 5 / f
h = math.floor(g)
i = h + 1
j = 5 - i
k = j * 240
l = e + k
m = l / 5
|
a ) 355600 , b ) 355800 , c ) 356500 , d ) 356800 , e ) 333200 | e | multiply(multiply(560000, subtract(const_1, divide(15, const_100))), divide(70, const_100)) | in an election , candidate a got 70 % of the total valid votes . if 15 % of the total votes were declared invalid and the total numbers of votes is 560000 , find the number of valid vote polled in favor of candidate ? | total number of invalid votes = 15 % of 560000 = 15 / 100 × 560000 = 8400000 / 100 = 84000 total number of valid votes 560000 – 84000 = 476000 percentage of votes polled in favour of candidate a = 70 % therefore , the number of valid votes polled in favour of candidate a = 70 % of 476000 = 70 / 100 × 476000 = 33320000 / 100 = 333200 e ) | a = 15 / 100
b = 1 - a
c = 560000 * b
d = 70 / 100
e = c * d
|
a ) 20 , b ) 22 , c ) 24 , d ) 1 , e ) 30 | d | subtract(power(3, 3), const_1) | a telephone company needs to create a set of 3 - digit area codes . the company is entitled to use only digits 2 , 4 and 5 , which can be repeated . if the product of the digits in the area code must be odd , how many different codes can be created ? | "total # of codes possible is 3 * 3 * 3 = 27 . oit of those 27 codes only the product of 555 will be odd , the remaining 26 will have either 2 or 4 in them , which ensures that their product will be even . therefore the number of codes where the product of the digits is even = ( total ) - ( restriction ) = 27 - 26 = 1 . answer : d ." | a = 3 ** 3
b = a - 1
|
a ) 24 , b ) 12 , c ) 6 , d ) 4 , e ) 2 | e | divide(divide(30, const_3), const_3) | if a * b denotes the greatest common divisor of a and b , then ( ( 12 * 16 ) * ( 30 * 24 ) ) = ? | "the greatest common divisor of 12 and 16 is 4 . hence 12 * 16 = 4 ( note that * here denotes the function not multiplication ) . the greatest common divisor of 30 and 24 is 6 . hence 30 * 24 = 6 . hence ( ( 12 * 16 ) * ( 30 * 24 ) ) = 4 * 6 . the greatest common divisor of 4 and 6 is 2 . answer ; e ." | a = 30 / 3
b = a / 3
|
a ) 10 , b ) 12 , c ) 14 , d ) 16 , e ) 18 | b | divide(60, add(const_4, divide(const_2, const_2))) | a certain number of horses and an equal number of men are going somewhere . half of the owners are on their horses ' back while the remaining ones are walking along leading their horses . if the number of legs walking on the ground is 60 , how many horses are there ? | "legs 12 * 4 = 48 now half on their horses so remaining on the walk so 6 men 6 men has 12 legs so , 12 + 48 = 60 legs walking answer : b" | a = 2 / 2
b = 4 + a
c = 60 / b
|
a ) 10 % , b ) 12 % , c ) 16 % , d ) 18 % , e ) 20 % | e | divide(subtract(const_1, divide(90, const_100)), divide(2, const_100)) | in a certain parking lot , 2 % of the cars are towed for parking illegally . however 90 % of the cars which are parked illegally are not towed . what percentage of cars in the parking lot are parked illegally ? | "let x be the number of cars and let y be the number of cars parked illegally . 2 % * x = 10 % * y y / x = 1 / 5 = 20 % the answer is e ." | a = 90 / 100
b = 1 - a
c = 2 / 100
d = b / c
|
a ) 1.5 , b ) 2.5 , c ) 3.5 , d ) 4.5 , e ) 5.5 | d | multiply(divide(90, multiply(const_100, const_2)), 10) | a certain sky blue paint contains 10 percent blue pigment and 90 percent red pigment by weight . a certain green paint contains 70 percent blue pigment and 30 percent yellow pigment . when these paints are mixed to produce a brown paint , the brown paint contains 40 percent blue pigment . if the brown paint weighs 10 grams , then the red pigment contributes how many grams of that weight ? | 10 grams of combined mixture and 40 % blue pigment means that the mixtures were mixed 50 % each . thus 5 grams a piece . out of the 5 grams of the dark blue paint , 60 % is red . therefore , 5 * . 9 = 4.5 grams of red pigment | a = 100 * 2
b = 90 / a
c = b * 10
|
a ) 25 , b ) 76 , c ) 29 , d ) 12 , e ) 20 | c | divide(subtract(subtract(subtract(985, multiply(16, 6)), multiply(5, 45)), multiply(7, 70)), 6) | alok ordered 16 chapatis , 5 plates of rice , 7 plates of mixed vegetable and 6 ice - cream cups . the cost of each chapati is rs . 6 , that of each plate of rice is rs . 45 and that of mixed vegetable is rs . 70 . the amount that alok paid the cashier was rs . 985 . find the cost of each ice - cream cup ? | explanation : let the cost of each ice - cream cup be rs . x 16 ( 6 ) + 5 ( 45 ) + 7 ( 70 ) + 6 ( x ) = 985 96 + 225 + 490 + 6 x = 985 6 x = 174 = > x = 29 . answer : c | a = 16 * 6
b = 985 - a
c = 5 * 45
d = b - c
e = 7 * 70
f = d - e
g = f / 6
|
a ) 70 min , b ) 15 min , c ) 20.4 min , d ) 15.6 min , e ) 40 min | d | multiply(const_60, divide(subtract(65, 48), 65)) | excluding stoppages , the speed of a bus is 65 kmph and including stoppages , it is 48 kmph . for how many minutes does the bus stop per hour ? | "d 15.6 min due to stoppages , it covers 17 km less . time taken to cover 17 km = ( 17 / 65 x 60 ) min = 15.6 min" | a = 65 - 48
b = a / 65
c = const_60 * b
|
a ) 777 , b ) 500 , c ) 789 , d ) 776 , e ) 881 | b | divide(multiply(multiply(multiply(const_2, multiply(const_4, add(const_2, const_3))), const_100), subtract(const_1, divide(85, const_100))), add(subtract(const_1, divide(95, const_100)), subtract(const_1, divide(85, const_100)))) | a and b ’ s salaries together amount to rs . 2,000 . a spends 95 % of his salary and b spends 85 % of his . if now their savings are the same , what is b ’ s salary ? | "( 5 / 100 ) a = ( 15 / 100 ) b a = 3 b a + b = 2000 4 b = 2000 = > b = 500 answer b" | a = 2 + 3
b = 4 * a
c = 2 * b
d = c * 100
e = 85 / 100
f = 1 - e
g = d * f
h = 95 / 100
i = 1 - h
j = 85 / 100
k = 1 - j
l = i + k
m = g / l
|
a ) 84 , b ) 12 , c ) 67 , d ) 28 , e ) 21 | a | add(14, divide(divide(440, const_pi), const_2)) | the inner circumference of a circular race track , 14 m wide is 440 m . find the radius of the outer circle . | "explanation : let inner radius be r meters . { \ color { black } then , 2 \ pi r = 440 \ rightarrow r = 440 \ times \ frac { 7 } { 22 } \ times \ frac { 1 } { 2 } = 70 m } radius of outer circle = 70 + 14 = 84 m answer : a ) 84 m" | a = 440 / math.pi
b = a / 2
c = 14 + b
|
a ) 73 , b ) 32 , c ) 34 , d ) 43 , e ) 42 | b | sqrt(divide(multiply(square_area(8), 8), inverse(const_2))) | the length of the rectangular field is double its width . inside the field there is square shaped pond 8 m long . if the area of the pond is 1 / 8 of the area of the field . what is the length of the field ? | "explanation : a / 8 = 8 * 8 = > a = 8 * 8 * 8 x * 2 x = 8 * 8 * 8 x = 16 = > 2 x = 32 answer : option b" | a = square_area * (
b = a / 8
c = 1/(2)
d = math.sqrt(b)
|
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