euclaise/mathqa_programs huggingface dataset:
Problem: if 36 men do a work in 70 days , in how many days will 40 men do it ?
Options: a ) 64 , b ) 63 , c ) 65 , d ) 66 , e ) 67
Rationale: "36 * 70 = 40 * x x = 63 days answer : b"
Answer: b
Python program:
a = 36 * 70
b = a / 40
Problem: last year , for every 100 million vehicles that traveled on a certain highway , 75 vehicles were involved in accidents . if 6 billion vehicles traveled on the highway last year , how many of those vehicles were involved in accidents ? ( 1 billion = 1,000 , 000,000 )
Options: a ) 2500 , b ) 4500 , c ) 3500 , d ) 4000 , e ) 1300
Rationale: "to solve we will set up a proportion . we know that “ 100 million vehicles is to 75 accidents as 6 billion vehicles is to x accidents ” . to express everything in terms of “ millions ” , we can use 6,000 million rather than 6 billion . creating a proportion we have : 100 / 75 = 6,000 / x cross multiplying gives us : 100 x = 6,000 * 75 x = 60 * 75 = 4500 answer : b"
Answer: b
Python program:
a = 6 * 10
b = 75 * a
Problem: on a certain road , 10 % of the motorists exceed the posted speed limit and receive speeding tickets , but 60 % of the motorists who exceed the posted speed limit do not receive speeding tickets . what percent of the motorists on that road exceed the posted speed limit ?
Options: a ) 10.5 % , b ) 12.5 % , c ) 15 % , d ) 25 % , e ) 30 %
Rationale: "suppose there are x motorists . 10 % of them exceeded the speed limit and received the ticket , i . e . x / 10 . again , suppose total no . of motorists who exceeded the speed limit are y . 60 % of y exceeded the speed limit but did n ' t received the ticket , i . e . 3 y / 5 . it means 2 y / 5 received the ticket . hence , 2 y / 5 = x / 10 or y / x = 1 / 4 or y / x * 100 = 1 / 4 * 100 = 25 % d"
Answer: d
Python program:
a = 100 - 60
b = 10 / a
c = b * 100
Problem: a and b can do a piece of work in 48 days , a and c can do it in 60 days , b and c can do it 72 days . in what time can c alone do it ?
Options: a ) 84 days , b ) 84 ½ days , c ) 85 days , d ) 87 days , e ) 89 days
Rationale: explanation : ( a + b ) 1 day work = 1 / 48 ( b + c ) 1 day work = 1 / 72 ( a + c ) 1 day work = 1 / 60 by adding 2 ( a + b + c ) = 1 / 48 + 1 / 72 + 1 / 60 = 37 / 720 ( a + b + c ) 1 day work = 37 / 1440 a 1 day work = 37 / 1440 – 1 / 72 = 17 / 1440 = 85 days ( approximately ) answer : option c
Answer: c
Python program:
a = 72 - 48
b = a + 60
Problem: if x is an integer such that 1 < x < 9 , 2 < x < 15 , 7 > x > – 1 , 4 > x > 0 , and x + 1 < 5 , then x is
Options: a ) 3 , b ) 4 , c ) 5 , d ) 6 , e ) 7
Rationale: "1 < x < 9 , 2 < x < 15 , - 1 < x < 7 0 < x < 4 x + 1 < 5 from above : 2 < x < 4 - - > x = 3 . answer : a ."
Answer: a
Python program:
a = 5 - 1
b = a - 1
Problem: 1 = 1,2 = 2,3 = 9,4 = 16,5 = 25 , then 9 = ?
Options: a ) 1 , b ) 255 , c ) 3 , d ) 445 , e ) 235
Rationale: "1 = 1,2 = 2,3 = 9,4 = 16,5 = 25 , then 9 = ? 9 = 3 check the third eqn . answer : c"
Answer: c
Python program:
a = 4 + 2 
b = 4 + 2 
c = a * b
d = c * 10
e = 25 - d
f = e - 1
g = f / 2
Problem: a train 300 m long can cross an electric pole in 10 sec and then find the speed of the train ?
Options: a ) 88 kmph , b ) 89 kmph , c ) 72 kmph , d ) 16 kmph , e ) 108 kmph
Rationale: "length = speed * time speed = l / t s = 300 / 10 s = 30 m / sec speed = 30 * 18 / 5 ( to convert m / sec in to kmph multiply by 18 / 5 ) speed = 108 kmph answer : e"
Answer: e
Python program:
a = 300 / 1000
b = 10 / 3600
c = a / b
Problem: if a book is sold at 10 % profit instead of 10 % loss , it would have brought rs 14 more . find out the cost price of the book
Options: a ) 75 , b ) 72 , c ) 60 , d ) 70 , e ) 80
Rationale: "let c . p . of the book be rs . ’ x ’ given , 1.10 x - 0.90 x = 14 = > 0.2 x = 14 = 14 / 0.2 = rs 70 answer : d"
Answer: d
Python program:
a = 10 / 2
b = 100 * a
c = b / 10
Problem: in the number 11,0 ab , a and b represent the tens and units digits , respectively . if 11,0 ab is divisible by 55 , what is the greatest possible value of b × a ?
Options: a ) 0 , b ) 5 , c ) 10 , d ) 15 , e ) 25
Rationale: "you should notice that 55 * 2 = 110 so 11,000 is divisible by 55 : 55 * 200 = 11,000 ( or you can notice that 11,000 is obviously divisible by both 5 and 11 so by 55 ) - - > b * a = 0 * 0 = 0 . next number divisible by 55 is 11,000 + 55 = 11,055 : b * a = 5 * 5 = 25 ( next number wo n ' t have 110 as the first 3 digits so we have only two options 0 and 25 ) . answer : e"
Answer: e
Python program:
a = 11 ** 0
b = a + 1000 
c = b / 55
d = c + 1 
e = d * 55
f = reminder * (
g = f - 10
Problem: how many liters of water must be evaporated from 50 liters of a 3 percent sugar solution to get a 4 percent sugar solution ?
Options: a ) 12.5 , b ) 15.5 , c ) 17.5 , d ) 21.5 , e ) 24.5
Rationale: "let x be the amount that needs to be evaporated . 0.03 ( 50 ) = 0.04 ( 50 - x ) 0.04 x = 2 - 1.5 x = 0.5 / 0.04 = 12.5 liters the answer is a ."
Answer: a
Python program:
a = 50 / 100
b = a * 4
c = 50 - b
Problem: the average of marks obtained by 120 candidates was 35 . if the avg of marks of passed candidates was 39 & that of failed candidates was 39 and that of failed candidates was 15 , the no . of candidateswho passed the examination is ?
Options: a ) 50 , b ) 90 , c ) 100 , d ) 120 , e ) 140
Rationale: "let the number of candidate who passed = y then , 39 y + 15 ( 120 - y ) = 120 x 35 ⇒ 24 y = 4200 - 1800 ∴ y = 2400 / 24 = 100 c"
Answer: c
Python program:
a = 120 * 35
b = 120 * 15
c = a - b
d = 39 - 15
e = c / d
Problem: a squirrel runs up a cylindrical post , in a perfect spiral path making one circuit for each rise of 4 feet . how many feet does the squirrel travels if the post is 16 feet tall and 2 feet in circumference ?
Options: a ) 10 feet , b ) 8 feet , c ) 13 feet , d ) 15 feet , e ) 18 feet
Rationale: "total circuit = 16 / 4 = 4 total feet squirrel travels = 4 * 2 = 8 feet answer : b"
Answer: b
Python program:
a = 16 / 4
b = a * 2
Problem: if ( t - 8 ) is a factor of t ^ 2 - kt - 46 , then k =
Options: a ) 16 , b ) 12 , c ) 2 , d ) 6 , e ) 14
Rationale: "t ^ 2 - kt - 48 = ( t - 8 ) ( t + m ) where m is any positive integer . if 48 / 8 = 6 , then we know as a matter of fact that : m = + 6 and thus k = 8 - 6 = 14 t ^ 2 - kt - m = ( t - a ) ( t + m ) where a > m t ^ 2 + kt - m = ( t - a ) ( t + m ) where a < m t ^ 2 - kt + m = ( t - a ) ( t - m ) e"
Answer: e
Python program:
a = 10 + 2
Problem: what will be the cost of building a fence around a rectangular plot with area equal to 289 sq ft , if the price per foot of building the fence is rs . 50 ?
Options: a ) a ) rs . 3944
b ) b ) rs . 3948
c ) c ) rs . 3519.5
d ) d ) rs . 3949
e ) e ) rs . 3923
Rationale: let the side of the rectangle plot be a ft . a * b = 289 = > 1.7 b * b = 289 b = 13.03 a = 22.17 length of the fence = perimeter of the plot = 2 ( a + b ) = 70.39 ft . cost of building the fence = 70.39 * 50 = rs . 3519.5 answer : c
Answer: c
Python program:
a = math.sqrt(289)
b = square_perimeter * (
Problem: how many liters of water must be evaporated from 50 liters of a 8 - percent sugar solution to get a 10 - percent solution ?
Options: a ) 8 , b ) 10 , c ) 12 , d ) 14 , e ) 16
Rationale: "8 % of a 50 liter solution is 4 l which is 10 % of the solution at the end . the solution at the end must be 40 l . we need to evaporate 10 liters . the answer is b ."
Answer: b
Python program:
a = 50 / 100
b = a * 10
c = 50 - b
Problem: . in a certain city , 60 percent of the registered voters are democrats and the rest are republicans . in a mayoral race , if 70 percent of the registered voters who are democrats and 20 percent of the registered voters who are republicans are expected to vote for candidate a , what percent of the registered voters are expected to vote for candidate a ?
Options: a ) 50 % , b ) 53 % , c ) 54 % , d ) 55 % , e ) 57 %
Rationale: registered voters = 100 d = 60 r = 40 70 % of d ( 60 ) = 42 20 % of r ( 40 ) = 8 total voter % of registered voters = 50 / 100 50 % ans a
Answer: a
Python program:
a = 70 / 100
b = 60 * a
c = 100 - 60
d = 20 / 100
e = c * d
f = b + e
Problem: a box contains 12 apples , 11 of which are red . an apple is drawn from the box and its color is noted before it is eaten . this is done a total of n times , and the probability that a red apple is drawn each time is less than 0.5 . what is the smallest possible value of n ?
Options: a ) 3 , b ) 4 , c ) 5 , d ) 6 , e ) 7
Rationale: "p ( choosing a red apple 7 times in a row ) = 11 / 12 * 10 / 11 * 9 / 10 * 8 / 9 * 7 / 8 * 6 / 7 * 5 / 6 = 5 / 12 < 0.5 the answer is e ."
Answer: e
Python program:
a = 0 * 5
b = a + 1
Problem: a train 110 meters long completely crosses a 280 meters long bridge in 38 seconds . what is the speed of the train is ?
Options: a ) 32 , b ) 45 , c ) 40 , d ) 66 , e ) 09
Rationale: "s = ( 110 + 280 / 38 = 390 / 38 * 18 / 5 = 40 answer : c"
Answer: c
Python program:
a = 110 + 280 
b = a / 1000
c = 38 / 3600
d = b / c
Problem: in a market , a dozen eggs cost as much as a pound of rice , and a half - liter of kerosene costs as much as 8 eggs . if the cost of each pound of rice is $ 0.33 , then how many f cents does a liter of kerosene cost ? [ one dollar has 100 cents . ]
Options: a ) 0.33 , b ) 0.44 , c ) 0.55 , d ) 44 , e ) 55
Rationale: "main thing to remember is answer is asked in cents , however when we calculate , it comes up as 0.44 $ just multiply by 100 , answer f = 44 . d"
Answer: d
Python program:
a = 1 / 2
b = 8 / a
c = b / 12
d = 0 * 33
e = c * d
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 ) 30 % , b ) 35 % , c ) 40 % , d ) 45 % , e ) 50 %
Rationale: "let the original income = rs . 100 . then , expenditure = rs . 75 and savings = rs . 25 new income = rs . 120 , new expenditure = rs . ( ( 110 / 100 ) * 75 ) = rs . 165 / 2 new savings = rs . ( 120 - ( 165 / 2 ) ) = rs . 75 / 2 increase in savings = rs . ( ( 75 / 2 ) - 25 ) = rs . 25 / 2 increase % = ( ( 25 / 2 ) * ( 1 / 25 ) * 100 ) % = 50 % . answer e 50 %"
Answer: e
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: in a college , the ratio of the number of boys to girls is 8 : 5 . if there are 160 girls , the total number of students in the college is
Options: a ) 2447 , b ) 377 , c ) 667 , d ) 416 , e ) 871
Rationale: "explanation : let the number of boys and girls be 8 x and 5 x . total number of students = 13 x = 13 * 32 = 416 . answer : d"
Answer: d
Python program:
a = 160 / 5
b = a * 8
c = 160 + b
Problem: the average weight of 5 students decreases by 12 kg when one of them weighing 72 kg is replaced by a new student . the weight of the student is
Options: a ) 12 kg , b ) 10 kg , c ) 20 kg , d ) 72 kg , e ) none of these
Rationale: "explanation : let the weight of student be x kg . given , difference in average weight = 12 kg = > ( 72 - x ) / 5 = 12 = > x = 12 answer : a"
Answer: a
Python program:
a = 5 * 12
b = 72 - a
Problem: find the least multiple of 23 , which when divided by 1821 and 24 leaves remainders 710 and 13 respectively .
Options: a ) 3002 , b ) 3013 , c ) 3024 , d ) 3036 , e ) none of these
Rationale: solution here ( 18 - 7 ) = 11 , ( 21 - 10 ) = 11 and ( 24 - 13 ) = 11 . l . c . m . of 1821 and 24 is 504 . let required number be 504 k - 11 . least value of k for which ( 504 k - 11 ) is divisible 23 is k = 6 . so , required number = 504 × 6 - 11 = 3024 - 11 = 3013 . answer b
Answer: b
Python program:
a = 24 * 10
b = 24 * 10
c = a + b 
d = 4 + 4 
e = d * 3
f = c + e 
g = 13 - 10
h = g + 3 
i = f * h
Problem: a boy is travelling from his home to school at 5 km / hr and reached 7 min late . next day he traveled at 10 km / hr and reached 8 min early . distance between home and school ?
Options: a ) 2.5 km , b ) 3.5 km , c ) 4.5 km , d ) 5.5 km , e ) 6.5 km
Rationale: let the distance be x t 1 = x / 5 hr t 2 = x / 10 hr difference in time = 7 + 8 = 15 = 1 / 4 hr x / 5 - x / 10 = 1 / 4 x / 10 = 1 / 4 x = 2.5 km answer is a
Answer: a
Python program:
a = 7 / const_60
b = 8 / const_60
c = a + b 
d = 1 / 10
e = c / d
Problem: how many of the positive factors of 16 are not factors of 20
Options: a ) 2 , b ) 3 , c ) 4 , d ) 1 , e ) 5
Rationale: "factors of 16 - 1 , 2 , 4 , 8 , 16 factors of 20 - 1 , 2 , 4 , 5 , 10 , 20 . comparing both , we have 2 factors of 16 which are not factors of 20 - 8,16 answer : a"
Answer: a
Python program:
a = 20 / 16
Problem: an investor deposited $ 10,000 to open a new savings account that earned 8 percent annual interest , compounded quarterly . if there were no other transactions in the account , what was the amount of money in the account 6 months after the account was opened ?
Options: a ) $ 10,200 , b ) $ 10,202 , c ) $ 10,400 , d ) $ 10,404 , e ) $ 10,800
Rationale: "the amount in the account after 6 months is 1.02 * 1.02 ( $ 10,000 ) = $ 10,404 . the answer is d ."
Answer: d
Python program:
a = 2 + 3 
b = a * 100
c = 2 + 3 
d = c * 2
e = b * d
f = 8 / 8
g = f / 100
h = g + 1 
i = h ** 2
j = e * i
Problem: a pipe can fill a cistern in 77 minutes . find the time in which 1 / 11 part of the cistern will be filled ?
Options: a ) 5 min , b ) 2 min , c ) 3 min , d ) 1 min , e ) 7 min
Rationale: "full cistern filled in = 77 minutes 1 / 11 part filled in = 77 * 1 / 11 = 7 minutes answer is e"
Answer: e
Python program:
a = 1 / 11
b = 77 * a
Problem: a can do a job in 10 days and b in 20 days . if they work on it together for 4 days , then the fraction of the work that is left is ?
Options: a ) 2 / 5 , b ) 8 / 15 , c ) 3 / 11 , d ) 1 / 12 , e ) 6 / 13
Rationale: "a ' s 1 day work = 1 / 10 b ' s 1 day work = 1 / 20 a + b 1 day work = 1 / 10 + 1 / 20 = 3 / 20 a + b 4 days work = 3 / 20 * 4 = 3 / 5 remaining work = 1 - 3 / 5 = 2 / 5 answer is a"
Answer: a
Python program:
a = 1 / 10
b = 1 / 20
c = a + b 
d = 4 * c
e = 1 - d
Problem: a trader sells 20 meters of cloth for rs . 4500 at the profit of rs . 10 per metre of cloth . what is the cost price of one metre of cloth ?
Options: a ) rs . 380 , b ) rs . 215 , c ) rs . 190 , d ) rs . 395 , e ) none of these
Rationale: "sp of 1 m of cloth = 4500 / 20 = rs . 225 cp of 1 m of cloth = sp of 1 m of cloth - profit on 1 m of cloth = rs . 225 - rs . 10 = rs . 215 . answer : c"
Answer: c
Python program:
a = 4500 / 20
b = a - 10
Problem: sahil purchased a machine at rs 10000 , then got it repaired at rs 5000 , then gave its transportation charges rs 1000 . then he sold it with 50 % of profit . at what price he actually sold it .
Options: a ) rs . 22000 , b ) rs . 24000 , c ) rs . 26000 , d ) rs . 28000 , e ) none of these
Rationale: "explanation : question seems a bit tricky , but it is very simple . just calculate all cost price , then get 150 % of cp . c . p . = 10000 + 5000 + 1000 = 16000 150 % of 16000 = 150 / 100 * 16000 = 24000 option b"
Answer: b
Python program:
a = 10000 + 5000 
b = a + 1000 
c = 10000 + 5000 
d = c + 1000 
e = d / 100
f = e * 50
g = b + f
Problem: the ages of 2 persons differ by 35 years . if 10 years ago the elder one be 6 times as old as the younger one , find the present age of elder person .
Options: a ) 30 , b ) 48.5 , c ) 52 , d ) 50 , e ) 55
Rationale: "age of the younger person = x age of the elder person = x + 35 6 ( x - 10 ) = x + 35 - 10 x = 15 age of elder person = 15 + 35 = 50 answer is d"
Answer: d
Python program:
a = 2 * 35
b = 35 - 1
c = a / b
d = c + 35 
e = d - 2
Problem: tom reads at an average rate of 30 pages per hour , while jan reads at an average rate of 38 pages per hour . if tom starts reading a novel at 4 : 30 , and jan begins reading an identical copy of the same book at 5 : 18 , at what time will they be reading the same page ?
Options: a ) 7 : 48 , b ) 8 : 18 , c ) 8 : 48 , d ) 9 : 18 , e ) 9 : 48
Rationale: "since tom reads an average of 1 page every 2 minutes , tom will read 24 pages in the first 48 minutes . jan can catch tom at a rate of 8 pages per hour , so it will take 3 hours to catch tom . the answer is b ."
Answer: b
Python program:
a = 5 - 4
b = 18 - 30
c = b / const_60
d = a + c 
e = d * 30
f = 38 - 30
g = e / f
h = 5 + g 
i = h / 18
Problem: for any positive integer n , the sum of the first n positive integers equals n ( n + 1 ) / 2 . what is the sum of all the integers between 1 and 50 ?
Options: a ) 1275 , b ) 1542 , c ) 985 , d ) 1024 , e ) 1125
Rationale: "sum = 50 * 51 / 2 = 25 * 51 = 1275 answer is a"
Answer: a
Python program:
a = 50 - 1
b = 1 + 1 
c = a - b
d = c / 2
e = d + 1
Problem: simplify : 896 x 896 - 204 x 204
Options: a ) 761200 , b ) 761400 , c ) 761800 , d ) 761500 , e ) none of them
Rationale: "( 896 ) ^ 2 - ( 204 ) ^ 2 = ( 896 + 204 ) ( 896 - 204 ) = 1100 x 692 = 761200 . answer is a ."
Answer: a
Python program:
a = 896 * 896
b = 204 * 204
c = a + b
Problem: a searchlight on top of the watch - tower makes 2 revolutions per minute . what is the probability that a man appearing near the tower will stay in the dark for at least 5 seconds ?
Options: a ) 1 / 4 , b ) 1 / 3 , c ) 1 / 2 , d ) 2 / 3 , e ) 5 / 6
Rationale: 2 revolutions per minute = 1 revolution every 30 seconds so no matter what anybody appearing at the tower can not stay in the dark for more than 30 seconds . this will be our total number of possibilities i . e the denominator . p ( man in dark for at least 5 seconds ) = 1 - p ( man in dark for max of 5 seconds ) = 1 - 5 / 30 = 1 - 1 / 6 = 5 / 6 or the other way would be : p ( man in dark for at least 5 seconds ) is like saying he can be in dark for 5 , 6,7 . . . all the way to 30 seconds because that is the max . in this approach it would be 25 / 30 seconds = 5 / 6 . answer is e
Answer: e
Python program:
a = const_60 * 1
b = a / 2
c = 5 / b
d = 1 - c
Problem: { - 10 , - 6 , - 5 , - 4 , - 2.5 , - 1 , 0 , 2.5 , 4 , 6 , 7 , 10 } a number is to be selected at random from the set above . what is the probability that the number selected will be a solution of the equation ( x - 5 ) ( x + 10 ) ( 2 x - 5 ) = 0 ?
Options: a ) 1 / 12 , b ) 1 / 6 , c ) 1 / 4 , d ) 1 / 3 , e ) 1 / 2
Rationale: roots of the equation ( x - 5 ) ( x + 10 ) ( 2 x - 5 ) = 0 are x = 5 , x = - 10 and x = 5 / 2 = 2.5 . so , two solutions present in our set of 12 distinct numbers , therefore p = 2 / 12 = 1 / 6 . answer : b .
Answer: b
Python program:
a = 6 * 2
b = 2 / a
Problem: a bag contains 10 red jellybeans and 10 blue jellybeans . if 3 jellybeans are removed one at a time , at random and are not replaced , what is the probability y that all 3 jellybeans removed from the bag are blue ?
Options: a ) 9 / 100 , b ) 2 / 19 , c ) 1 / 8 , d ) 3 / 20 , e ) 3 / 10
Rationale: "method - 1 10 red jellybeans and 10 blue jellybeans total outcomes = no . of ways to choose 3 jelly bean at random out of a total 20 jellybeans = 20 c 3 = 1140 favourable outcomes = no . of ways to choose 3 jelly bean such that they are all blue out of 10 blue = 10 c 3 = 120 probability = favourable outcomes / total outcomes = 10 c 3 / 20 c 3 probability y = 120 / 1140 = 2 / 19 answer : option b method - 2 probability of first jelly bean to be blue = 10 / 20 [ total 10 blue out of total 20 jellybeans ] probability of second jelly bean to be blue = 9 / 19 [ total 9 blue remaining out of total 19 jellybeans remaining ] probability of third jelly bean to be blue = 8 / 18 [ total 8 blue remaining out of total 18 jellybeans remaining ] required probability = ( 10 / 20 ) * ( 9 / 19 ) * ( 8 / 18 ) = 2 / 19 answer : option b"
Answer: b
Python program:
a = math.comb(10, 3)
b = 10 + 10 
c = math.comb(b, 3)
d = a / c
Problem: how many positive factors of 42 are not factors of 56 ?
Options: a ) 1 , b ) 2 , c ) 3 , d ) 4 , e ) 5
Rationale: "42 = 2 * 3 * 7 . so , total number of factors for 42 = 2 * 2 * 2 = 8 factors for 42 = 1 , 2,3 , 6,7 , 14,21 and 42 56 = 2 * 2 * 2 * 7 so , total number of factors for 56 = 4 * 2 = 8 factors of 56 = 1 , 2,4 , 7,8 , 14,28 and 56 . factors same in 42 and 56 are 1 , 2,7 and 14 . hence , answer will be d ."
Answer: d
Python program:
a = 56 - 10
b = a / 10
Problem: when processing flower - nectar into honey bees ' extract , a considerable amount of water gets reduced . how much flower - nectar must be processed to yield 1 kg of honey , if nectar contains 50 % water , and the honey obtained from this nectar contains 40 % water ?
Options: a ) 1.2 kg , b ) 1.5 kg , c ) 1.7 kg , d ) 1.9 kg , e ) none of these
Rationale: "explanation : flower - nectar contains 50 % of non - water part . in honey this non - water part constitutes 60 % ( 100 - 40 ) . therefore 0.5 x amount of flower - nectar = 0.60 x amount of honey = 0.60 x 1 kg therefore amount of flower - nectar needed = ( 0.60 / 0.51 ) kg = 1.2 kgs answer : a"
Answer: a
Python program:
a = 100 - 40
b = a / 100
c = 50 / 100
d = b / c
Problem: sale of rs 6835 , rs . 9927 , rs . 6855 , rs . 7230 and rs . 6562 for 5 consecutive months . how much sale must he have in the sixth month so that he gets an average sale of rs , 7000 ?
Options: a ) 4966 , b ) 2477 , c ) 2877 , d ) 7991 , e ) 8881
Rationale: "total sale for 5 months = rs . ( 6435 + 6927 + 6855 + 7230 + 6562 ) = rs . 34009 . required sale = rs . [ ( 6500 x 6 ) - 34009 ] = rs . ( 42000 - 34009 ) = rs . 7991 answer : d"
Answer: d
Python program:
a = 6835 + 9927 
b = a + 6855 
c = b + 7230 
d = c + 6562 
e = d / 5
f = e - 7000
g = f * 5
Problem: the number of sailors on a ship is 50 % more than the number of officers . the ratio of sailors to officers would be
Options: a ) 33 : 25 , b ) 47 : 20 , c ) 3 : 2 , d ) 22 : 25 , e ) 97 : 50
Rationale: "sailor = 1.50 * officer sailor / officer = 1.50 / 1 = 150 / 100 = 3 / 2 answer will be c"
Answer: c
Python program:
a = 50 + 100 
b = a / 100
Problem: in the x - y plane , there are 4 points ( 0,0 ) , ( 0,4 ) , ( 5,4 ) , and ( 5,0 ) . if these 4 points makes a rectangle , what is the probability that x + y < 4 ?
Options: a ) 2 / 3 , b ) 2 / 5 , c ) 3 / 4 , d ) 3 / 7 , e ) 5 / 8
Rationale: the line y = - x + 4 intersects the rectangle and these three points of intersection ( 0,0 ) , ( 0,4 ) and ( 4,0 ) form a triangle . the points below the line y = - x + 4 satisfy x + y < 4 . the area of this triangle is ( 1 / 2 ) ( 4 ) ( 4 ) = 8 the area of the rectangle is 20 . p ( x + y < 4 ) = 8 / 20 = 2 / 5 the answer is b .
Answer: b
Python program:
a = 4 * 4
b = a / 2
c = 1 + 4 
d = 4 * c
e = b / d
Problem: we define that k @ j is the product of j number from k in increasing order for positive integers k , j . for example , 6 @ 4 = 6 * 7 * 8 * 9 . if a = 2020 and b = 2120 , what is the value q of the ratio a / b ?
Options: a ) 1 / 2 , b ) 1 / 3 , c ) 2 / 3 , d ) 1 / 4 , e ) 1 / 5
Rationale: q - > a / b = 20 * 21 * … … * 39 / 21 * 22 * … . * 39 * 40 = 20 / 40 = 1 / 2 . therefore , the answer is a .
Answer: a
Python program:
a = 2020 / 2020
b = 2020 / 2020
c = 2020 / 2020
d = b + c 
e = a / d
Problem: 3 numbers are in the ratio of 2 : 3 : 4 . if the sum of the squares of the extremes is 180 , then the middle number is :
Options: a ) 6 , b ) 12 , c ) 15 , d ) 9 , e ) 7
Rationale: number be = 2 x , 3 x , 4 x , ( 2 x ) 2 + ( 4 x ) 2 = 180 20 x = 180 ⇒ x = 9 ⇒ x = 3 , midline number = 3 × 3 = 9 answer : d
Answer: d
Python program:
a = 2 ** 2
b = 4 ** 2
c = a + b 
d = 180 / c
e = math.sqrt(d)
f = 3 * e
Problem: 20 men do a work in 20 days . how many men are needed to finish the work in 5 days ?
Options: a ) 50 , b ) 20 , c ) 80 , d ) 10 , e ) 15
Rationale: "men required to finish the work in 5 days = 20 * 20 / 5 = 80 answer is c"
Answer: c
Python program:
a = 20 * 20
b = a / 5
Problem: a man can row his boat with the stream at 22 km / h and against the stream in 10 km / h . the man ' s rate is ?
Options: a ) 1 kmph , b ) 6 kmph , c ) 7 kmph , d ) 4 kmph , e ) 9 kmph
Rationale: "explanation : ds = 22 us = 10 s = ? s = ( 22 - 10 ) / 2 = 6 kmph answer : b"
Answer: b
Python program:
a = 22 - 10
b = a / 2
Problem: suganya and suriya are partners in a business . suganya invests rs . 35,000 for 8 months and suriya invests rs . 42,000 for 10 months . out of a profit of rs . 31,570 . suganya ' s share is
Options: a ) rs . 9471 , b ) rs . 12,628 , c ) rs . 18,040 , d ) rs . 18,942 , e ) none
Rationale: "solution ratio of their shares = ( 35000 × 8 ) : ( 42000 × 10 ) = 2 : 3 . suganya ' s share = rs . ( 31570 × 2 / 5 ) = rs . 12628 . answer c"
Answer: c
Python program:
a = const_0_25 * 100
b = a * 10