euclaise/mathqa_programs huggingface dataset:
Problem: in arun ' s opinion , his weight is greater than 64 kg but leas than 72 kg . his brother does not agree with arun and he thinks that arun ' s weight is greater than 60 kg but less than 70 kg . his mother ' s view is that his weight can not be greater than 67 kg . if all of them are correct in their estimation , what is the average of diferent probable weights of arun ?
Options: a ) 86.5 kg , b ) 66.5 kg , c ) 46.5 kg , d ) 65.5 kg , e ) 16.5 kg
Rationale: "let arun ' s weight be x kg . according to arun , 64 < x < 72 . according to arun ' s brother , 60 < x < 70 . according to arun ' s mother , x < 67 . the values satisfying all the above conditions are 65 and 66 . required average = ( 65 + 66 ) / 2 = 65.5 kg answer : d"
Answer: d
Python program:
a = 64 + 1 
b = 67 + a 
c = b / 2
Problem: two trains are moving in opposite directions with speed of 110 km / hr and 90 km / hr respectively . their lengths are 1.10 km and 0.9 km respectively . the slower train cross the faster train in - - - seconds
Options: a ) 26 , b ) 48 , c ) 47 , d ) 36 , e ) 25
Rationale: "explanation : relative speed = 110 + 90 = 200 km / hr ( since both trains are moving in opposite directions ) total distance = 1.1 + . 9 = 2 km time = 2 / 200 hr = 1 / 100 hr = 3600 / 100 = 36 seconds answer : option d"
Answer: d
Python program:
a = 1 + 10 
b = 110 + 90 
c = a / b
d = c * 3600
Problem: in the xy - plane , a triangle has vertices ( 0,0 ) , ( 4,0 ) and ( 4,10 ) . if a point ( a , b ) is selected at random from the triangular region , what is the probability that a - b > 0 ?
Options: a ) 1 / 5 , b ) 1 / 3 , c ) 1 / 2 , d ) 2 / 3 , e ) 2 / 5
Rationale: the area of the right triangle is ( 1 / 2 ) * 4 * 10 = 20 . only the points ( a , b ) below the line y = x satisfy a - b > 0 . the part of the triangle which is below the line y = x has an area of ( 1 / 2 ) ( 4 ) ( 4 ) = 8 . p ( a - b > 0 ) = 8 / 20 = 2 / 5 the answer is e .
Answer: e
Python program:
a = 0 + 10 
b = 4 / a
Problem: into a room you store 38 black bottles and 4 green bottles , and you turn off the light . if you ask to someone look for 2 bottles without turn on the light , what is the probability of both the selected bottles will be green ?
Options: a ) 1 / 574 , b ) 2 / 574 , c ) 1 / 287 , d ) 2 / 287 , e ) 3 / 287
Rationale: there are 4 green bottles in a group of 38 + 4 that is 42 . thus the probability of picking 2 green bottles is : ( 4 / 42 ) ( 3 / 41 ) = 2 / 287 . the correct answer is d .
Answer: d
Python program:
a = 4 - 1
b = 4 * a
c = 38 + 4 
d = 38 + 4 
e = d - 1
f = c * e
g = b / f
Problem: a , b and c enter into partnership . a invests some money at the beginning , b invests double the amount after 6 months , and c invests thrice the amount after 8 months . if the annual gain be rs . 27000 . a ' s share is ?
Options: a ) 9000 , b ) 2778 , c ) 6000 , d ) 2889 , e ) 6612
Rationale: x * 12 : 2 x * 6 : 3 x * 4 1 : 1 : 1 1 / 3 * 27000 = 9000 answer : a
Answer: a
Python program:
a = 1 * 12
b = 1 * 12
c = 12 - 6
d = c * 2
e = b + d 
f = 12 - 8
g = f * 3
h = e + g 
i = 27000 / h
j = a * i
Problem: a man swims downstream 120 km and upstream 50 km taking 5 hours each time ; what is the speed of the current ?
Options: a ) 3 kmph , b ) 7 kmph , c ) 13 kmph , d ) 6.5 kmph , e ) 7 : 3 kmph
Rationale: "explanation : 120 - - - 5 ds = 24 ? - - - - 1 50 - - - - 5 us = 10 ? - - - - 1 s = ? s = ( 24 - 10 ) / 2 = 7 answer : option b"
Answer: b
Python program:
a = 50 / 5
b = 120 / 5
c = a + b 
d = c / 2
Problem: pat , kate and mark charged a total of 198 hours to a certain project . if pat charged twice as much time to the project as kate and 1 / 3 as much times as mark , how many more hours did mark charge to the project than kate .
Options: a ) 18 , b ) 36 , c ) 72 , d ) 110 , e ) 108
Rationale: "let kate charge for x hours , then pat charged for 2 x and mat - for 6 x . so , 2 x + 6 x + x = 198 - total hours charged for , x = 22 . mat charged 6 x - x or 5 x for more hours than kate , or for 110 hours . d is correct"
Answer: d
Python program:
a = 1 + 2 
b = 2 * 3
c = a + b 
d = 198 / c
e = 2 * 3
f = e - 1
g = d * f
Problem: in the junior basketball league there are 18 teams , 1 / 3 of them are bad and ½ are rich . what ca n ' t be the number of teams that are rich and bad ?
Options: a ) 4 . , b ) 6 . , c ) 7 . , d ) 8 . , e ) 10 .
Rationale: "total teams = 18 bad teams = ( 1 / 3 ) * 18 = 6 rich teams = 9 so maximum value that the both rich and bad can take will be 9 . so e = 10 can not be that value . ans e ."
Answer: e
Python program:
a = 1 / 1
b = 18 * a
c = b + 1
Problem: kul is 22 years old and saras is 33 years . find the ratio of saras ' s age to kul ' s age .
Options: a ) 3 / 1 , b ) 3 / 2 , c ) 5 / 2 , d ) 5 / 3 , e ) none of these
Rationale: explanation : kul is 22 years old . saras is 33 years old . saras ' s age : kul ' s age = 33 : 22 = 3 : 2 answer : b
Answer: b
Python program:
a = 33 / 22
Problem: what is the cp of rs 100 stock at 7 discount , with 1 / 5 % brokerage ?
Options: a ) 93.9 , b ) 96.3 , c ) 93.2 , d ) 96.7 , e ) 96.21
Rationale: "explanation : use the formula , cp = 100 â € “ discount + brokerage % cp = 100 - 7 + 1 / 5 93.2 thus the cp is rs 93.2 . answer : c"
Answer: c
Python program:
a = 100 - 7
b = 1 / 5
c = a + b
Problem: right triangle pqr is the base of the prism in the figure above . if pq = pr = â ˆ š 14 and the height of the prism is 8 , what is the volume of the prism ?
Options: a ) 12 , b ) 45 , c ) 87 , d ) 56 , e ) 23
Rationale: "volume of prism = area of base * height = 1 / 2 * ( square root of 14 ) * ( square root of 14 ) * 8 = 56 answer : d"
Answer: d
Python program:
a = math.sqrt(14)
b = math.sqrt(14)
c = triangle_area * (
Problem: a city with a population of 97,500 is to be divided into 6 voting districts , and no district is to have a population that is more than 10 percent greater than the population of any other district . what is the minimum possible population that the least populated district could have ?
Options: a ) 15,000 , b ) 15,500 , c ) 16,000 , d ) 16,500 , e ) 17,000
Rationale: the minimum possible population occurs when all the other districts have a population that is 10 % greater than the least populated district . let p be the population of the least populated district . then 97,500 = p + 5 ( 1.1 ) p 6.5 p = 97,5000 p = 15,000 the answer is a .
Answer: a
Python program:
a = 1000 * 100
b = 3600 - 100
c = b - 1000
d = a - c
e = d / 1000
f = 10 / 100
g = 1 + f 
h = 6 - 1
i = g * h
j = i + 1 
k = e / j
Problem: find the c . i . on a sum of rs . 1800 for 6 months at 20 % per annum , interest being compounded quarterly ?
Options: a ) 792 , b ) 892 , c ) 8920 , d ) 802 , e ) 9920
Rationale: "c . i . = 1800 ( 21 / 20 ) ^ 2 - 1800 = 792 answer : c"
Answer: c
Python program:
a = const_0_25 / 4
b = 1 + a 
c = const_0_25 / 4
d = 1 + c 
e = b * d
f = 1800 * e
g = f - 1800
Problem: in a recent election , james received 15 percent of the 10000 votes cast . to win the election , a candidate needed to receive more than 51 percent of the vote . how many additional votes would james have needed to win the election ?
Options: a ) 1004 , b ) 1000 , c ) 3600 , d ) 1201 , e ) 3601
Rationale: "james = ( 15 / 100 ) * 10000 = 1500 votes to win = ( 51 / 100 ) * total votes + 1 = ( 51 / 100 ) * 10000 + 1 = 5101 remaining voted needed to win election = 5101 - 1500 = 3601 answer : option e"
Answer: e
Python program:
a = 1000 + 1000 
b = 1000 + 1000 
c = b * 15
d = a - c
Problem: how many 5 digit ( digit = 0 - 9 ) zip codes can exist in which at least one digit is repeated ?
Options: a ) 39760 , b ) 49760 , c ) 59760 , d ) 69760 , e ) 70000
Rationale: zip codes with 5 digits ( all five digits can be repeated ) : 10 ^ 5 = 100,000 zip codes with no digit being repeated : 10 * 9 * 8 * 7 * 6 = 30,240 zip codes with at least one digit being repeated : 100,000 - 30,240 = 69,760 = 69760 ans : d
Answer: d
Python program:
a = 10 ** 5
b = 10 * 9
c = 5 + 3 
d = b * c
e = 5 + 2 
f = d * e
g = 5 + 1 
h = f * g
i = a - h
Problem: a train 400 m long is running at a speed of 54 km / hr . if it crosses a tunnel in 2 minutes . then what is the length of tunnel ?
Options: a ) 1200 m , b ) 1400 m , c ) 1600 m , d ) 1800 m , e ) 2200 m
Rationale: "speed of train in m / sec = ( speed of train in km / hr ) x 5 / 18 ∴ speed of train in m / sec = 54 x 5 / 18 = 15 m / sec time taken to cross the tunnel = 2 minutes = 120 sec therefore , total length covered by train in crossing the tunnel = speed of train x time taken to cross the tunnel = 15 m / sec x 120 sec = 1800 m total length covered by train in crossing the tunnel = length of train + length of tunnel given , length of train = 400 m and calculated above , length covered by train in crossing the tunnel = 1800 m therefore , length of tunnel = 1800 m - 400 m = 1400 m correct answer : option : b"
Answer: b
Python program:
a = 54 - 2
b = a * const_0_2778
c = 400 / b
Problem: if i walk at 3 km / h , i miss the bus by 12 minutes . if i walk at 6 km / h , i reach 10 minutes before the arrival of the bus . how far i walk to reach the bus stand ?
Options: a ) 2.19 km , b ) 2.22 km , c ) 2.00 km , d ) 1.19 km , e ) 1.99 km
Rationale: "d = product of speed difference of time / difference of speed d = 3 x 6 / 60 [ 12 â ˆ ’ ( â ˆ ’ 10 ) / 6 - 3 ] [ here , â € “ ve sign indicates before the schedule time ] â ‡ ’ d = 2.19 km answer a"
Answer: a
Python program:
a = 3 * 6
b = 6 - 3
c = a / b
d = 12 + 10 
e = d / const_60
f = c * e
Problem: g ( x ) is defined as the product of all even integers k such that 0 < k ≤ x . for example , g ( 14 ) = 2 × 4 × 6 × 8 × 10 × 12 × 14 . if g ( e ) is divisible by 4 ^ 11 , what is the smallest possible value for e ?
Options: a ) 22 , b ) 24 , c ) 28 , d ) 32 , e ) 44
Rationale: "g ( e ) = 4 ^ 11 = 2 ^ 22 . so we have to find a product with atleast 22 2 ' s in it . in option 1 22 the total no of 2 ' s = [ 22 / 2 ] + [ 22 / 4 ] + [ 22 / 8 ] + [ 22 / 16 ] = 11 + 5 + 2 + 1 = 19 in option 2 24 the total no of 2 ' s = [ 24 / 2 ] + [ 24 / 4 ] + [ 24 / 8 ] + [ 24 / 16 ] = 12 + 6 + 3 + 1 = 22 . hence b"
Answer: b
Python program:
a = 2 * 12
Problem: the ratio of boarders to day students at a school was originally 5 to 12 . however , after a number of new boarders join the initial 220 boarders , the ratio changed to 1 to 2 . if no boarders became day students and vice versa , and no students left the school , how many new boarders joined the school ?
Options: a ) 44 , b ) 64 , c ) 70 , d ) 80 , e ) 84
Rationale: "let x be the number of new boarders . the ratio changed from 5 : 12 up to 1 : 2 = 6 : 12 . 220 / ( 220 + x ) = 5 / 6 x = 44 the answer is a ."
Answer: a
Python program:
a = 220 / 5
b = a * 12
c = b / 2
d = c - 220
Problem: recipe requires 15 mins to cook . you have 7 mins hourglass and a 11 mins hourglass with you . how will you measure 15 mins using them ?
Options: a ) 15 mins , b ) 12 mins , c ) 13 mins , d ) 17 mins , e ) 20 mins
Rationale: correct answer : a put up both hour glasses . time starts when 7 min hourglass turns empty . and 11 min hourglass will run for 4 min . now flip 11 min hour glass upside down as soon as it runs empty . it will be empty in another 11 mins . and time is up . so 4 + 11 = 15 mins
Answer: a
Python program:
a = 11 - 7
b = 11 + a
Problem: what will be the result of 7 ^ 8 - 6 / 2 + 9 ^ 3 + 3 + 12 ?
Options: a ) 95 , b ) 64 , c ) 1012 , d ) 9 , e ) 0
Rationale: the multiplication ( e . g . 7 ^ 8 ) and division ( e . g . 6 / 2 ) is done first and then the sum ( e . g . 3 + 12 ) and subtraction ( e . g . 56 - 3 ) , and the answer is 95 , option a .
Answer: a
Python program:
a = 7 * 8
b = a - 6
c = b / 2
d = c + 9 
e = d * 3
f = e - 7
Problem: erik ' s mother gave him $ 86 to go to the store . erik bought 3 loaves of bread and 3 cartons of orange juice . each loaf of bread cost $ 3 and each carton of orange juice cost $ 6 . how much money does erik have left ?
Options: a ) $ 24 , b ) $ 27 , c ) $ 59 , d ) $ 75 , e ) $ 35
Rationale: step 1 : find the cost of the loaves of bread . 3 × $ 3 = $ 9 step 2 : find the cost of the orange juice . 3 × $ 6 = $ 18 step 3 : find the total cost of the groceries . $ 9 + $ 18 = $ 27 step 4 : find the amount of money left . $ 86 – $ 27 = $ 59 erik has $ 59 left . answer is c .
Answer: c
Python program:
a = 3 * 3
b = 3 * 6
c = a + b 
d = 86 - c
Problem: the value of a machine depreciates at 22 % per annum . if its present value is $ 1 , 50,000 , at what price should it be sold after two years such that a profit of $ 24,000 is made ?
Options: a ) $ 255260 , b ) $ 435260 , c ) $ 125260 , d ) $ 115260 , e ) $ 155260
Rationale: "the value of the machine after two years = 0.78 * 0.78 * 1 , 50,000 = $ 91,260 sp such that a profit of $ 24,000 is made = 91,260 + 24,000 = $ 1 , 15,260 d"
Answer: d
Python program:
a = 22 / 100
b = 1 - a
c = 22 / 100
d = 1 - c
e = b * d
f = 100 * 100
g = math.sqrt(100)
h = f * g
i = math.sqrt(100)
j = i / 2
k = j * 100
l = k * 100
m = h + l 
n = e * m
o = 22 + 2 
p = o * 100
q = math.sqrt(100)
r = p * q
s = n + r
Problem: a team won 50 percent of its first 60 games in a particular season , and 80 percent of its remaining games . if the team won a total of 65 percent of its games that season , what was the total number of games that the team played ?
Options: a ) 180 , b ) 120 , c ) 90 , d ) 85 , e ) 70
Rationale: "65 % is 15 % - points above 50 % and 15 % - points below 80 % . thus the ratio of ` ` the first 60 games ' ' to ` ` remaining games ' ' is 1 : 1 . so the team played a total of 60 + 60 = 120 games . the answer is b ."
Answer: b
Python program:
a = 50 / 100
b = 60 * a
c = 80 / 100
d = 65 / 100
e = c - d
f = b / e
Problem: in a class of 210 students , 70 did not opt for math . 55 did not opt for science and 42 did not opt for either . how many students of the class opted for both math and science ?
Options: a ) 123 , b ) 125 , c ) 127 , d ) 137 , e ) 148
Rationale: "210 students total 70 did not opt for math 55 did not opt for science 42 did not opt for either total of 140 students in math and 13 did not opt for sci but did for math 140 - 13 = 127 127 students of the class opted for both math and science answer : c"
Answer: c
Python program:
a = 210 - 70
b = 210 - 55
c = b - 42
d = a - c
Problem: 1 ltr of water is added with 3 ltr of a solution containing 33 % of alcohol in the water . the % of alcohol in the new mixture is ?
Options: a ) 22 % , b ) 23 % , c ) 24.5 % , d ) 24.75 % , e ) 30 %
Rationale: "we have a 3 litre solution containing 33 % of alcohol in the water . = > quantity of alcohol in the solution = 3 ã — 33 / 100 now 1 litre of water is added to the solution . = > total quantity of the new solution = 3 + 1 = 4 percentage of alcohol in the new solution = 3 ã — 33 / 100 4 ã — 100 = 3 ã — 331004 ã — 100 = 3 ã — 8.25 / 100 = 24.75 % d"
Answer: d
Python program:
a = 33 / 100
b = a * 3
c = 1 + 3 
d = b / c
e = 100 * d
Problem: 12 welders work at a constant rate they complete an order in 8 days . if after the first day , 9 welders start to work on the other project , how many more days the remaining welders will need to complete the rest of the order ?
Options: a ) 5 , b ) 12 , c ) 18 , d ) 24 , e ) 28
Rationale: "1 . we need to find out the time taken by 3 workers after day 1 . 2 . total no . of wokers * total time taken = time taken by 1 worker 3 . time taken by 1 worker = 12 * 8 = 96 days 4 . but on day 1 twelve workers had already worked finishing 1 / 8 of the job . so 3 workers have to finish only 7 / 8 of the job . 5 . total time taken by 3 workers can be got from formula used at ( 2 ) . i . e . , 3 * total time taken = 96 . total time taken by 3 workers to finish the complete job is 96 / 3 = 32 days . 6 . time taken by 6 workers to finish 7 / 8 of the job is 7 / 8 * 32 = 28 days . the answer is choice e"
Answer: e
Python program:
a = 12 * 8
b = 1 / a
c = b * 12
d = 1 - c
e = 12 - 9
f = d / e
g = 12 * 8
h = 1 / g
i = f / h
Problem: a ’ s speed is 20 / 15 times that of b . if a and b run a race , what part of the length of the race should a give b as a head start , so that the race ends in a dead heat ?
Options: a ) 1 / 17 , b ) 3 / 17 , c ) 1 / 10 , d ) 5 / 20 , e ) 3 / 10
Rationale: "we have the ratio of a ’ s speed and b ’ s speed . this means , we know how much distance a covers compared with b in the same time . this is what the beginning of the race will look like : ( start ) a _________ b ______________________________ if a covers 20 meters , b covers 15 meters in that time . so if the race is 20 meters long , when a reaches the finish line , b would be 5 meters behind him . if we want the race to end in a dead heat , we want b to be at the finish line too at the same time . this means b should get a head start of 5 meters so that he doesn ’ t need to cover that . in that case , the time required by a ( to cover 20 meters ) would be the same as the time required by b ( to cover 15 meters ) to reach the finish line . so b should get a head start of 5 / 20 th of the race . answer ( d )"
Answer: d
Python program:
a = 20 - 15
b = a / 20
Problem: the sum of the even numbers between 1 and n is 81 * 82 , where n is an odd number , then n = ?
Options: a ) 163 , b ) 171 , c ) 177 , d ) 185 , e ) 193
Rationale: "let n - 1 = 2 a . 2 + 4 + . . . + 2 a = 2 * ( 1 + 2 + . . . + a ) = 2 * ( a ) ( a + 1 ) / 2 = ( a ) ( a + 1 ) = 81 * 82 then a = 81 and n = 163 . the answer is a ."
Answer: a
Python program:
a = 81 * 2
b = a + 1
Problem: saleem bought 4 baskets with the average cost of $ 4 . if saleem also buys the fifth basket with the price of $ 8 , what is the average ( arithmetic mean ) price of those 5 baskets ?
Options: a ) $ 4.50 , b ) $ 6.00 , c ) $ 4.00 , d ) $ 5.50 , e ) $ 4.80
Rationale: 4 baskets - > total cost = 4 * avg cost = 4 * 4 = 16 fifth basket cost = 8 total cost for 5 baskets = 16 + 8 = 24 am = 24 / 5 = 4.80 answer : e
Answer: e
Python program:
a = 4 * 4
b = a + 8 
c = b / 5
Problem: in a covering a distance of 30 km , abhay takes 2 hours more than sameer . if abhay double his speed , then he would take 1 hour less than sammer . abhay ' s speed is ?
Options: a ) 5 km / hr , b ) 1 km / hr , c ) 6 km / hr , d ) 3 km / hr , e ) 7 km / hr
Rationale: a 5 km / hr let abhay ' s speed be x km / / hr . then , 30 / x - 30 / 2 x = 3 x = 5 km / hr .
Answer: a
Python program:
a = 2 * 3
b = 30 / a
Problem: from a pack of 52 cards , 1 card is drawn at random . what is the probability that a jack , queen , or king is drawn ?
Options: a ) 1 / 4 , b ) 1 / 12 , c ) 2 / 13 , d ) 3 / 13 , e ) 3 / 26
Rationale: the total number of cards is 52 . the number of jacks , queens , or kings is 12 . p ( jack , queen , king ) = 12 / 52 = 3 / 13 the answer is d .
Answer: d
Python program:
a = 4 * 3
b = a / 52
Problem: a sum was put at simple interest at a certain rate for 9 years had it been put at 5 % higher rate , it would have fetched 1350 more . find the sum .
Options: a ) 3000 , b ) 3100 , c ) 3200 , d ) 3300 , e ) 3400
Rationale: "difference in s . i . = p × t / 100 ( r 1 − r 2 ) ⇒ 1350 = p × 9 x 5 / 100 ( ∵ r 1 - r 2 = 2 ) ⇒ p = 1350 × 100 / 9 x 5 = 3000 answer a"
Answer: a
Python program:
a = 5 / 100
b = a * 9
c = 1350 / b
Problem: three table runners have a combined area of 224 square inches . by overlapping the runners to cover 80 % of a table of area 175 square inches , the area that is covered by exactly two layers of runner is 24 square inches . what is the area of the table that is covered with three layers of runner ?
Options: a ) 18 square inches , b ) 20 square inches , c ) 24 square inches , d ) 28 square inches , e ) 30 square inches
Rationale: "total = a + b + c - ( sum of exactly 2 - group overlaps ) - 2 * ( all three ) + neither 80 % * 175 = 224 - 24 - 2 * ( all three ) + 0 2 * ( all three ) = 224 - 24 - 140 all three = 30 answer : e"
Answer: e
Python program:
a = 224 - 24
b = 80 / 100
c = 175 * b
d = a - c
e = d / 2
Problem: this year , mbb consulting fired 9 % 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 ?
Options: a ) 98.5 % , b ) 100.1 % , c ) 102.8 % , d ) 104.5 % , e ) 105.0 %
Rationale: 100 employees getting 1000 $ avg , so total salary for 100 ppl = 100000 9 % reduction in employees lead to 91 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 91 employees is 91 * 1100 = 100100 now the new salary is more than previous salary by x % . x = ( 100100 / 100000 ) * 100 = 100.1 % so the answer is b
Answer: b
Python program:
a = 100 * 10
b = 100 + a 
c = 100 - 9
d = c + 4 
e = b * d
f = 100 * 10
g = e / f
Problem: the sum of two consecutive integers is 21 . find the numbers .
Options: a ) 17 , 18 , b ) 7 , 8 , c ) 10 , 11 , d ) 1 , 2 , e ) 8 , 9
Rationale: "n + ( n + 1 ) = 21 2 n + 1 = 21 2 n = 20 n = 10 answer : c"
Answer: c
Python program:
a = 21 - 10
b = a - 2
c = b / 4
d = c + 2 
e = d + 2 
f = e ** 2
g = 21 - 10
h = g - 2
i = h / 4
j = i + 2 
k = j + 2 
l = k + 2 
m = l ** 2
n = f + m 
o = 21 - 10
p = o - 2
q = p / 4
r = q ** 2
s = 21 - 10
t = s - 2
u = t / 4
v = u + 2 
w = v ** 2
x = r + w 
y = n + x
Problem: one pipe can fill a tank three times as fast as another pipe . if together the two pipes can fill the tank in 35 minutes , then the slower pipe alone will be able to fill the tank in
Options: a ) 144 mins , b ) 140 mins , c ) 136 mins , d ) 132 minw , e ) none of these
Rationale: "explanation : let the slower pipe alone fill the tank in x minutes then faster will fill in x / 3 minutes . part filled by slower pipe in 1 minute = 1 / x part filled by faster pipe in 1 minute = 3 / x part filled by both in 1 minute = 1 / x + 3 / x = 1 / 35 = > 4 / x = 1 / 35 x = 35 ∗ 4 = 140 mins option b"
Answer: b
Python program:
a = 1 + 4 
b = a * 35
Problem: if k is a non - negative integer and 15 ^ k is a divisor of 823,435 then 5 ^ k - k ^ 5 =
Options: a ) 0 , b ) 1 , c ) 35 , d ) 120 , e ) 245
Rationale: "8 + 2 + 3 + 4 + 3 + 5 = 25 , so this number is not divisible by 3 and thus not divisible by 15 . therefore , k = 0 5 ^ k - k ^ 5 = 1 - 0 = 1 the answer is b ."
Answer: b
Python program:
a = 1 - 1
b = 5 ** a
c = 1 - 1
d = c ** 5
e = b - d
Problem: p alone can complete a job in 5 days . the work done by q alone in one day is equal to one - fourth of the work done by p alone in one day . in how many days can the work be completed if p and q work together ?
Options: a ) 2.5 , b ) 3.0 , c ) 3.5 , d ) 4.0 , e ) 4.5
Rationale: "p ' s rate is 1 / 5 q ' s rate is 1 / 20 the combined rate is 1 / 5 + 1 / 20 = 1 / 4 if they work together , the job will take 4 days . the answer is d ."
Answer: d
Python program:
a = 1 / 5
b = 1 / 5
c = b / 3
d = a + c 
e = 1 / d
Problem: what must be added to each of the numbers 7 , 11 and 19 , so that the resulting numbers may be in continued proportion ?
Options: a ) 3 , b ) 5 , c ) 4 , d ) - 3 , e ) - 2
Rationale: let x be the required number , then ( 7 + x ) : ( 11 + x ) : : ( 11 + x ) : ( 19 + x ) ( 7 + x ) ( 19 + x ) = ( 11 + x ) 2 x 2 + 26 x + 133 = x 2 + 22 x + 121 4 x = - 12 or x = - 3 answer : d
Answer: d
Python program:
a = 11 ** 2
Problem: find the number , difference between number and its 3 / 5 is 64 .
Options: a ) 160 , b ) 163 , c ) 164 , d ) 165 , e ) 166
Rationale: explanation : let the number = x , then , x - ( 3 / 5 ) x = 64 , = > ( 2 / 5 ) x = 64 = > 2 x = 64 * 5 , = > x = 160 answer : option a
Answer: a
Python program:
a = 64 / 2
b = a * 5
Problem: convert the 8 / 36 m / s into kilometers per hour ?
Options: a ) 0.8 kmph , b ) 9.9 kmph , c ) 1.3 kmph , d ) 1.2 kmph , e ) 5.7 kmph
Rationale: "8 / 36 m / s = 8 / 36 * 18 / 5 = 8 / 10 = 0.8 kmph . answer : a"
Answer: a
Python program:
a = 8 / 36
b = const_3_6 * a
Problem: the mean proportional between 234 and 104 is :
Options: a ) 12 , b ) 39 , c ) 54 , d ) 64 , e ) 156
Rationale: required mean proportion is = ( root of 234 ) ( root of 104 ) = root of ( 13 * 9 * 2 * 13 * 18 ) = ( 13 * 3 * 4 ) = 156 answer : e
Answer: e
Python program:
a = 234 * 104
b = math.sqrt(a)