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 ) 10.11 , b ) 11.11 , c ) 12.11 , d ) 13.11 , e ) 14.11 | b | add(9, const_1) | the average of first 9 prime numbers is ? | "sum of 10 prime no . = 100 average = 100 / 9 = 11.11 answer : b" | a = 9 + 1
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a ) 1250 , b ) 625 , c ) 600 , d ) 7500 , e ) 720 | e | multiply(6, 120) | a trailer carries 3 , 4 and 6 crates on a trip . each crate weighs no less than 120 kg . what is the maximum weight of the crates on a single trip ? | "max no . of crates = 6 . max weight = 120 kg max . weight carried = 6 * 120 = 720 kg = e" | a = 6 * 120
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a ) 2 : 3 , b ) 20 : 17 , c ) 5 : 4 , d ) 3 : 5 , e ) 6 : 11 | b | divide(add(multiply(4, divide(21, add(4, 3))), 8), add(multiply(3, divide(21, add(4, 3))), 8)) | the ratio of the ages of mini and minakshi is 4 : 3 . the sum of their ages is 21 years . the ratio of their ages after 8 years will be | "let mini β s age = 4 x and minakshi β s age = 3 x then 4 x + 3 x = 21 x = 3 mini β s age = 12 years and minakshi β s age = 9 years ratio of their ages after 8 years = ( 12 + 8 ) : ( 9 + 8 ) = 20 : 17 answer : b" | a = 4 + 3
b = 21 / a
c = 4 * b
d = c + 8
e = 4 + 3
f = 21 / e
g = 3 * f
h = g + 8
i = d / h
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a ) 0.9 , b ) 1.2 , c ) 1.5 , d ) 1.8 , e ) 2.1 | c | multiply(divide(add(1.7, divide(100, const_1000)), 72), const_60) | a train with a length of 100 meters , is traveling at a speed of 72 km / hr . the train enters a tunnel 1.7 km long . how many minutes does it take the train to pass through the tunnel from the moment the front enters to the moment the rear emerges ? | "72 km / hr = 1.2 km / min the total distance is 1.8 km . 1.8 / 1.2 = 1.5 minutes the answer is c ." | a = 100 / 1000
b = 1 + 7
c = b / 72
d = c * const_60
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a ) 425 , b ) 300 , c ) 255 , d ) 300 , e ) 400 | a | divide(multiply(510, add(const_4, const_1)), add(const_1, const_2)) | the difference between a number and its two - fifth is 510 . what is 5 % of that number ? | "let the number be x . then , x - 2 / 5 x = 510 x = ( 510 * 5 ) / 3 = 850 5 % of 850 = 425 . answer : a" | a = 4 + 1
b = 510 * a
c = 1 + 2
d = b / c
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a ) 15 : 32 , b ) 21 : 28 , c ) 31 : 74 , d ) 33 : 37 , e ) 41 : 92 | c | divide(add(multiply(1, 2), multiply(2, 2)), add(multiply(2, 2), multiply(5, 2))) | the contents of two vessels containing copper and tin in the ratio 1 : 2 and 2 : 5 are mixed in the ratio 1 : 4 . the resulting mixture will have copper and tin in the ratio ? | "the ratio of copper and tin the new vessel = ( 1 / 3 * 1 / 5 + 2 / 7 * 4 / 5 ) : ( 2 / 3 * 1 / 5 + 5 / 7 * 4 / 5 ) = 31 / 105 : 74 / 105 = 31 : 74 answer is c" | a = 1 * 2
b = 2 * 2
c = a + b
d = 2 * 2
e = 5 * 2
f = d + e
g = c / f
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a ) 22 days , b ) 8 days , c ) 67 days , d ) 1 days , e ) 18 days | b | divide(multiply(4, 8), divide(subtract(multiply(4, 8), multiply(add(divide(multiply(4, 8), 4), divide(multiply(4, 8), 8)), 2)), 2)) | a can do a piece of work in 4 days . b can do it in 8 days . with the assistance of c they completed the work in 2 days . find in how many days can c alone do it ? | "c = 1 / 2 - 1 / 4 - 1 / 8 = 1 / 8 = > 8 days answer : b" | a = 4 * 8
b = 4 * 8
c = 4 * 8
d = c / 4
e = 4 * 8
f = e / 8
g = d + f
h = g * 2
i = b - h
j = i / 2
k = a / j
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a ) a - 179 , b ) b - 240 , c ) c - 280 , d ) d - 100 , e ) e - 155 | c | subtract(add(100, 12), 6) | a cargo ships engines failed 100 miles away from the port . due to the changing wind direction , it is moving 12 miles towards the port and 6 miles away from the port . if the wind pattern remains same , how many miles it will travel before reaching the port ? | ships overall distance covered per cycle is + 6 miles take 100 - 6 take 94 / 6 to lowest divisible number - 90 / 6 this means that it will take 15 ` ` overall ' ' actions to reach the 90 th mile . - 15 * 18 miles added later set cycle start at 90 . travel 10 miles and reach the anchor point - add 10 to total 15 * 18 + ... | a = 100 + 12
b = a - 6
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a ) 6 , b ) 14 , c ) 22 , d ) 30 , e ) 174 | b | add(subtract(18, 6), subtract(8, 6)) | if x and y are sets of integers , x # y denotes the set of integers that belong to set x or set y , but not both . if x consists of 8 integers , y consists of 18 integers , and 6 of the integers are in both x and y , then x # y consists of how many integers ? | "the number of integers that belong to set x only is 8 - 6 = 2 ; the number of integers that belong to set y only is 18 - 6 = 12 ; the number of integers that belong to set x or set y , but not both is 2 + 12 = 14 . answer : b ." | a = 18 - 6
b = 8 - 6
c = a + b
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a ) 50 , b ) 80 , c ) 100 , d ) 125 , e ) 250 | d | multiply(divide(subtract(power(add(divide(multiply(50, const_2), const_1000), const_3), const_2), const_4), const_4), const_100) | a circular logo is enlarged to fit the lid of a jar . the new diameter is 50 per cent larger than the original . by what percentage has the area of the logo increased ? | "let old diameter be 4 , so radius is 2 old area = 4 Ο new diameter is 6 , so radius is 3 new area = 9 Ο increase in area is 5 Ο % increase in area = 5 / 4 * 100 so , % increase is 125 % answer will be ( d )" | a = 50 * 2
b = a / 1000
c = b + 3
d = c ** 2
e = d - 4
f = e / 4
g = f * 100
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a ) 3 , b ) 4.2 , c ) 3.4 , d ) 5.5 , e ) 5.7 | a | multiply(divide(add(3.5, divide(100, const_1000)), 72), const_60) | a train with a length of 100 meters , is traveling at a speed of 72 km / hr . the train enters a tunnel 3.5 km long . how many minutes does it take the train to pass through the tunnel from the moment the front enters to the moment the rear emerges ? | "72 km / hr = 1.2 km / min the total distance is 3.6 km . 3.6 / 1.2 = 3 minutes the answer is a ." | a = 100 / 1000
b = 3 + 5
c = b / 72
d = c * const_60
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a ) rs . 170 , b ) rs . 160 , c ) rs . 1.70 , d ) rs . 4.25 , e ) none | b | divide(80, 0.5) | if 0.5 % of a = 80 paise , then the value of a is ? | "answer β΅ 0.5 / 100 of a = 80 / 100 β΄ a = rs . ( 80 / 0.5 ) = rs . 160 correct option : b" | a = 80 / 0
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a ) 12 and 22 , b ) 11 and 21 , c ) 15 and 25 , d ) 9 and 19 , e ) 20 and 30 | e | add(subtract(subtract(add(multiply(add(multiply(10, 12), multiply(10, 2)), 10), multiply(multiply(10, 12), 10)), add(multiply(add(const_3, const_4), const_10), const_100)), multiply(add(multiply(10, 12), multiply(10, 2)), 10)), multiply(10, const_100)) | it takes 2 team of farm workers 12 days to completely prepare a piece of land for planting . if both team of workers were to work separately , one of them can complete the work 10 days earlier than the other , how many days will it take each of them to separately complete the work ? | work = ( a ) ( b ) / ( a + b ) where a and b are the individual times of each entity . here , we ' re told that ( working together ) the two team of workers would complete a job in 12 days . this means that ( individually ) each of team would take more than 12 days to do the job . answers d , a and b are illogical , si... | a = 10 * 12
b = 10 * 2
c = a + b
d = c * 10
e = 10 * 12
f = e * 10
g = d + f
h = 3 + 4
i = h * 10
j = i + 100
k = g - j
l = 10 * 12
m = 10 * 2
n = l + m
o = n * 10
p = k - o
q = 10 * 100
r = p + q
|
a ) 3109 , b ) 3209 , c ) 3108 , d ) 3107 , e ) 3100 | a | add(add(multiply(8000, divide(15, const_100)), multiply(add(8000, multiply(8000, divide(15, const_100))), divide(15, const_100))), multiply(add(add(8000, multiply(8000, divide(15, const_100))), multiply(add(8000, multiply(8000, divide(15, const_100))), divide(15, const_100))), divide(divide(15, const_100), const_3))) | find compound interest on $ 8000 at 15 % per annum for 2 years 4 months , compounded annually . | time = 2 years 4 months = 2 ( 4 / 12 ) years = 2 ( 1 / 3 ) years . amount = $ [ 8000 x ( 1 + Β ( 15 / 100 ) ) 2 x ( 1 + ( ( 1 / 3 ) * 15 ) / 100 ) ] = $ [ 8000 * ( 23 / 20 ) * ( 23 / 20 ) * ( 21 / 20 ) ] = $ 11109 . . : . c . i . = rs . ( 11109 - 8000 ) = $ 3109 . answer a . | a = 15 / 100
b = 8000 * a
c = 15 / 100
d = 8000 * c
e = 8000 + d
f = 15 / 100
g = e * f
h = b + g
i = 15 / 100
j = 8000 * i
k = 8000 + j
l = 15 / 100
m = 8000 * l
n = 8000 + m
o = 15 / 100
p = n * o
q = k + p
r = 15 / 100
s = r / 3
t = q * s
u = h + t
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a ) 75 kg , b ) 65 kg , c ) 85 kg , d ) 80 kg , e ) 60 kg | b | add(multiply(8, 2.5), 45) | the average weight of 8 person ' s increases by 2.5 kg when a new person comes in place of one of them weighing 45 kg . what is the weight of the new person ? | "explanation : total increase in weight = 8 Γ£ β 2.5 = 20 if x is the weight of the new person , total increase in weight = x Γ’ Λ β 45 = > 20 = x - 45 = > x = 20 + 45 = 65 answer : option b" | a = 8 * 2
b = a + 45
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a ) 2.5 , b ) 2.9 , c ) 6.67 , d ) 2.8 , e ) 2.1 | c | divide(100, multiply(54, const_0_2778)) | in what time will a train 100 m long cross an electric pole , it its speed be 54 km / hr ? | "speed = 54 * 5 / 18 = 15 m / sec time taken = 100 / 15 = 6.67 sec . answer : c" | a = 54 * const_0_2778
b = 100 / a
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['a ) 4.1 cm', 'b ) 5.1 cm', 'c ) 6.1 cm', 'd ) 7.1 cm', 'e ) 8.1 cm'] | c | divide(multiply(triangle_area_three_edges(41, 28, 15), const_2), 41) | find the area of a triangle whose sides are 41 cm , 28 cm , 15 cm . also , find the length of the altitude corresponding to the largest side of the triangle . | semi - perimeter of the triangle = ( a + b + c ) / 2 = ( 41 + 28 + 15 ) / 2 = 84 / 2 = 42 cm therefore , area of the triangle = β ( s ( s - a ) ( s - b ) ( s - c ) ) = β ( 42 ( 42 - 41 ) ( 42 - 28 ) ( 42 - 15 ) ) cm Β² = β ( 42 Γ 1 Γ 27 Γ 14 ) cm Β² = β ( 3 Γ 3 Γ 3 Γ 3 Γ 2 Γ 2 Γ 7 Γ 7 ) cm Β² = 3 Γ 3 Γ 2 Γ 7 cm Β² = 126 cm... | a = triangle_area_three_edges * (
b = a / 2
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a ) 480 , b ) 520 , c ) 460 , d ) 400 , e ) 520 | a | divide(multiply(multiply(multiply(6, const_100), sqrt(const_100)), 6), const_100) | alex takes a loan of $ 8,000 to buy a used truck at the rate of 6 % simple interest . calculate the annual interest to be paid for the loan amount . | "from the details given in the problem principle = p = $ 8,000 and r = 6 % or 0.06 expressed as a decimal . as the annual interest is to be calculated , the time period t = 1 . plugging these values in the simple interest formula , i = p x t x r = 8,000 x 1 x 0.06 = 480.00 annual interest to be paid = $ 480 answer : a" | a = 6 * 100
b = math.sqrt(100)
c = a * b
d = c * 6
e = d / 100
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a ) 4 km , b ) 6 km , c ) 6.8 km , d ) 7.2 km , e ) none of these | b | add(multiply(4, multiply(divide(const_2, const_3), add(1, divide(24, const_60)))), multiply(multiply(subtract(const_1, divide(const_2, const_3)), add(1, divide(24, const_60))), 5)) | if john covers a certain distance in 1 hr . 24 min . by covering two third of the distance at 4 kmph and the rest at 5 kmph , then find the total distance | explanation : let the total distance be y km . then , ( 2 / 3 ) y / 4 + ( 1 / 3 ) y / 5 = 7 / 5 y / 6 + y / 15 = 7 / 5 7 y = 42 y = 6 km answer b | a = 2 / 3
b = 24 / const_60
c = 1 + b
d = a * c
e = 4 * d
f = 2 / 3
g = 1 - f
h = 24 / const_60
i = 1 + h
j = g * i
k = j * 5
l = e + k
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a ) 120 , b ) 144 , c ) 160 , d ) 210 , e ) 180 | b | multiply(factorial(4), factorial(3)) | in how many ways 4 boys and 3 girls can be seated in a row so that they are alternative ? | "4 boys can be seated in 4 ! three girls can be seated in 3 ! required number = 4 ! 3 ! = 144 answer is b" | a = math.factorial(4)
b = math.factorial(3)
c = a * b
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a ) 12 , b ) 16 , c ) 20 , d ) 32 , e ) 48 | c | multiply(10, const_2) | if ( 10 ^ 4 * 3.456789 ) ^ 10 is written as a single term , how many digits would be to the right of the decimal place ? | "3.456789 ^ 10 has 6 * 10 = 60 decimal places . 10 ^ 40 moves the decimal place to the right 40 places . ( 10 ^ 4 * 3.456789 ) ^ 10 has 60 - 40 = 20 digits after the decimal point . the answer is c ." | a = 10 * 2
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a ) 69 , b ) 72 , c ) 64 , d ) 61 , e ) 75 | a | multiply(const_100, divide(subtract(power(add(const_100, 30), const_3), power(const_100, const_3)), power(const_100, const_3))) | if each edge of cube increased by 30 % , the percentage increase in | "100 Γ ( 130 ) / 100 Γ ( 130 ) / 100 = 169 = > 69 % answer is a ." | a = 100 + 30
b = a ** 3
c = 100 ** 3
d = b - c
e = 100 ** 3
f = d / e
g = 100 * f
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a ) 7 , b ) 14 , c ) 21 , d ) 28 , e ) 35 | c | subtract(divide(multiply(multiply(divide(4, add(4, 3)), 63), 4), 3), multiply(divide(3, add(4, 3)), 63)) | a certain drink of type a is prepared by mixing 4 parts milk with 3 parts fruit juice . another drink of type b is prepared by mixing 4 parts of fruit juice and 3 parts of milk . how many liters of fruit juice must be added to 63 liters of drink a to convert it to drink b ? | "in 63 liters of drink a , there are 36 liters of milk and 27 liters of juice . with 36 liters of milk , we need a total of 48 liters of juice to make drink b . we need to add 21 liters of juice . the answer is c ." | a = 4 + 3
b = 4 / a
c = b * 63
d = c * 4
e = d / 3
f = 4 + 3
g = 3 / f
h = g * 63
i = e - h
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a ) 3 , b ) 3.5 , c ) 4 , d ) 4.5 , e ) 5 | c | divide(12, divide(subtract(222, 198), subtract(198, 190))) | james went on a diet 12 months ago when he weighed 222 pounds . if he now weighs 198 pounds and continues to lose at the same average monthly rate , in approximately how many months will he weigh 190 pounds ? | 222 - 198 = 24 pounds lost in 12 months 24 / 12 = 2 , so joe is losing weight at a rate of 2 pounds per month . . . . in approximately how many months will he weigh 190 pounds ? a simple approach is to just list the weights . now : 198 lbs in 1 month : 196 lbs in 2 months : 194 lbs in 3 months : 192 lbs in 4 months : 1... | a = 222 - 198
b = 198 - 190
c = a / b
d = 12 / c
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a ) 2 : 5 , b ) 5 : 9 , c ) 5 : 16 , d ) 25 : 7 , e ) 32 : 25 | b | divide(const_10, add(add(multiply(9, const_2), const_2), const_1)) | the dimensions of a rectangular solid are 4 inches , 5 inches , and 9 inches . if a cube , a side of which is equal to one of the dimensions of the rectangular solid , is placed entirely within thespherejust large enough to hold the cube , what the ratio of the volume of the cube to the volume within thespherethat is n... | answer : b . | a = 9 * 2
b = a + 2
c = b + 1
d = 10 / c
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a ) 941,1009 , b ) 993,1007 , c ) 991,1009 , d ) 791,1009 , e ) 931,1009 | b | divide(999951, add(multiply(const_100, const_10), add(const_3, const_2))) | there are cats got together and decided to kill the mice of 999951 . each cat kills equal number of mice and each cat kills more number of mice than cats there were . then what are the number of cats ? | "999951 can be written as 1000000 Γ’ β¬ β 49 = 10002 Γ’ β¬ β 72 ie of the form a 2 - b 2 = ( a + b ) ( a - b ) = ( 1000 + 7 ) * ( 1000 - 7 ) = ( 1007 ) * ( 993 ) given that number of cats is less than number if mice . so number of cats is 993 and number of mice were 1007 answer b" | a = 100 * 10
b = 3 + 2
c = a + b
d = 999951 / c
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a ) 4 miles , b ) 5 3 / 4 miles , c ) 6 1 / 2 miles , d ) 7 3 / 4 miles , e ) 8 1 / 4 miles | d | add(multiply(divide(multiply(subtract(6.5, 2.75), const_100), 12.5), const_0_25), const_0_25) | a taxi company costs $ 2.75 for the first quarter - mile and 12.5 cents for each additional quarter mile . what is the maximum distance you can travel with $ 6.50 ? | use reverse calculation - total cost = fixed cost ( for 1 / 4 miles ) + variable cost ( distance travelled ) or , 6.50 = 2.75 + 0.125 * d or , 3.75 = d / 8 or , d = 30 quarter miles so , total distance = ( 30 + 1 ) quarter miles so , distance = 31 / 4 = > 73 / 4 miles hence answer will be ( d ) | a = 6 - 5
b = a * 100
c = b / 12
d = c * const_0_25
e = d + const_0_25
|
a ) 84 , b ) 50 , c ) 54 , d ) 57 , e ) 60 | a | add(subtract(96, 25), const_1) | claire has a total of 96 pets consisting of gerbils and hamsters only . one - quarter of the gerbils are male , and one - third of the hamsters are male . if there are 25 males altogether , how many gerbils does claire have ? | "g + h = 96 . . . 1 ; g / 4 + h / 3 = 25 . . . . 2 or 3 g + 4 h = 25 * 12 = 300 g = 96 - h or 3 ( 96 - h ) + 4 h = 300 h = 300 - 288 = 12 then g = 96 - 12 = 84 a" | a = 96 - 25
b = a + 1
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a ) 93 / 198 , b ) 93 / 12 , c ) 93 / 18 , d ) 93 / 10 , e ) 93 / 11 | c | divide(94, 97) | find 94 Γ Γ 97 | "here both numbers are less than 100 . so they are deficient of - 6 and - 3 compared with 100 . so answer : c" | a = 94 / 97
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a ) 266 sec , b ) 200 sec , c ) 776 sec , d ) 166 sec , e ) 997 sec | b | divide(add(1200, 800), divide(1200, 120)) | a 1200 m long train crosses a tree in 120 sec , how much time will i take to pass a platform 800 m long ? | "l = s * t s = 1200 / 120 s = 10 m / sec . total length ( d ) = 2000 m t = d / s t = 2000 / 10 t = 200 sec answer : b" | a = 1200 + 800
b = 1200 / 120
c = a / b
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a ) 9.09 % , b ) 4.54 % , c ) 8 . 2 % , d ) 4.94 % , e ) 5.54 % | a | divide(const_100, 11) | at what rate percent of simple interest will a sum of money double itself in 11 years ? | "let sum = x . then , s . i . = x . rate = ( 100 * s . i . ) / ( p * t ) = ( 100 * x ) / ( x * 11 ) = 100 / 11 = 9.09 % answer : a" | a = 100 / 11
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a ) 72 , b ) 224 , c ) 320 , d ) 512 , e ) 1,395 | e | gcd(137, const_4) | if m and n are positive integers and m ^ 2 + n ^ 2 = 137 , what is the value of m ^ 3 + n ^ 3 ? | you need to integers which squared are equal 40 . which could it be ? let ' s start with the first integer : 1 ^ 2 = 1 2 ^ 2 = 4 3 ^ 2 = 9 4 ^ 2 = 16 5 ^ 2 = 25 6 ^ 2 = 36 7 ^ 2 = 49 8 ^ 2 = 64 9 ^ 2 = 81 10 ^ 2 = 100 11 ^ 2 = 121 stop . the integers ca n ' t be greater than 6 or we will score above 137 . the second in... | a = math.gcd(137, 4)
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a ) 7 , b ) 14 , c ) 21 , d ) 28 , e ) 35 | a | multiply(divide(divide(divide(630, const_3), add(const_3, const_4)), add(const_3, const_4)), const_3) | if the product of the integers from 1 to n is divisible by 630 , what is the least possible value of n ? | "630 = 2 x 3 x 3 x 5 x 7 n must include at least up to the number 7 . the answer is a ." | a = 630 / 3
b = 3 + 4
c = a / b
d = 3 + 4
e = c / d
f = e * 3
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a ) 15 hrs , b ) 18 hrs , c ) 20 hrs , d ) 17 hrs , e ) 16 hrs | c | subtract(divide(22, subtract(3, 2)), 2) | a monkey start climbing up a tree 22 ft tall . each hour it hops 3 ft and slips back 2 ft . how much time would it take the monkey to reach the top . | "if monkey hops 3 ft and slips back 2 ft in a hour , it means the monkey hops ( 3 ft - 2 ft ) = 1 ft / hr . similarly in 19 hrs it wil be 19 ft . bt since the height of the tree is 22 ft , so if the monkey hops up the tree in the next hr i . e 20 th hr then it reaches at the top of the tree . hence it takes 20 hrs for ... | a = 3 - 2
b = 22 / a
c = b - 2
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a ) 50 , b ) 52 , c ) 54 , d ) 56 , e ) 58 | a | multiply(divide(26, 6), const_12) | the first doughnut is priced at $ 1 and then if you purchase additional doughnuts as dozens then the price is $ 6 / dozen . what is the total number of doughnuts purchased if you paid $ 26 ? | "$ 26 = 4 * $ 6 + $ 2 the number of doughnuts is 4 * 12 + 2 = 50 the answer is a ." | a = 26 / 6
b = a * 12
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a ) 3 / 13 , b ) 2 / 31 , c ) 5 / 36 , d ) 7 / 41 , e ) 7 / 43 | c | add(divide(2, power(6, 2)), divide(const_3, power(6, 2))) | when you draw 2 dices together , find the probability of getting a total of 6 ? | s = { ( 1,1 ) , ( 1,2 ) , ( 1,3 ) , ( 1,4 ) , ( 1,5 ) , ( 1,6 ) , ( 4,1 ) , ( 4,2 ) , ( 4,3 ) , ( 4,4 ) , ( 4,5 ) , ( 4,6 ) , ( 2,1 ) , ( 2,2 ) , ( 2,3 ) , ( 2,4 ) , ( 2,5 ) , ( 2,6 ) , ( 5,1 ) , ( 5,2 ) , ( 5,3 ) , ( 5,4 ) , ( 5,5 ) , ( 5,6 ) , ( 3,1 ) , ( 3,2 ) , ( 3,3 ) , ( 3,4 ) , ( 3,5 ) , ( 3,6 ) , ( 6,1 ) , ( 6,... | a = 6 ** 2
b = 2 / a
c = 6 ** 2
d = 3 / c
e = b + d
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a ) $ 5 , b ) $ 10 , c ) $ 14 , d ) $ 24 , e ) $ 28 | d | subtract(multiply(50, const_2), 76) | elvin ' s monthly telephone bill is the sum of the charge for the calls he made during the month and a fixed monthly charge for internet service . elvin ' s total telephone bill for january was $ 50 and elvin ' s total telephone bill for february was 76 $ . if elvin ' s charge for the calls he made in february was twic... | "bill = fixed charge + charge of calls made in jan , bill = fixed charge ( let , y ) + charge of calls made in jan ( let , x ) = $ 50 in feb , bill = fixed charge ( let , y ) + charge of calls made in feb ( then , 2 x ) = $ 76 i . e . x + y = 50 and 2 x + y = 76 take the difference if two equations i . e . ( 2 x + y ) ... | a = 50 * 2
b = a - 76
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a ) 12028 , b ) 12000 , c ) 12019 , d ) 12197 , e ) 18000 | c | divide(600, divide(5, const_100)) | a salesman β s terms were changed from a flat commission of 5 % on all his sales to a fixed salary of rs . 1300 plus 2.5 % commission on all sales exceeding rs . 4,000 . if his remuneration as per new scheme was rs . 600 more than that by the previous schema , his sales were worth ? | [ 1300 + ( x - 4000 ) * ( 2.5 / 100 ) ] - x * ( 5 / 100 ) = 600 x = 18000 answer : c | a = 5 / 100
b = 600 / a
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a ) rs 14000 , b ) rs 25000 , c ) rs 16000 , d ) rs 17000 , e ) none of these | b | divide(multiply(9000, const_100), multiply(12, 3)) | a man took a loan at rate of 12 % per annum simple interest . after 3 years he had to pay 9000 interest . the principal amount borrowed by him was . | explanation : s . i . = p Γ’ Λ β r Γ’ Λ β t / 100 = > p = s . i . Γ’ Λ β 100 / r Γ’ Λ β t = > p = 9000 Γ’ Λ β 100 / 12 Γ’ Λ β 3 = rs 25000 option b | a = 9000 * 100
b = 12 * 3
c = a / b
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a ) 8 mph , b ) 5.25 mph , c ) 3.5 mph , d ) 5 mph , e ) 0.5 mph | d | divide(add(1, 9), const_2) | tabby is training for a triathlon . she swims at a speed of 1 mile per hour . she runs at a speed of 9 miles per hour . she wants to figure out her average speed for these two events . what is the correct answer for her ? | "( 1 mph + 9 mph ) / 2 = 5 mph correct option is : d" | a = 1 + 9
b = a / 2
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a ) $ 1.50 , b ) $ 2.50 , c ) $ 5.25 , d ) $ 4.50 , e ) $ 5.50 | c | subtract(subtract(14, multiply(3, 2.25)), 2) | suppose you want to buy 3 loaves of bread that cost $ 2.25 each and a jar of peanut butter that costs $ 2 . a jar of jelly is $ 2.75 , but you don Γ’ β¬ β’ t need any jelly . you have $ 14 . how much money will you have left over ? | the jelly is extra information . 14.00 Γ’ β¬ β 3 x 2.25 Γ’ β¬ β 2.00 = 14.00 Γ’ β¬ β 6.75 Γ’ β¬ β 2.00 = 5.25 . you have $ 5.25 left . correct answer c | a = 3 * 2
b = 14 - a
c = b - 2
|
a ) 50 % , b ) 40 % , c ) 60 % , d ) 70 % , e ) 45.45 % | e | multiply(divide(subtract(110, add(multiply(3, 8), multiply(8, 3))), 110), const_100) | a batsman scored 110 runs which included 3 boundaries and 8 sixes . what percent of his total score did he make by running between the wickets ? | "number of runs made by running = 110 - ( 3 x 4 + 8 x 6 ) = 110 - ( 60 ) = 50 now , we need to calculate 50 is what percent of 110 . = > 50 / 110 x 100 = 45.45 % answer : e" | a = 3 * 8
b = 8 * 3
c = a + b
d = 110 - c
e = d / 110
f = e * 100
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a ) 1.9 , b ) 1.7 , c ) 1.2 , d ) 1.5 , e ) 1.1 | c | divide(subtract(multiply(3.6, const_2), 3.6), const_3) | a man can row 3.6 km / hr in still water . it takes him twice as long to row upstream as to row downstream . what is the rate of the current ? | "speed of boat in still water ( b ) = 3.6 km / hr . speed of boat with stream ( down stream ) , d = b + u speed of boat against stream ( up stream ) , u = b β u it is given upstream time is twice to that of down stream . β downstream speed is twice to that of upstream . so b + u = 2 ( b β u ) β u = b / 3 = 1.2 km / hr ... | a = 3 * 6
b = a - 3
c = b / 3
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a ) 0.1 , b ) 0.6 , c ) 1 , d ) 1.2 , e ) 2 | c | divide(20, subtract(50, 30)) | two cars are traveling in the same direction along the same route . the red car travels at a constant speed of 30 miles per hour , and the black car is traveling at a constant speed of 50 miles per hour . if the red car is 20 miles ahead of the black car , how many hours will it take the black car to overtake the red c... | "option c 20 + 30 t = 50 t t = 1" | a = 50 - 30
b = 20 / a
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a ) 2 , b ) 4 , c ) 6 , d ) 8 , e ) 9 | c | subtract(multiply(log(divide(power(4, 4), const_2)), const_2), 4) | the population of locusts in a certain swarm doubles every two hours . if 4 hours ago there were 1,000 locusts in the swarm , in approximately how many hours will the swarm population exceed 32,000 locusts ? | "- 4 hours : 1,000 - 2 hours : 2,000 now : 4,000 + 2 hours : 8,000 + 4 hours : 16,000 + 6 hours : 32,000 answer : c" | a = 4 ** 4
b = a / 2
c = math.log(b)
d = c * 2
e = d - 4
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a ) 2 : 0 , b ) 3 : 4 , c ) 2 : 1 , d ) 2 : 2 , e ) 2 : 8 | b | divide(subtract(6.30, 5.70), subtract(7.10, 6.30)) | find the ratio in which rice at rs . 7.10 a kg be mixed with rice at rs . 5.70 a kg to produce a mixture worth rs . 6.30 a kg | "by the rule of alligation : cost of 1 kg rice of 1 st kind cost of 1 kg rice of 2 nd kind required ratio = 60 : 80 = 3 : 4 answer : b" | a = 6 - 30
b = 7 - 10
c = a / b
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a ) 357000 , b ) 357003 , c ) 277677 , d ) 699377 , e ) 267877 | a | multiply(multiply(560000, subtract(const_1, divide(15, const_100))), divide(75, const_100)) | in an election , candidate a got 75 % 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 favour of candidate . | "total number of invalid votes = 15 % of 560000 = 15 / 100 Γ 560000 = 8400000 / 100 = 84000 total number of valid votes 560000 β 84000 = 476000 percentage of votes polled in favour of candidate a = 75 % therefore , the number of valid votes polled in favour of candidate a = 75 % of 476000 = 75 / 100 Γ 476000 = 35700000... | a = 15 / 100
b = 1 - a
c = 560000 * b
d = 75 / 100
e = c * d
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a ) 0 , b ) 4 , c ) 6 , d ) 8 , e ) 10 | d | add(10, 2) | there is a 40 cm line marked at each centimeter and an insect is placed at every centimeter . 9 frogs are trained to jump a constant distance . the first one jumps 2 cm in every leap , the second one jumps 3 cm and so on until the 9 th one jumps 10 cm in every leap and they eat any insect that is available at that spot... | "only the prime numbers greater than 10 and less than 40 were left . that is 11 , 13 , 17 , 19 , 23 , 29 , 31 , and 37 . the total is 8 . the answer is d ." | a = 10 + 2
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a ) 25 , b ) 20 , c ) 15 , d ) 30 , e ) 18 | a | divide(subtract(multiply(5, 5000), multiply(500, 5)), subtract(1000, 500)) | the average salary of all the workers in a workshop is $ 1000 . the average salary of 5 technicians is $ 5000 and the average salary of the rest is $ 500 . the total number of workers in the shop is ? | "let the total number of workers be x 1000 x = 5000 * 5 + 500 ( x - 5 ) x = 25 answer is a" | a = 5 * 5000
b = 500 * 5
c = a - b
d = 1000 - 500
e = c / d
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a ) 145 , b ) 143 , c ) 147 , d ) 141 , e ) 142 | b | add(add(add(45, 30), 33), 37) | you have been given a physical balance and 7 weights of 43 , 45 , 30 , 33 , 28 , 37 and 55 kgs . keeping weights on one pan and object on the other , what is the maximum you can weigh less than 145 kgs . | 55 + 43 + 45 = 143 answer : b | a = 45 + 30
b = a + 33
c = b + 37
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a ) 2 minutes , b ) 10 minutes , c ) 20 minutes , d ) 40 minutes , e ) 60 minutes | c | divide(subtract(12.00, 11.00), subtract(0.25, 0.20)) | united telephone charges a base rate of $ 11.00 for service , plus an additional charge of $ 0.25 per minute . atlantic call charges a base rate of $ 12.00 for service , plus an additional charge of $ 0.20 per minute . for what number of minutes would the bills for each telephone company be the same ? | "lets take number of minutesx . given that , 11 + 0.25 x = 12 + 0.2 x - > 0.05 x = 2 - > x = 20 minutes ans c" | a = 12 - 0
b = 0 - 25
c = a / b
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a ) 8 / 15 , b ) 1 / 3 , c ) 2 / 5 , d ) 4 / 5 , e ) 7 / 6 | a | divide(multiply(8, 1), multiply(3, 5)) | if the ratio of a to b is 8 to 3 and the ratio of b to c is 1 to 5 , what is the ratio of a to c ? | "a : b = 8 : 3 - - 1 b : c = 1 : 5 = > b : c = 3 : 15 - - 2 from 1 and 2 , we get a : c = 8 : 15 answer a" | a = 8 * 1
b = 3 * 5
c = a / b
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a ) 1677 , b ) 1683 , c ) 2523 , d ) 3363 , e ) none of these | b | add(multiply(multiply(multiply(5, add(5, const_1)), add(5, const_2)), 8), 3) | the least number which when divided by 5 , 67 and 8 leaves a remainder 3 , but when divided by 9 leaves no remainder , is : | solution l . c . m . of 5 , 6 , 7 , 8 = 840 . so , required number is of the form 840 k + 3 . least value of k for which ( 840 k + 3 ) is divisible by 9 is k = 2 . so , required number = ( 840 Γ 2 + 3 ) = 1683 . answer b | a = 5 + 1
b = 5 * a
c = 5 + 2
d = b * c
e = d * 8
f = e + 3
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a ) rs . 537600 , b ) rs . 180000 , c ) rs . 201600 , d ) rs . 504000 , e ) none of these | a | multiply(multiply(multiply(16000, add(const_1, divide(12, const_100))), divide(5, 2)), 12) | the monthly incomes of a and b are in the ratio 5 : 2 . b ' s monthly income is 12 % more than c ' s monthly income . if c ' s monthly income is rs . 16000 , then find the annual income of a ? | b ' s monthly income = 16000 * 112 / 100 = rs . 17920 b ' s monthly income = 2 parts - - - - > rs . 17920 a ' s monthly income = 5 parts = 5 / 2 * 17920 = rs . 44800 a ' s annual income = rs . 44800 * 12 = rs . 537600 answer : a | a = 12 / 100
b = 1 + a
c = 16000 * b
d = 5 / 2
e = c * d
f = e * 12
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a ) 161 , b ) 154 , c ) 216 , d ) 158 , e ) none | a | subtract(negate(67), multiply(subtract(13, 35), divide(subtract(13, 35), subtract(1, 13)))) | 1 , 13 , 35 , 67 , 109 , ____ | "1 , 13 , 35 , 67 , 109 , . . . . . 13 = 1 + 12 35 = 13 + 22 67 = 35 + 32 109 = 67 + 42 so 109 + 52 = 161 answer : a" | a = negate - (
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a ) 65 , b ) 38 , c ) 20 , d ) 28 , e ) 21 | a | subtract(subtract(150, 35), add(25, 25)) | two cars start from the opposite places of a main road , 150 km apart . first car runs for 25 km and takes a right turn and then runs 15 km . it then turns left and then runs for another 25 km and then takes the direction back to reach the main road . in the mean time , due to minor break down the other car has run onl... | answer : a ) 65 km | a = 150 - 35
b = 25 + 25
c = a - b
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a ) 647 , b ) 718 , c ) 654 , d ) 847 , e ) 976 | b | subtract(820, divide(multiply(subtract(854, 820), 3), 4)) | a sum of money at simple interest amounts to rs . 820 in 3 years and to rs . 854 in 4 years . the sum is : | "s . i . for 1 year = rs . ( 854 - 820 ) = rs . 34 . s . i . for 3 years = rs . ( 34 x 3 ) = rs . 102 . principal = rs . ( 820 - 102 ) = rs . 718 . answer : b" | a = 854 - 820
b = a * 3
c = b / 4
d = 820 - c
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a ) 0.0004 , b ) 0.0009 , c ) 0.0002 , d ) 0.0003 , e ) 0.0008 | e | subtract(multiply(divide(add(add(const_12, const_4), const_2), const_100), divide(add(add(const_12, const_4), const_2), const_100)), 0.0568) | what is the least number . which should be added to 0.0568 to make it a perfect square ? | "0.0568 + 0.0008 = 0.0576 ( 0.24 ) ^ 2 answer : e" | a = 12 + 4
b = a + 2
c = b / 100
d = 12 + 4
e = d + 2
f = e / 100
g = c * f
h = g - 0
|
a ) 9 , b ) 15 , c ) 17 , d ) 8 , e ) 10 | b | add(5, const_1) | the average of first five multiples of 5 is : | "explanation : ( 5 ( 1 + 2 + 3 + 4 + 5 ) / 5 = 5 x 15 / 5 = 15 answer : b" | a = 5 + 1
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a ) 90 cm , b ) 1 dm , c ) 1 m , d ) 1.1 cm , e ) none of these | b | subtract(multiply(multiply(3.3, 2.6), 1.1), divide(8000, const_1000)) | a cistern of capacity 8000 litres measures externally 3.3 m by 2.6 m by 1.1 m and its walls are 5 cm thick . the thickness of the bottom is : | "explanation : let the thickness of the bottom be x cm . then , [ ( 330 - 10 ) Γ ( 260 - 10 ) Γ ( 110 - x ) ] = 8000 Γ 1000 = > 320 Γ 250 Γ ( 110 - x ) = 8000 Γ 1000 = > ( 110 - x ) = 8000 Γ 1000 / 320 = 100 = > x = 10 cm = 1 dm . answer : b" | a = 3 * 3
b = a * 1
c = 8000 / 1000
d = b - c
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a ) 90 , b ) 110 , c ) 120 , d ) 130 , e ) 240 | e | subtract(divide(subtract(multiply(12, 380), add(add(multiply(const_3, const_1000), multiply(const_3, const_100)), multiply(const_2, const_10))), subtract(12, 8)), subtract(380, divide(subtract(multiply(12, 380), add(add(multiply(const_3, const_1000), multiply(const_3, const_100)), multiply(const_2, const_10))), subtrac... | a theater charges $ 12 for seats in the orchestra and $ 8 for seats in the balcony . on a certain night , a total of 380 tickets were sold for a total cost of $ 3,320 . how many more tickets were sold that night for seats in the balcony than for seats in the orchestra ? | "orchestra seats - a balcony seats - b a + b = 380 and 12 a + 8 b = 3320 solving equations simultaneously ( multiply equation 1 with 8 and subtract from second equation ) 4 a = 3320 - 8 * 380 = 3320 - 3040 = 280 i . e . a = 70 and b = 380 - 70 = 310 more seats in balcony than orchestra = b - a = 310 - 70 = 240 answer :... | a = 12 * 380
b = 3 * 1000
c = 3 * 100
d = b + c
e = 2 * 10
f = d + e
g = a - f
h = 12 - 8
i = g / h
j = 12 * 380
k = 3 * 1000
l = 3 * 100
m = k + l
n = 2 * 10
o = m + n
p = j - o
q = 12 - 8
r = p / q
s = 380 - r
t = i - s
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a ) 7 / 30 , b ) 11 / 30 , c ) 11 / 15 , d ) 30 / 11 , e ) 15 / 11 | d | divide(multiply(6, 5), add(5, 6)) | in an electric circuit , two resistors with resistances x and y are connected in parallel . if r is the combined resistance of these two resistors , then the reciprocal of r is equal to the sum of the reciprocals of x and y . what is r if x is 5 ohms and y is 6 ohms ? | 1 / r = 1 / x + 1 / y 1 / r = 1 / 5 + 1 / 6 = 11 / 30 r = 30 / 11 the answer is d . | a = 6 * 5
b = 5 + 6
c = a / b
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a ) 2500 , b ) 2000 , c ) 1600 , d ) 4545 , e ) 6565 | a | divide(500, divide(subtract(const_100, add(add(add(divide(multiply(subtract(subtract(const_100, 10), 10), add(20, 25)), const_100), 24), 10), 10)), const_100)) | in a practice paper at 2 iim . com , questions were given from 5 topics . out of the appearing students , 10 % passed in all topics while 10 % did not pass in any . of the remaining , 20 % passed in one topic only and 25 % in two topics only . if 24 % of the total students passed 4 topics only and 500 students passed i... | detailed solution let the number of appearing students be 100 . pass only in 0 topic β 10 1 β 16 ( 20 % of 80 ) 2 β 20 ( 25 % of 80 ) 3 β 20 % ( 100 β ( 16 + 20 + 24 + 20 ) ) 4 β 24 % 5 β 20 % therefore , 20 % of x = 500 = ) x = 2500 correct answer : a | a = 100 - 10
b = a - 10
c = 20 + 25
d = b * c
e = d / 100
f = e + 24
g = f + 10
h = g + 10
i = 100 - h
j = i / 100
k = 500 / j
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a ) 600 , b ) 715 , c ) 269 , d ) 261 , e ) 281 | b | add(650, multiply(650, divide(10, const_100))) | a person buys an article at rs . 650 . at what price should he sell the article so as to make a profit of 10 % ? | "cost price = rs . 650 profit = 10 % of 650 = rs . 65 selling price = cost price + profit = 650 + 65 = rs . 715 answer : b" | a = 10 / 100
b = 650 * a
c = 650 + b
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a ) 1 / 20 , b ) 3 / 40 , c ) 13 / 40 , d ) 7 / 10 , e ) 13 / 22 | d | multiply(divide(7, 8), subtract(1, divide(1, 7))) | wink , inc . follows a certain procedure that requires two tasks to be finished independently in order for a job to be done . on any given day , there is a 7 / 8 probability that task 1 will be completed on time , and a 1 / 5 probability that task 2 will be completed on time . on a certain day , what is the probability... | "p ( 1 and not 2 ) = 7 / 8 * ( 1 - 1 / 5 ) = 7 / 10 . answer : d ." | a = 7 / 8
b = 1 / 7
c = 1 - b
d = a * c
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a ) 10 , b ) 30 , c ) 50 , d ) 20 , e ) 30 | d | divide(multiply(10, divide(2, 3)), subtract(divide(3, add(3, 2)), multiply(divide(2, add(3, 2)), divide(2, 3)))) | a mixture contains milk and water in the ratio 3 : 2 . on adding 10 litters of water , the ratio of milk to water becomes 2 : 3 . total quantity of milk & water before adding water to it ? | "explanation : milk : water = 3 : 2 after adding 10 liters of water milk : water = 2 : 3 olny water patrs increase when mixture of water milk : wate = 3 : 2 = 2 * ( 3 : 2 ) = 6 : 4 after adding 10 liters of water milk : water = 2 : 3 = 3 * ( 2 : 3 ) = 6 : 9 milk parts always same short cut method : milk : water = 6 : 4... | a = 2 / 3
b = 10 * a
c = 3 + 2
d = 3 / c
e = 3 + 2
f = 2 / e
g = 2 / 3
h = f * g
i = d - h
j = b / i
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a ) 35 , b ) 37 , c ) 42 , d ) 30 , e ) 38 | b | add(divide(368, gcd(gcd(80, 144), 368)), add(divide(80, gcd(gcd(80, 144), 368)), divide(144, gcd(gcd(80, 144), 368)))) | a drink vendor has 80 liters of maaza , 144 liters of pepsi and 368 liters of sprite . he wants to pack them in cans , so that each can contains the same number of liters of a drink , and does n ' t want to mix any two drinks in a can . what is the least number of cans required ? | "the number of liters in each can = hcf of 80 , 144 and 368 = 16 liters . number of cans of maaza = 80 / 16 = 5 number of cans of pepsi = 144 / 16 = 9 number of cans of sprite = 368 / 16 = 23 the total number of cans required = 5 + 9 + 23 = 37 cans . answer : b" | a = math.gcd(80, 144)
b = math.gcd(a, 368)
c = 368 / b
d = math.gcd(80, 144)
e = math.gcd(d, 368)
f = 80 / e
g = math.gcd(80, 144)
h = math.gcd(g, 368)
i = 144 / h
j = f + i
k = c + j
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a ) 505 , b ) 515 , c ) 525 , d ) 538 , e ) 567 | c | divide(multiply(divide(112, const_100), 2348), 4.98) | ( 112 % of 2348 ) Γ· 4.98 = ? | "explanation : ? = ( 112 x 2348 / 100 ) Γ· 5 = 2630 / 5 = 526 = 525 answer : option c" | a = 112 / 100
b = a * 2348
c = b / 4
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a ) 0 , b ) 1 , c ) 2 , d ) 3 , e ) 4 | a | subtract(multiply(multiply(multiply(1256, 6785), 4587), 9785), subtract(multiply(multiply(multiply(1256, 6785), 4587), 9785), add(const_4, const_4))) | the unit digit in the product 1256 * 6785 * 4587 * 9785 is ? | "unit digit in the given product = unit digit in 6 * 5 * 7 * 5 = 0 answer is a" | a = 1256 * 6785
b = a * 4587
c = b * 9785
d = 1256 * 6785
e = d * 4587
f = e * 9785
g = 4 + 4
h = f - g
i = c - h
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a ) 75 kmph , b ) 65 kmph , c ) 30 kmph , d ) 73 kmph , e ) 65 kmph | a | divide(add(60, 90), const_2) | a man can row upstream at 60 kmph and downstream at 90 kmph , and then find the speed of the man in still water ? | us = 60 ds = 90 m = ( 60 + 90 ) / 2 = 75 answer : a | a = 60 + 90
b = a / 2
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a ) 130 m , b ) 786 m , c ) 566 m , d ) 546 m , e ) 440 m | a | multiply(divide(multiply(52, const_1000), const_3600), 9) | a train running at the speed of 52 km / hr crosses a pole in 9 sec . what is the length of the train ? | "speed = 52 * 5 / 18 = 130 / 9 m / sec length of the train = speed * time = 130 / 9 * 9 = 130 m answer : a" | a = 52 * 1000
b = a / 3600
c = b * 9
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a ) 387 , b ) 400 , c ) 776 , d ) 268 , e ) 181 | b | divide(441, power(add(const_1, divide(5, const_100)), 2)) | find the sum lend at c . i . at 5 p . c per annum will amount to rs . 441 in 2 years ? | "441 = p ( 21 / 20 ) 2 p = 400 answer : b" | a = 5 / 100
b = 1 + a
c = b ** 2
d = 441 / c
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a ) 30 % , b ) 40 % , c ) 60 % , d ) 19 % , e ) 29 % | c | divide(const_100, add(const_1, 36)) | solve the quickfire maths brain teaser Γ’ Λ Ε‘ 36 % = ? | "Γ’ Λ Ε‘ 36 % = > Γ’ Λ Ε‘ 36 / Γ’ Λ Ε‘ 100 = > 6 / 10 = > 60 / 100 = > 60 % c" | a = 1 + 36
b = 100 / a
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a ) 10000 , b ) 12000 , c ) 12019 , d ) 12197 , e ) 12012 | a | divide(600, divide(5, const_100)) | a salesman β s terms were changed from a flat commission of 5 % on all his sales to a fixed salary of rs . 900 plus 2.5 % commission on all sales exceeding rs . 4,000 . if his remuneration as per new scheme was rs . 600 more than that by the previous schema , his sales were worth ? | "[ 900 + ( x - 4000 ) * ( 2.5 / 100 ) ] - x * ( 5 / 100 ) = 600 x = 10000 answer : a" | a = 5 / 100
b = 600 / a
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a ) 5 , b ) 22 , c ) 17 , d ) 25 , e ) 30 | b | add(divide(lcm(30, 55), 30), const_10) | jaime earned enough money by selling seashells at 30 cents each to buy several used paperback books at 55 cents each . if he spent all of the money he earned selling seashells to buy the books , what is the least number of seashells he could have sold ? | "let ' s test answer b : 22 seashells . . . with 22 seashells , jamie would have 22 ( 30 ) = 660 cents . this would allow him to buy 12 books for 660 cents total , with no money left over . this is an exact match for what we were told , so this must be the answer . final answer : [ reveal ] spoiler : b" | a = math.lcm(30, 55)
b = a / 30
c = b + 10
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a ) 3.5 gallons , b ) 2.7 gallons , c ) 5.7 gallons , d ) 4.5 gallons , e ) 7.5 gallons | d | divide(180, 40) | a car gets 40 kilometers per gallon of gasoline . how many gallons of gasoline would the car need to travel 180 kilometers ? | "each 40 kilometers , 1 gallon is needed . we need to know how many 40 kilometers are there in 180 kilometers ? 180 Γ· 40 = 4.5 Γ 1 gallon = 4.5 gallons correct answer is d ) 4.5 gallons" | a = 180 / 40
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a ) 120 sq m , b ) 250 sq m , c ) 200 sq m , d ) 180 sq m , e ) 100 sq m | d | divide(square_area(18), const_2) | what is the area of a square field whose diagonal of length 18 m ? | "d 2 / 2 = ( 18 * 18 ) / 2 = 180 answer : d" | a = square_area / (
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a ) 104 kmph , b ) 195 kmph , c ) 109 kmph , d ) 174 kmph , e ) 101 kmph | b | divide(624, add(3, divide(1, 5))) | a car covers a distance of 624 km in 3 1 / 5 hours . find its speed ? | "624 / 3 1 / 5 = 195 kmph answer : b" | a = 1 / 5
b = 3 + a
c = 624 / b
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a ) 56 sec , b ) 40 sec , c ) 36 sec , d ) 29 sec . , e ) 19 sec . | b | divide(400, subtract(divide(45, const_3_6), divide(divide(9, const_2), const_3_6))) | a train which has 400 m long , is running 45 kmph . in what time will it cross a person moving at 9 kmph in same direction ? | "time taken to cross a moving person = length of train / relative speed time taken = 400 / ( ( 45 - 9 ) ( 5 / 18 ) = 400 / 36 * ( 5 / 18 ) = 400 / 10 = 40 sec answer : b" | a = 45 / const_3_6
b = 9 / 2
c = b / const_3_6
d = a - c
e = 400 / d
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a ) 1 / 5 , b ) 1 / 3 , c ) 1 / 2 , d ) 2 / 3 , e ) 2 / 5 | e | divide(const_2, 5) | if an integer n is to be selected at random from 1 to 100 , inclusive , what is probability n ( n + 1 ) will be divisible by 5 ? | "for n ( n + 1 ) to be a multiple of 5 , either n or n + 1 has to be a multiple of 5 . thus n must be of the form 5 k or 5 k - 1 . the probability is 2 / 5 . the answer is e ." | a = 2 / 5
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a ) 1 / 12 , b ) 1 / 10 , c ) 1 / 8 , d ) 1 / 42 , e ) 5 / 9 | d | multiply(multiply(multiply(divide(add(4, const_1), add(9, const_1)), divide(subtract(add(4, const_1), const_1), subtract(add(9, const_1), const_1))), divide(subtract(subtract(add(4, const_1), const_1), const_1), subtract(subtract(add(9, const_1), const_1), const_1))), divide(subtract(subtract(subtract(add(4, const_1), ... | each of the integers from 0 to 9 , inclusive , is written on a separate slip of blank paper and the ten slips are dropped into a hat . if 4 of the slips are the drawn , without replacement , what is the probability that all 4 have a odd number written on it ? | "key is that there is no replacement , so each successive choice will become more skewed towards picking a neg ( i . e . the pool of positives decreases , while the pool of negatives stay the same ) p ( + on 1 st pick ) = 5 / 10 p ( + on 2 nd pick ) = 4 / 9 p ( + on 3 rd pick ) = 3 / 8 p ( + on 4 rd pick ) = 2 / 7 5 / ... | a = 4 + 1
b = 9 + 1
c = a / b
d = 4 + 1
e = d - 1
f = 9 + 1
g = f - 1
h = e / g
i = c * h
j = 4 + 1
k = j - 1
l = k - 1
m = 9 + 1
n = m - 1
o = n - 1
p = l / o
q = i * p
r = 4 + 1
s = r - 1
t = s - 1
u = t - 1
v = 9 + 1
w = v - 1
x = w - 1
y = x - 1
z = u / y
A = q * z
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a ) 6000 , b ) 36000 , c ) 60000 , d ) 600 , e ) 3600 | b | multiply(multiply(1000, const_60), 0.6) | a superhero flies at an incredible rate of 1000 kilometers per minute . what is her speed in miles per hour ? [ 1 km = 0.6 miles ] | to calculate the equivalent of miles in a kilometer 0.6 kilometers = 1 mile 1000 kilometers = ( 0.6 ) * 1000 = 600 miles speed in miles per minute = 600 = 600 1 hour = 60 minutes speed in miles per hour = 600 * 60 = 36,000 correct answer - b | a = 1000 * const_60
b = a * 0
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a ) 5200 , b ) 5150 , c ) 5250 , d ) 6150 , e ) 5095 | e | subtract(5100, divide(102, 20.4)) | 5100 β ( 102 Γ· 20.4 ) = ? | explanation : = 5100 β ( 102 / 204 Γ 10 ) = 5100 β 5 = 5095 option e | a = 102 / 20
b = 5100 - a
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a ) 7 , b ) 8 , c ) 9 , d ) 10 , e ) 11 | d | subtract(add(add(17, 21), 2), 30) | in a sports club with 30 members , 17 play badminton and 21 play tennis and 2 do not play either . how many members play both badminton and tennis ? | "let x play both badminton and tennis so 17 - x play only badminton and 19 - x play only tennis . 2 play none and there are total 30 students . hence , ( 17 - x ) + ( 21 - x ) + x + 2 = 30 40 - 2 x + x = 30 40 - x = 30 x = 10 so 10 members play both badminton and tennis . d" | a = 17 + 21
b = a + 2
c = b - 30
|
a ) rs . 1000 , b ) rs . 1200 , c ) rs . 1400 , d ) rs . 1600 , e ) rs . 2500 | d | subtract(multiply(multiply(multiply(divide(3, 1), divide(7, 1)), 40), const_2), multiply(40, const_2)) | in 40 litres of a mixture , the ratio of milk to water is 7 : 1 . in order to make the ratio of milk to water as 3 : 1 , the quantity of water that should be added to the mixture will be ? | explanation : total simple interest received , i = rs . 1600 principal , p = 7000 period , n = 5 years rate of interest , r = ? simple interest , i = p n r 100 i = pnr 100 β 1600 = 7000 Γ 5 Γ r 100 β r = 1600 Γ 100 7000 Γ 5 = 160 35 = 32 7 % β 1600 = 7000 Γ 5 Γ r 100 β r = 1600 Γ 1007000 Γ 5 = 16035 = 327 % by rule of ... | a = 3 / 1
b = 7 / 1
c = a * b
d = c * 40
e = d * 2
f = 40 * 2
g = e - f
|
a ) 388 , b ) 266 , c ) 350 , d ) 112 , e ) 134 | c | subtract(multiply(speed(300, 18), 39), 300) | 300 meter long train crosses a platform in 39 seconds while it crosses a signal pole in 18 seconds . what is the length of the platform ? | speed = [ 300 / 18 ] m / sec = 50 / 3 m / sec . let the length of the platform be x meters . then , x + 300 / 39 = 50 / 3 3 ( x + 300 ) = 1950 Γ¨ x = 350 m . answer : c | a = speed * (
b = a - 39
|
a ) $ 1800 , b ) $ 2800 , c ) $ 3800 , d ) $ 5800 , e ) $ 4800 | e | multiply(divide(5, add(add(const_2.0, const_3.0), 3)), 12000) | a person want to give his money of $ 12000 to his 5 children a , b , c , d , e in the ratio 2 : 4 : 3 : 1 : 5 . what is the d + e share ? | "d ' s share = 12000 * 1 / 15 = $ 800 d ' s share = 12000 * 5 / 15 = $ 4000 a + d = $ 4800 answer is e" | a = 2 + 0
b = a + 3
c = 5 / b
d = c * 12000
|
a ) rs 219 , b ) rs 220 , c ) rs 20 Β² , d ) rs 20 , e ) rs 30 | a | subtract(multiply(1, 20), 1) | an enterprising businessman earns an income of re 1 on the first day of his business . on every subsequent day , he earns an income which is just double of that made on the previous day . on the 20 th day of business , he earns an income of : | "2 nd day he earns = 2 = 2 ( 2 β 1 ) 3 rd day he earns = 2 ( 3 β 1 ) on 20 th day he earns 2 ( 20 - 1 ) = 219 rupees answer : a" | a = 1 * 20
b = a - 1
|
a ) 8 am , b ) 10 am , c ) 11 am , d ) 12 am , e ) 14 am | b | add(divide(450, add(40, 50)), 5) | two cars started from the same point , at 5 am , traveling in opposite directions at 40 and 50 mph respectively . at what time will they be 450 miles apart ? | after t hours the distances d 1 and d 2 , in miles per hour , traveled by the two cars are given by d 1 = 40 t and d 2 = 50 t after t hours the distance d separating the two cars is given by d = d 1 + d 2 = 40 t + 50 t = 90 t distance d will be equal to 450 miles when d = 90 t = 450 miles t = 5 hours . 5 am + 5 hours =... | a = 40 + 50
b = 450 / a
c = b + 5
|
a ) 10 days , b ) 11 days , c ) 12 days , d ) 15 days , e ) 17 days | c | inverse(add(divide(6, multiply(8, 20)), divide(11, multiply(12, 20)))) | if 8 men or 12 women can do a piece of work in 20 days , in how many days can the same work be done by 6 men and 11 women ? | "8 men = 12 women ( i . e 2 men = 3 women ) 12 women 1 day work = 1 / 20 soln : 6 men ( 9 women ) + 11 women = 20 women = ? 1 women 1 day work = 12 * 20 = 1 / 240 so , 20 women work = 20 / 240 = 1 / 12 ans : 12 days answer : c" | a = 8 * 20
b = 6 / a
c = 12 * 20
d = 11 / c
e = b + d
f = 1/(e)
|
a ) 2 , b ) 4 , c ) 5 , d ) 6 , e ) 7 | a | divide(multiply(subtract(const_1, divide(const_2, 6)), multiply(3, 6)), 6) | 3 men can complete a piece of work in 6 days . two days after they started the work , 3 more men joined them . how many days will they take to complete the remaining work ? | explanation : 3 man 1 day work = 1616 3 man 2 days work = 2626 remaining work = ( 1 β 2626 ) = 2 / 3 parts . 6 man together perform the work in 1 day is = 1616 + 1616 = 2626 parts 2626 parts completed in 1 day 2323 parts will b completed in 2 days answer : a | a = 2 / 6
b = 1 - a
c = 3 * 6
d = b * c
e = d / 6
|
['a ) 76', 'b ) 55', 'c ) 44', 'd ) 12', 'e ) 91'] | d | divide(36, const_3) | 36 people { a 1 , a 2 β¦ a 36 } meet and shake hands in a circular fashion . in other words , there are totally 36 handshakes involving the pairs , { a 1 , a 2 } , { a 2 , a 3 } , β¦ , { a 35 , a 36 } , { a 36 , a 1 } . then size of the smallest set of people such that the rest have shaken hands with at least one person ... | ans : { a 1 , a 2 } , { a 2 , a 3 } , { a 3 , a 4 } , { a 4 , a 5 } , { a 5 , a 6 } , { a 6 , a 7 } β¦ , { a 35 , a 36 } , { a 36 , a 1 } from the above arrangement , if we separate a 3 , a 6 , a 9 , . . . . . a 36 . total 12 persons the reamining persons must have shaked hand with atleast one person . so answer is 12 .... | a = 36 / 3
|
a ) $ 860 , b ) $ 850 , c ) $ 840 , d ) $ 830 , e ) $ 820 | a | add(add(multiply(100, 6), multiply(35, 4)), multiply(multiply(15, 4), const_2)) | rates for having a manuscript typed at a certain typing service are $ 6 per page for the first time a page is typed and $ 4 per page each time a page is revised . if a certain manuscript has 100 pages , of which 35 were revised only once , 15 were revised twice , and the rest required no revisions , what was the total ... | "50 pages typed 1 x 35 pages typed 2 x ( original + one revision ) 15 pages typed 3 x ( original + two revisions ) 50 ( 6 ) + 35 ( 6 + 4 ) + 15 ( 6 + 4 + 4 ) = 300 + 350 + 210 = 860 answer - a" | a = 100 * 6
b = 35 * 4
c = a + b
d = 15 * 4
e = d * 2
f = c + e
|
a ) 26 , b ) 48 , c ) 98 , d ) 37 , e ) 42 | e | divide(216, add(const_2, const_pi)) | the perimeter of a semi circle is 216 cm then the radius is ? | "36 / 7 r = 216 = > r = 42 answer : e" | a = 2 + math.pi
b = 216 / a
|
a ) 30 , b ) 35 , c ) 40 , d ) 45 , e ) 50 | c | multiply(divide(divide(add(360, 140), const_1000), 45), const_3600) | a train 360 metre long runs with a speed of 45 km / hr . what time will it take to pass a platform of 140 metre long ? | speed = 45 km / hr = 45 Γ 5 / 18 = 25 / 2 m / s distance travelled = ( speed x time ) time = ( distance travelled / speed ) distance travelled = length of the train + length of the platform = 360 + 140 = 500 m = 500 / 25 / 2 = 40 sec answer : c | a = 360 + 140
b = a / 1000
c = b / 45
d = c * 3600
|
a ) 12 / 112 , b ) 6 / 81 , c ) 11 / 61 , d ) 12 / 33 , e ) 3 / 19 | e | multiply(divide(add(const_2, const_1), add(multiply(18, const_2), const_2)), const_2) | the events a and b are independent , the probability that event a occurs is greater than 0 , and the probability that event a occurs is twice the probability that event b occurs . the probability that at least one of events a and b occurs is 18 times the probability that both events a and b occur . what is the probabil... | "let us say probability of a occuring is a . let us say probability of b occuring is b . a = 2 b probability ( either a or b or both ) = 8 times probability ( a and b ) a * ( 1 - b ) + b * ( 1 - a ) + ab = 18 * ab substituting a = 2 b in the second equation : 2 b * ( 1 - b ) + b * ( 1 - 2 b ) + 2 b * b = 18 * 2 b * b 3... | a = 2 + 1
b = 18 * 2
c = b + 2
d = a / c
e = d * 2
|
a ) 12 , b ) 16 , c ) 8 , d ) 24 , e ) 26 | c | divide(24, add(const_1, const_2)) | a student got twice as many sums wrong as he got right . if he attempted 24 sums in all , how many did he solve correctly ? | explanation : suppose the boy got x sums right and 2 x sums wrong . then , x + 2 x = 24 3 x = 24 x = 8 . answer : c | a = 1 + 2
b = 24 / a
|
a ) 287 , b ) 350 , c ) 828 , d ) 277 , e ) 400 | e | subtract(multiply(speed(300, 18), 42), 300) | a 300 m long train crosses a platform in 42 sec while it crosses a signal pole in 18 sec . what is the length of the platform ? | "speed = 300 / 18 = 50 / 3 m / sec . let the length of the platform be x meters . then , ( x + 300 ) / 42 = 50 / 3 3 x + 900 = 2200 = > x = 400 m . answer : e" | a = speed * (
b = a - 42
|
a ) 54 % , b ) 70 % , c ) 75 % , d ) 85 % , e ) 95 % | a | multiply(subtract(divide(multiply(multiply(const_100, add(const_1, divide(40, const_100))), add(const_1, divide(10, const_100))), const_100), const_1), const_100) | a fashion designer sold a pair of jeans to a retail store for 40 percent more than it cost to manufacture the pair of jeans . a customer bought the pair of jeans for 10 percent more than the retailer paid for them . the price the customer paid was what percent greater than the cost of manufacturing the jeans ? | "find the product of the two increases : ( 1.4 ) * ( 1.1 ) , which is 1.54 and a 54 % increase . a" | a = 40 / 100
b = 1 + a
c = 100 * b
d = 10 / 100
e = 1 + d
f = c * e
g = f / 100
h = g - 1
i = h * 100
|
a ) 40 , b ) 54 , c ) 62 , d ) 70 , e ) 80 | c | divide(add(negate(10), sqrt(subtract(power(negate(10), 2), multiply(const_4, negate(divide(multiply(900, 10), 2)))))), 2) | the time it took car p to travel 900 miles was 2 hours less than the time it took car r to travel the same distance . if car p β s average speed was 10 miles per hour greater than that of car r , what was car r β s average speed , in miles per hour ? | "let speed of car r be = x then speed of car p = x + 10 a / q , ( 900 / x ) - ( 900 / ( x + 10 ) ) = 2 solving for x = 62 miles \ hr . c" | a = negate + (
b = negate ** (
c = b - 2
d = 900 * 10
e = d / 2
f = 4 * negate
g = math.sqrt(c)
h = a / g
|
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