euclaise/mathqa_programs huggingface dataset:
Problem: a company has 15 managers and 75 associates . the 15 managers have an average salary of $ 90000 . the 75 associates have an average salary of $ 30000 . what is the average salary for the company ?
Options: a ) $ 35,000 , b ) $ 40,000 , c ) $ 55,000 , d ) $ 65,000 , e ) $ 75,000
Rationale: another method is to get ratios say 30000 = a and we know the # of people are in 1 : 5 ratio average = ( 3 a * 1 + a * 5 ) / 6 = 8 a / 6 = 40000 answer is b . $ 40,000
Answer: b
Python program:
a = 15 * 90000
b = 75 * 30000
c = a + b 
d = 15 + 75 
e = c / d
Problem: a man can row upstream at 37 kmph and downstream at 53 kmph , and then find the speed of the man in still water ?
Options: a ) 29 , b ) 92 , c ) 30 , d ) 32 , e ) 45
Rationale: "us = 37 ds = 53 m = ( 53 + 37 ) / 2 = 45 answer : e"
Answer: e
Python program:
a = 37 + 53 
b = a / 2
Problem: a certain car dealership sells economy cars , luxury cars , and sport utility vehicles . the ratio of economy to luxury cars is 3 : 2 . the ratio of economy cars to sport utility vehicles is 5 : 4 . what is the ratio of luxury cars to sport utility vehicles ?
Options: a ) 9 : 8 , b ) 8 : 9 , c ) 3 : 2 , d ) 10 : 12 , e ) 1 : 2
Rationale: "the ratio of economy to luxury cars is 3 : 2 - - > e : l = 3 : 2 = 15 : 10 . the ratio of economy cars to sport utility vehicles is 5 : 4 - - > e : s = 5 : 4 = 15 : 12 . thus , l : s = 10 : 12 . answer : d ."
Answer: d
Python program:
a = 4 * 3
b = 4 * 4
c = a / b
d = 4 * 4
e = 2 * 4
f = d / e
g = c / f
Problem: in a certain apartment building , there are one - bedroom and two - bedroom apartments . the rental prices of the apartment depend on a number of factors , but on average , two - bedroom apartments have higher rental prices than do one - bedroom apartments . let m be the average rental price for all apartments in the building . if m is $ 1,500 higher than the average rental price for all one - bedroom apartments , and if the average rental price for all two - bedroom apartments is $ 6,000 higher that m , then what percentage of apartments in the building are two - bedroom apartments ?
Options: a ) 40 % , b ) 35 % , c ) 30 % , d ) 20 % , e ) 28 %
Rationale: "ratio of 2 bedroom apartment : 1 bedroom apartment = 1500 : 6000 - - - - - > 1 : 4 let total number of apartments be x no . of 2 bedroom apartment = ( 1 / 5 ) * x percentage of apartments in the building are two - bedroom apartments - - - - > ( 1 / 5 ) * 100 - - - > 20 % answer : d"
Answer: d
Python program:
a = 1 * 500
b = 2 * 1000
c = b + 100 
d = c + 1 
e = a / d
Problem: solve below question 2 x - 1 = 17
Options: a ) - 8 , b ) - 9 , c ) - 5 , d ) - 4 , e ) 9
Rationale: 1 . add 1 to both sides : 2 x - 1 + 1 = 17 + 1 2 . simplify both sides : 2 x = 18 3 . divide both sides by 2 : 4 . simplify both sides : x = 9 e
Answer: e
Python program:
a = 17 + 1 
b = negate / (
Problem: john and jane went out for a dinner and they ordered the same dish . both used a 10 % discount coupon . john paid a 15 % tip over the original price of the dish , while jane paid the tip over the discounted price for the coupon . if john paid $ 0.54 more than jane , what was the original price of the dish ?
Options: a ) 24 , b ) 34.8 , c ) 36 , d ) 42 , e ) 84
Rationale: "the difference between the amounts john paid and jane paid is the deference between 15 % of p and 15 % of 0.9 p : 0.15 p - 0.15 * 0.9 p = 0.54 - - > 15 p - 13.5 p = 54 - - > p = 36 . answer : c ."
Answer: c
Python program:
a = 15 / 100
b = 10 / 100
c = 1 - b
d = 15 / 100
e = c * d
f = a - e
g = 0 / 54
Problem: 80 % of 5 / 8 =
Options: a ) 0.2 , b ) 0.5 , c ) 0.6 , d ) 0.75 , e ) 1.0
Rationale: "should be simple . 0.8 * 5 / 8 = 4 / 8 = 1 / 2 = 0.5 correct option : b"
Answer: b
Python program:
a = 8 * 5
b = a / 100
c = b * 80
d = c / 100
Problem: if n is a positive integer and n ^ 2 is divisible by 72 , then the largest positive integer t that must divide n is ?
Options: a ) 6 , b ) 12 , c ) 24 , d ) 36 , e ) 48
Rationale: "q : if n is a positive integer and n ^ 2 is divisible by 72 , then the largest positive integer t that must divide n is : a 6 , b 12 , c 24 , d 36 , e 48 n ^ 2 is divisible by 72 , but it must also be greater than 72 . if n is an integer , then n ^ 2 must be a perfect square . the factorization of 72 is ( 8 ) ( 9 ) , so if it is multiplied by 2 , it will be ( 2 ) ( 8 ) ( 9 ) = ( 16 ) ( 9 ) = 144 , a perfect square . so n ^ 2 must be at least 144 or a multiple of 144 , which means that n must be 12 or a multiple of 12 . b"
Answer: b
Python program:
a = 72 / 2
b = math.sqrt(a)
c = b * 2
Problem: angelina walked 720 meters from her home to the grocery at a constant speed . she then walked 480 meters to the gym at double the speed . she spent 40 seconds less on her way from the grocery to the gym than on her way from home to the grocery . what was angelina ' s speed , in meters per second , from the grocery to the gym ?
Options: a ) 2 , b ) 3 , c ) 4 , d ) 6 , e ) 24
Rationale: "let the speed be x . . . so time taken from home to grocery = 720 / x . . the speed to gym = 2 x . . so time taken = 480 / 2 x = 240 / x . . its given 720 / x - 240 / x = 40 . . 480 / x = 40 . . x = 12 m / secs . . so grocery to gym = 2 * 12 = 24 m / s . . . e"
Answer: e
Python program:
a = 480 / 2
b = 720 - a
c = b / 40
d = c * 2
Problem: the average age of 15 students of a class is 15 years . out of these , the average age of 5 students is 14 years and that of the other 9 students is 16 years . tee age of the 15 th student is :
Options: a ) 11 , b ) 14 , c ) 15 , d ) 13 , e ) 18
Rationale: "age of the 15 th student = [ 15 * 15 - ( 14 * 5 + 16 * 9 ) ] = ( 225 - 214 ) = 11 years . answer a"
Answer: a
Python program:
a = 15 * 15
b = 5 * 14
c = 9 * 16
d = b + c 
e = a - d
Problem: john and peter are among the 9 players a volleyball coach can choose from to field a 6 - player team . if all 6 players are chosen at random , what is the probability of choosing a team that includes john and peter ?
Options: a ) 3 / 10 , b ) 4 / 11 , c ) 5 / 12 , d ) 6 / 13 , e ) 7 / 15
Rationale: the total possible ways of selecting a 6 - member team is 9 c 6 = 84 the possible ways which include john and peter is 7 c 4 = 35 the probability of choosing both john and peter is 35 / 84 = 5 / 12 the answer is c .
Answer: c
Python program:
a = 9 - 2
b = math.factorial(a)
c = 6 - 2
d = math.factorial(c)
e = 9 - 2
f = 6 - 2
g = e - f
h = math.factorial(g)
i = d * h
j = b / i
k = math.factorial(9)
l = math.factorial(6)
m = 9 - 6
n = math.factorial(m)
o = l * n
p = k / o
q = j / p
Problem: a certain company has records stored with a record storage firm in 15 - inch by 12 - inch by 10 - inch boxes . the boxes occupy 1.08 million cubic inches of space . if the company pays $ 0.6 per box per month for the record storage , what is the total amount that the company pays each month for record storage ?
Options: a ) a . 150 , b ) b . 300 , c ) c . 600 , d ) d . 1,200 , e ) e . 360
Rationale: "volume per box : 15 x 12 x 10 = 1,800 total volume : 1 , 080,000 number of boxes : total volume / volume per box = 1 , 080,000 / 1,800 = 600 price per month : number of boxes * price per box = 600 * 0.6 = 360 answer : e"
Answer: e
Python program:
a = 15 * 12
b = a * 10
c = b / 100
d = c / 100
e = d / 100
f = 1 / 8
g = 0 * 6
Problem: how many diagonals does a 62 - sided convex polygon have ?
Options: a ) 1829 , b ) 2356 , c ) 3458 , d ) 3843 , e ) 4820
Rationale: "a 62 - sided convex polygon has 62 vertices . if we examine a single vertex , we can see that we can connect it with 59 other vertices to create a diagonal . note that we ca n ' t connect the vertex to itself and we ca n ' t connect it to its adjacent vertices , since this would not create a diagonal . if each of the 62 vertices can be connected with 59 vertices to create a diagonal then the total number of diagonals would be ( 62 ) ( 59 ) = 3658 however , we must recognize that we have counted every diagonal twice . to account for counting each diagonal twice , we must divide 3658 by 2 to get 1829 . the answer is a ."
Answer: a
Python program:
a = math.factorial(62)
b = 62 - 2
c = math.factorial(b)
d = math.factorial(2)
e = c * d
f = a / e
Problem: if y > 0 , ( 8 y ) / 20 + ( 3 y ) / 10 is what percent of y ?
Options: a ) 40 % , b ) 50 % , c ) 60 % , d ) 70 % , e ) 80 %
Rationale: "can be reduced to 4 y / 10 + 3 y / 10 = 7 y / 10 = 70 % answer d"
Answer: d
Python program:
a = 8 / 20
b = 3 / 10
c = a + b 
d = 100 * c
Problem: how many kg of pure salt must be added to 30 kg of 2 % solution of salt and water to increase it to a 10 % solution ?
Options: a ) 8 / 3 , b ) 9 / 7 , c ) 7 / 4 , d ) 5 / 2 , e ) 6 / 7
Rationale: "amount salt in 30 kg solution = 2 * 30 / 100 = 0.6 kg let x kg of pure salt be added then ( 0.6 + x ) / ( 30 + x ) = 10 / 100 60 + 100 x = 300 + 10 x 90 x = 240 x = 8 / 3 answer is a"
Answer: a
Python program:
a = 10 - 2
b = 10 / 30
c = 1 - b
d = a / c
Problem: on dividing 14698 by a certain number , we get 89 as quotient and 14 as remainder . what is the divisor ?
Options: a ) 743 , b ) 154 , c ) 852 , d ) 741 , e ) 165
Rationale: "divisor * quotient + remainder = dividend divisor = ( dividend ) - ( remainder ) / quotient ( 14698 - 14 ) / 89 = 165 answer ( e )"
Answer: e
Python program:
a = 14698 - 14
b = a / 89
Problem: how long does a train 110 m long traveling at 60 kmph takes to cross a bridge of 190 m in length ?
Options: a ) 18.9 sec , b ) 88.9 sec , c ) 22.9 sec , d ) 18.0 sec , e ) 72.0 sec
Rationale: "d = 110 + 190 = 300 m s = 60 * 5 / 18 = 50 / 3 t = 300 * 3 / 50 = 18.0 sec answer : d"
Answer: d
Python program:
a = 110 + 190 
b = 60 * const_0_2778
c = a / b
Problem: paulson spends 75 % of his income . his income is increased by 20 % and he increased his expenditure by 10 % . find the percentage increase in his savings ?
Options: a ) 20 % , b ) 25 % , c ) 50 % , d ) 75 % , e ) 60 %
Rationale: "let original income = $ 100 expenditure = $ 75 savings = $ 25 new income = $ 120 new expenditure = $ 110 / 100 * 75 = $ 165 / 2 new savings = 120 - 165 / 2 = $ 75 / 2 increase in savings = 75 / 2 - 25 = $ 25 / 2 increase % = 25 / 2 * 1 / 25 * 100 = 50 % answer is c"
Answer: c
Python program:
a = 20 / 100
b = 1 + a 
c = 10 / 100
d = 1 + c 
e = 75 / 100
f = d * e
g = b - f
h = 75 / 100
i = 1 - h
j = g - i
k = 75 / 100
l = 1 - k
m = j / l
n = m * 100
Problem: rice weighing 33 / 4 pounds was divided equally and placed in 4 containers . how many ounces of rice were in each container ? ( note that 1 pound = 16 ounces )
Options: a ) 27 , b ) 30 , c ) 33 , d ) 36 , e ) 39
Rationale: "33 / 4 ÷ 4 = 33 / 16 pounds in each container 33 / 16 pounds * 16 ounces / pound = 33 ounces in each container the answer is c ."
Answer: c
Python program:
a = 33 / 4
b = a * 16
c = b / 4
Problem: ratio between rahul and deepak is 4 : 3 , after 6 years rahul age will be 22 years . what is deepak present age ?
Options: a ) 22 , b ) 15 , c ) 77 , d ) 266 , e ) 12
Rationale: "present age is 4 x and 3 x , = > 4 x + 6 = 22 = > x = 4 so deepak age is = 3 ( 4 ) = 12 answer : e"
Answer: e
Python program:
a = 22 - 6
b = a * 3
c = b / 4
Problem: in a certain company , a third of the workers do not have a retirement plan . 20 % of the workers who do not have a retirement plan are women , and 40 % of the workers who do have a retirement plan are men . if 112 of the workers of that company are men , how many of the workers are women ?
Options: a ) 80 , b ) 98 , c ) 105 , d ) 120 , e ) 210
Rationale: "set up equation : x = total number of workers 112 = 0,4 * 2 / 3 * x + 0,8 * 1 / 3 * x 112 = 16 / 30 x x = 210 210 - 112 = 98 answer b"
Answer: b
Python program:
a = 1 / 3
b = 1 / 3
c = 20 / 100
d = b * c
e = a - d
f = 1 / 3
g = 1 - f
h = 40 / 100
i = g * h
j = e + i 
k = 112 / j
l = 1 / 3
m = 20 / 100
n = l * m
o = 1 / 3
p = 1 - o
q = 1 / 3
r = 1 - q
s = 40 / 100
t = r * s
u = p - t
v = n + u 
w = k * v
Problem: if an object travels 70 feet in 2 seconds , what is the object ’ s approximate speed in miles per hour ? ( note : 1 mile = 5280 feet )
Options: a ) 15.95 , b ) 17.28 , c ) 19.54 , d ) 21.73 , e ) 23.86
Rationale: "70 feet / 2 seconds = 35 feet / second ( 35 feet / second ) * ( 3600 seconds / hour ) * ( 1 mile / 5280 feet ) = 23.86 miles / hour ( approximately ) the answer is e ."
Answer: e
Python program:
a = 70 / 5280
b = 1 / 3600
c = 2 * b
d = a / c
Problem: 85 litres of diesel is required to travel 600 km using a 800 cc engine . if the volume of diesel required to cover a distance varies directly as the capacity of the engine , then how many litres of diesel is required to travel 800 km using 1200 cc engine ?
Options: a ) 80 litres , b ) 90 litres , c ) 120 litres , d ) 170 litres , e ) none of these
Rationale: "explanatory answer to cover a distance of 800 kms using a 800 cc engine , the amount of diesel required = 800 / 600 * 85 = 113.33 litres . however , the vehicle uses a 1200 cc engine and the question states that the amount of diesel required varies directly as the engine capacity . i . e . , for instance , if the capacity of engine doubles , the diesel requirement will double too . therefore , with a 1200 cc engine , quantity of diesel required = 1200 / 800 * 113.33 = 170 litres . answer d"
Answer: d
Python program:
a = 800 * 600
b = 85 / a
c = 800 * b
d = 1200 * c
Problem: evaluate 28 % of 650 + 45 % of 280
Options: a ) 232 , b ) 308 , c ) 252 , d ) 262 , e ) 282
Rationale: "explanation : = ( 28 / 100 ) * 650 + ( 45 / 100 ) * 280 = 182 + 126 = 308 answer : option b"
Answer: b
Python program:
a = 650 / 28
b = 28 / a
Problem: a can give b 300 meters start and c 600 meters start in a kilometer race . how much start can b give c in a kilometer race ?
Options: a ) 111.12 , b ) 111.67 , c ) 428.57 , d ) 111.11 , e ) 101.12
Rationale: "a runs 1000 m while b runs 700 m and c runs 400 m . the number of meters that c runs when b runs 1000 m , = ( 1000 * 400 ) / 700 = 571.43 m . b can give c = 1000 - 571.43 = 428.57 m . answer : c"
Answer: c
Python program:
a = 100 * 10
b = 100 * 10
c = 100 * 10
d = c - 600
e = b * d
f = 100 * 10
g = f - 300
h = e / g
i = a - h
Problem: there are 2000 students in a school and among them 10 % of them attends chess class . 50 % of the students who are in the chess class are also enrolled for swimming . no other students are interested in swimming so how many will attend the swimming class if all enrolled attends ?
Options: a ) 1 , b ) 10 , c ) 100 , d ) 50 , e ) 20
Rationale: "10 % of 2000 gives 200 . so 200 attends chess and 50 % of 200 gives 100 so 100 enrolled for swimming answer : c"
Answer: c
Python program:
a = 10 * 2000
b = a / 100
c = b * 50
d = c / 100
Problem: a new tower has just been built at the verbico military hospital ; the number of beds available for patients at the hospital is now 6 times the number available before the new tower was built . currently , 1 / 3 of the hospital ' s original beds , as well as 1 / 5 of the beds in the new tower , are occupied . for the purposes of renovating the hospital ' s original wing , all of the patients in the hospital ' s original beds must be transferred to beds in the new tower . if patients are neither admitted nor discharged during the transfer , what fraction of the beds in the new tower will be unoccupied once the transfer is complete ?
Options: a ) 11 / 30 , b ) 29 / 60 , c ) 17 / 30 , d ) 19 / 30 , e ) 11 / 15
Rationale: "i think e - 11 / 15 is the correct answer . here goes : lets assume originally the number of beds = x after the new tower , the total combined no of beds = 6 x so old = x , new = 5 x now 1 / 3 of x are occupied and 1 / 5 of 5 x are occupied which simplifies to ( 5 / 5 ) x we are shifting 1 / 3 of x to the new ward so there will now be : 1 / 3 of x plus 5 / 5 of x occupied in the new ward . add them up to get 4 / 3 of x there are 5 x beds in new tower so ratio is : ( 4 / 3 ) x / 5 x = 4 / 15 of x subtract that from 15 / 15 of x and you get the number of un - occupied beds to total capacity of new tower = 11 / 15 . e"
Answer: e
Python program:
a = 6 * 3
b = a + 1 
c = 1 / 3
d = 1 / 5
e = c * d
f = b * e
Problem: the sum of two numbers is 40 and their difference is 4 . the ratio of the numbers is
Options: a ) 11 : 9 , b ) 11 : 18 , c ) 21 : 19 , d ) 21 : 19 , e ) none
Rationale: sol . let the numbers be x and y . then , x + y / x - y = 40 / 4 = 10 ⇔ ( x + y ) = 10 ( x - y ) ⇔ 9 x = 11 y ⇔ x / y = 11 / 9 . answer a
Answer: a
Python program:
a = 40 / 2
b = a - 2
c = 40 - b
d = c / 2
e = 40 / 2
f = e - 2
g = f / 2
h = d / g
Problem: on a race track a maximum of 5 horses can race together at a time . there are a total of 25 horses . there is no way of timing the races . what is the minimum number q of races we need to conduct to get the top 3 fastest horses ?
Options: a ) 5 , b ) 7 , c ) 8 , d ) 10 , e ) 11
Rationale: q = 7 is the correct answer . good solution buneul . b
Answer: b
Python program:
a = 25 / 5
b = a + 2
Problem: the ages of 2 persons differ by 21 years . if 15 years ago the elder one be 8 times as old as the younger one , find the present age of elder person .
Options: a ) 30 , b ) 48.5 , c ) 50.4 , d ) 62.6 , e ) 47.9
Rationale: "age of the younger person = x age of the elder person = x + 21 8 ( x - 15 ) = x + 21 - 15 x = 18 age of elder person = 18 + 21 = 39 answer is e"
Answer: e
Python program:
a = 2 * 21
b = 21 - 1
c = a / b
d = c + 21 
e = d - 2
Problem: in a 100 m race , a covers the distance in 30 seconds and b in 45 second . in this race a beats b by :
Options: a ) 33.33 m , b ) 25 m , c ) 45 m , d ) 30 m , e ) none of these
Rationale: solution distance covered by b in 15 sec . = ( 100 / 45 x 15 ) m = 33.33 m . ∴ a beats b by 33.33 metres . answer a
Answer: a
Python program:
a = 100 / 45
b = 45 - 30
c = a * b
Problem: if ( 2 to the x ) - ( 2 to the ( x - 2 ) ) = 3 ( 2 to the 12 ) , what is the value of x ?
Options: a ) 9 , b ) 11 , c ) 13 , d ) 15 , e ) 14
Rationale: i am guessing the question is : ( 2 to the power x ) - ( 2 to the power ( x - 2 ) ) = 3 ( 2 to the power 12 ) 2 ^ x - 2 ^ ( x - 2 ) = 3 . 2 ^ 12 hence x = 14 . answer is e
Answer: e
Python program:
a = 12 + 2
Problem: a , b , c can do a work in 15 , 20,45 days respectively . they get rs 500 for their work . what is the share of a ?
Options: a ) rs . 240 , b ) rs . 340 , c ) rs . 260 , d ) rs . 280 , e ) rs . 440
Rationale: lcm = 180 share of a = ( lcm / a x total amount ) / lcm / a + lcm / b + lcm / c = ( 180 / 15 ) / ( 180 / 15 + 180 / 20 + 180 / 45 ) = ( 12 / 25 ) * 500 = rs . 240 answer : a
Answer: a
Python program:
a = 1/(15)
b = 2 * 10
c = 1/(b)
d = 2 * 10
e = 100 * const_0_25
f = d + e 
g = 1/(f)
h = c + g 
i = 1/(15)
j = h + i 
k = a / j
l = 500 * k
Problem: express a speed of 252 kmph in meters per second ?
Options: a ) 10 mps , b ) 05 mps , c ) 09 mps , d ) 12 mps , e ) 70 mps
Rationale: "e 70 mps 252 * 5 / 18 = 70 mps"
Answer: e
Python program:
a = const_0_2778 * 252
Problem: the temperature of a certain cup of coffee 10 minutes after it was poured was 120 degrees fahrenheit . if the temperature f of the coffee t minutes after it was poured can be determined by the formula f = 120 ( 2 ^ - at ) + 60 , where f is in degrees fahrenheit and a is a constant . then the temperature of the coffee 40 minutes after it was poured was how many degrees fahrenheit ?
Options: a ) 67.5 , b ) 75 , c ) 80 , d ) 85 , e ) 90
Rationale: "answer : b the temperature of coffee 10 minutes after it was poured ( 120 f ) will help in solving the constant “ a ” . 120 = 120 ( 2 ^ 10 a ) + 60 2 ^ - 1 = 2 ^ 10 a a = - 1 / 10 the temperature of coffee 40 minutes after it was poured is : f = 120 ( 2 ^ - 40 / 10 ) + 60 f = 120 * 1 / 16 + 60 f = 15 / 2 + 60 f = 135 / 2 = 67.5 a"
Answer: a
Python program:
a = 60 / 10
b = 1 - 2
c = a * b
d = 2 ** c
e = d * 120
f = e + 60
Problem: a circular garden is surrounded by a fence of negligible width along the boundary . if the length of the fence is 1 / 3 of th area of the garden . what is the radius of the circular garden ?
Options: a ) 6 , b ) 2 , c ) 4 , d ) 8 , e ) 16
Rationale: "as per the question - - width is negligible now , let l be the length of the fence = 2 pir l = 1 / 3 ( pir ^ 2 ) pir ^ 2 = 6 pir r = 6 answer : a"
Answer: a
Python program:
a = 3 ** 2
b = math.sqrt(a)
c = 2 * b
Problem: jean drew a gumball at random from a jar of pink and blue gumballs . since the gumball she selected was blue and she wanted a pink one , she replaced it and drew another . the second gumball also happened to be blue and she replaced it as well . if the probability of her drawing the two blue gumballs was 25 / 49 , what is the probability that the next one she draws will be pink ?
Options: a ) 1 / 49 , b ) 2 / 7 , c ) 3 / 7 , d ) 16 / 49 , e ) 40 / 49
Rationale: "the probability of drawing a pink gumball both times is the same . the probability that she drew two blue gumballs = 25 / 49 = ( 5 / 7 ) * ( 5 / 7 ) therefore probability that the next one she draws is pink = 2 / 7 option ( b )"
Answer: b
Python program:
a = 25 / 49
b = math.sqrt(a)
c = 1 - b
Problem: the areas of the two spheres are in the ratio 1 : 4 . the ratio of their volume is ?
Options: a ) 1 : 4
b ) 1 : 16
c ) 1 : 8
d ) 1 : 64
e ) 2 : 3
Rationale: 4 π r 12 : 4 π r 22 = 1 : 4 r 1 : r 2 = 1 : 2 4 / 3 π r 13 : 4 / 3 π r 23 r 13 : r 23 = 1 : 8 answer : c
Answer: c
Python program:
a = 4 * 2
b = 1 / a
Problem: a hostel had provisions for 250 men for 40 days . if 50 men left the hostel , how long will the food last at the same rate ?
Options: a ) 30 , b ) 40 , c ) 50 , d ) 60 , e ) 65
Rationale: "a hostel had provisions for 250 men for 40 days if 50 men leaves the hostel , remaining men = 250 - 50 = 200 we need to find out how long the food will last for these 200 men . let the required number of days = x days more men , less days ( indirect proportion ) ( men ) 250 : 200 : : x : 40 250 × 40 = 200 x 5 × 40 = 4 x x = 5 × 10 = 50 answer c"
Answer: c
Python program:
a = 250 * 40
b = 250 - 50
c = a / b
Problem: the distance between parallel sides of the hexagon is 9 . determine the length of the hexagon
Options: a ) 18 * sqrt 3
b ) 18 * sqrt 2
c ) 18 * sqrt 4
d ) 19 * sqrt 3
e ) 17 * sqrt 3
Rationale: length of each side of regular hexagon will be 3 * sqrt 3 . total length ( perimeter ) of regular hexagon will be 18 * sqrt 3 answer : a
Answer: a
Python program:
a = 2 * 3
b = math.sqrt(3)
c = 9 / b
d = a * c
Problem: a train covers a distance of 12 km in 10 min . if it takes 3 sec to pass a telegraph post , then the length of the train is ?
Options: a ) 70 m , b ) 16 m , c ) 60 m , d ) 80 m , e ) 88 m
Rationale: "speed = ( 12 / 10 * 60 ) km / hr = ( 72 * 5 / 18 ) m / sec = 20 m / sec . length of the train = 20 * 3 = 60 m . answer : c"
Answer: c
Python program:
a = 12 / 10
b = a - 3
c = 12 / b
Problem: if g and f are both odd prime numbers andg < f , then how many different positive integer factors does 2 gfhave ?
Options: a ) 3 , b ) 4 , c ) 6 , d ) 8 , e ) 12
Rationale: g and f are both odd prime numbers - it means either g or f is not 2 and since prime numbers have only two factors - 1 and the number itself g and f each will have ( 1 + 1 ) = 2 factors hence 2 gf will have ( 1 + 1 ) ( 1 + 1 ) ( 1 + 1 ) = 8 factors d is the answer
Answer: d
Python program:
a = 2 * 2
b = 2 * a
Problem: a and b go around a circular track of length 600 m on a cycle at speeds of 30 kmph and 60 kmph . after how much time will they meet for the first time at the starting point ?
Options: a ) 120 sec , b ) 176 sec , c ) 178 sec , d ) 72 sec , e ) 189 sec
Rationale: "time taken to meet for the first time at the starting point = lcm { length of the track / speed of a , length of the track / speed of b } = lcm { 600 / ( 30 * 5 / 18 ) , 600 / ( 60 * 5 / 18 ) } = 72 sec . answer : d"
Answer: d
Python program:
a = 60 * const_0_2778
b = 30 * const_0_2778
c = a - b
d = 600 / c
Problem: if $ 5,000 is invested in an account at a simple annual rate of r percent , the interest is $ 250 . when $ 18,000 is invested at the same interest rate , what is the interest from the investment ?
Options: a ) $ 700 , b ) $ 750 , c ) $ 800 , d ) $ 850 , e ) $ 900
Rationale: "- > 250 / 5,000 = 5 % and 18,000 * 5 % = 900 . thus , e is the answer ."
Answer: e
Python program:
a = 2 * 100
b = a * 100
c = 250 * b
d = 2 * 100
e = d * 100
f = e / 4
g = c / f