euclaise/mathqa_programs huggingface dataset:
Problem: sum of two numbers is 10 . two times of the first exceeds by 5 from the three times of the other . then the numbers will be ?
Options: a ) a ) 7 , b ) b ) 9 , c ) c ) 11 , d ) d ) 13 , e ) e ) 15
Rationale: "explanation : x + y = 10 2 x – 3 y = 5 x = 7 y = 3 a )"
Answer: a
Python program:
a = 5 / 2
b = 10 - a
c = b / 2
d = 10 - c
Problem: ram covers a part of the journey at 20 kmph and the balance at 70 kmph taking total of 8 hours to cover the distance of 400 km . how many hours has been driving at 20 kmph ?
Options: a ) 3.2 hr , b ) 3.4 hr , c ) 3.6 hr , d ) 3.8 hr , e ) 4.2 hr
Rationale: let see d / t = v then x / 20 + ( 400 - x ) / 70 = 8 x = 64 kmh t = 64 / 20 = 3.2 hr answer : a
Answer: a
Python program:
a = 8 * 70
b = a - 400
c = 70 - 20
d = b / c
Problem: a shopkeeper sells 10 % of his stock at 20 % profit ans sells the remaining at a loss of 5 % . he incurred an overall loss of rs . 400 . find the total worth of the stock ?
Options: a ) 20000 , b ) 16000 , c ) 18000 , d ) 17000 , e ) 15000
Rationale: "let the total worth of the stock be rs . x . the sp of 20 % of the stock = 1 / 10 * x * 6 / 5 = 6 x / 50 the sp of 80 % of the stock = 9 / 10 * x * 0.95 = 171 x / 200 total sp = 24 x / 200 + 171 / 200 = 49 x / 50 overall loss = x - 195 / 20050 = 5 x / 200 5 x / 200 = 400 = > x = 16000 answer : b"
Answer: b
Python program:
a = 5 / 100
b = 100 - 10
c = b / 100
d = a * c
e = 20 / 100
f = 10 / 100
g = e * f
h = d - g
i = 400 / h
Problem: in one hour , a boat goes 13 km along the stream and 9 km against the stream . the speed of the boat in still water ( in km / hr ) is :
Options: a ) 3 , b ) 5 , c ) 11 , d ) 9 , e ) 10
Rationale: "solution speed in still water = 1 / 2 ( 13 + 9 ) kmph . = 11 kmph . answer c"
Answer: c
Python program:
a = 13 + 9 
b = a / 2
Problem: if 5 spiders make 2 webs in 8 days , then how many days are needed for 1 spider to make 1 web ?
Options: a ) 10 , b ) 15 , c ) 30 , d ) 20 , e ) 16
Rationale: "explanation : let , 1 spider make 1 web in x days . more spiders , less days ( indirect proportion ) more webs , more days ( direct proportion ) hence we can write as ( spiders ) 5 : 1 ( webs ) 1 : 8 } : : x : 2 â ‡ ’ 5 ã — 1 ã — 8 = 1 ã — 2 ã — x â ‡ ’ x = 20 answer : option d"
Answer: d
Python program:
a = 1 * 5
Problem: an employee ’ s annual salary was increased $ 5,000 . if her new annual salary now equals $ 25000 what was the percent increase ?
Options: a ) 15 % , b ) 80 % , c ) 20 % , d ) 22 % , e ) 24 %
Rationale: "new annual salary = $ 25000 salary increase = $ 5000 . original salary = $ 25000 - $ 5,000 . = $ 20,000 % increase = ( $ 15,000 / $ 75,000 ) * 100 = 80 % hence b ."
Answer: b
Python program:
a = 100 - 10
b = a * 1000
c = 100 - 10
d = c * 1000
e = const_0_25 * 100
f = e * 1000
g = d - f
h = b / g
i = h - 1
j = i * 100
Problem: the price of a cycle is reduced by 25 per cent . the new price is reduced by a further 50 per cent . the two reductions together are equal to a single reduction of
Options: a ) 45 % , b ) 62.5 % , c ) 35 % , d ) 32.5 % , e ) 30 %
Rationale: "price = p initially price reduced by 25 % which means new price is 3 / 4 p now on this new price further 50 percent is reduced which means the new price is merely 50 percent of 3 / 4 p = = > ( 3 / 4 ) x ( 1 / 2 ) p = 3 / 8 p is the new price after both deduction which is 37.5 percent of the original value p . this implies this entire series of deduction is worth having discounted 62.5 % of p . so answer is b = 62.5 %"
Answer: b
Python program:
a = 100 - 50
b = a / 100
c = 100 - 25
d = b * c
e = 100 - d
Problem: in a school 10 % of the boys are same in number as 1 / 2 th of the girls . what is the ratio of boys to the girls in the school ?
Options: a ) 5 : 1 , b ) 2 : 3 , c ) 1 : 4 , d ) 3 : 7 , e ) 2 : 5
Rationale: "10 % of b = 1 / 2 g 10 b / 100 = g / 2 b = 5 g / 1 b / g = 5 / 1 b : g = 5 : 1 answer is a"
Answer: a
Python program:
a = 10 / 100
b = 1 / 2
c = a / b
Problem: audrey 4 hours to complete a certain job . ferris can do the same job in 3 hours . audrey and ferris decided to collaborate on the job , working at their respective rates . while audrey worked continuously , ferris took 6 breaks of equal length . if the two completed the job together in 2 hours , how many minutes long was each of ferris ’ breaks ?
Options: a ) 2 , b ) 5 , c ) 15 , d ) 20 , e ) 25
Rationale: audery and ferris collective work rate : 1 / 4 + 1 / 3 = 7 / 12 collective work time = 12 / 7 = 1.7 hrs job was actually done in = 2 ( includes breaks ) breaks = actual time taken - collective work time = 2 - 1.7 = . 3 hrs = 1 / 2 so ferrais took 6 breaks = . 3 / 6 = . 06 hrs = 5 m so answer is b ) 10 mins
Answer: b
Python program:
a = 6 * 10
b = 2 * a
c = 3 / 2
d = 6 * 10
e = c * d
f = b - e
g = f / 6
Problem: by selling an article at rs . 250 , a profit of 25 % is made . find its cost price ?
Options: a ) s . 486 , b ) s . 455 , c ) s . 220 , d ) s . 480 , e ) s . 200
Rationale: "sp = 250 cp = ( sp ) * [ 100 / ( 100 + p ) ] = 250 * [ 100 / ( 100 + 25 ) ] = 250 * [ 100 / 125 ] = rs . 200 answer : e"
Answer: e
Python program:
a = 250 * 100
b = 100 + 25 
c = a / b
Problem: a can do a work in 6 days , b can do a work in 8 days and c can do it in 12 days . b left work after 6 days . for how many number of days should a and c should work together to complete the remaining work ?
Options: a ) 1 , b ) 2 , c ) 3 , d ) 4 , e ) 5
Rationale: "b work 1 / 8 * 6 = 3 / 4 remaining work = 1 - 3 / 4 = 1 / 4 a and c work together = 1 / 6 + 1 / 12 = 3 / 12 = 1 / 4 take reciprocial 4 * remaining work = 4 * 1 / 4 = 1 answer : a"
Answer: a
Python program:
a = 6 / 6
b = 6 / 8
c = a + b
Problem: 4 guys buy same cellphones cost them 250 each . two guy have 25 % of for his first cellphone . what is the total cost all of them pay to seller .
Options: a ) 1000 , b ) 850 , c ) 875 , d ) 775 , e ) 750
Rationale: solution : c . 250 * 2 = 500 for 2 guy without discount , for other 2 ( 250 * 2 ) with 25 % is 375 . total cost 500 + 375 = 875
Answer: c
Python program:
a = 250 * 4
b = a - 100
Problem: if x and y are integers and | x - y | = 11 , what is the minimum possible value of xy ?
Options: a ) - 10 , b ) - 18 , c ) - 28 , d ) - 30 , e ) - 32
Rationale: sometimes the answer choices to a given question provide a big ' hint ' as to how you can go about solving it . this prompt can also be solved without any complex math ideas - you just need to do a bit of ' brute force ' math and you ' ll have the answer relatively quickly . we ' re told that x and y are integers and | x - y | = 11 . we ' re asked for the minimum possible value of ( x ) ( y ) . since all of the answer choices are negative , this tells us that one of the two variables must be negative ( and the other must be positive ) , so we should restrict our work to those options . if . . . x = 10 , y = - 1 , then xy = - 10 x = 9 , y = - 2 , then xy = - 18 x = 8 , y = - 3 , then xy = - 24 x = 7 , y = - 4 , then xy = - 28 x = 6 , y = - 5 , then xy = - 30 x = 5 , y = - 6 , then xy = - 30 x = 4 , y = - 7 , then xy = - 28 from this , we can conclude the xy will start to get bigger as x continues to decrease down to 1 , so there ' s no need to do any additional work . final answer : d
Answer: d
Python program:
a = 2 + 3 
b = negate * (
Problem: 15 : 5 seconds : : ? : 10 minutes
Options: a ) 10 , b ) 15 , c ) 30 , d ) 25 , e ) 30
Rationale: "15 * 10 = 5 * x x = 30 answer : c"
Answer: c
Python program:
a = 15 / 5
b = 10 * a
Problem: a train 75 m long takes 6 sec to cross a man walking at 5 kmph in a direction opposite to that of the train . find the speed of the train ?
Options: a ) 35 kmph , b ) 40 kmph , c ) 45 kmph , d ) 50 kmph , e ) 55 kmph
Rationale: "let the speed of the train be x kmph speed of the train relative to man = x + 5 = ( x + 5 ) * 5 / 18 m / sec 75 / [ ( x + 5 ) * 5 / 18 ] = 6 30 ( x + 5 ) = 1350 x = 40 kmph answer is b"
Answer: b
Python program:
a = 75 / 6
b = a / const_0_2778
c = b - 5
Problem: two trains , each 100 m long , moving in opposite directions , cross other in 5 sec . if one is moving twice as fast the other , then the speed of the faster train is ?
Options: a ) 26 km / hr , b ) 17 km / hr , c ) 60 km / hr , d ) 42 km / hr , e ) 46 km / hr
Rationale: "let the speed of the slower train be x m / sec . then , speed of the train = 2 x m / sec . relative speed = ( x + 2 x ) = 3 x m / sec . ( 100 + 100 ) / 5 = 3 x = > x = 20 / 3 . so , speed of the faster train = 40 / 3 = 40 / 3 * 18 / 5 = 42 km / hr . answer : d"
Answer: d
Python program:
a = 100 + 100 
b = 1 + 2 
c = 5 * b
d = a / c
e = d * 2
f = e * 3600
g = f / 1000
Problem: shreehari has 125 pencils . there are 25 students are studying in his class . he would like to give each student the same amount of pencils , how much should he give to each student ?
Options: a ) 12 , b ) 7 , c ) 5 , d ) 15 , e ) 6
Rationale: 125 / 25 = 5 the answer is c .
Answer: c
Python program:
a = 125 / 25
Problem: what is the value of 3 x ^ 2 − 1.8 x + 0.5 for x = 0.6 ?
Options: a ) − 0.3 , b ) 0 , c ) 0.3 , d ) 1.08 , e ) 0.5
Rationale: "3 x ^ 2 - 1.8 x + 0.5 for x = 0.6 = 3 ( 0.6 * 0.6 ) - 3 * 0.6 * ( 0.6 ) + 0.5 = 0 + 0.5 = 0.5 answer : e"
Answer: e
Python program:
a = 3 ** 2
b = 1 ** 8
c = a - b
d = c / 1000
e = d / 1000
f = e * 3
g = 3 ** 2
h = 1 ** 8
i = g - h
j = i / 1000
k = j / 1000
l = f - k
Problem: the consumption of diesel per hour of a bus varies directly as square of its speed . when the bus is travelling at 60 kmph its consumption is 1 litre per hour . if each litre costs $ 60 and other expenses per hous is $ 60 , then what would be the minimum expenditure required to cover a distance of 600 km ?
Options: a ) 120 , b ) 1250 , c ) 1200 , d ) 1100 , e ) 1150
Rationale: "60 kmph consumption is 1 lt / hr so 600 km will take 10 hrs and the consumption is 10 lt for entire distance . 1 lt costs $ 60 so 10 lt costs $ 600 extra expenses for 1 hr - $ 60 10 hrs - $ 600 total expense - $ 600 + $ 600 = $ 1200 answer : c"
Answer: c
Python program:
a = 600 / 60
b = a * 60
c = 600 / 60
d = c * 60
e = b + d
Problem: there were two candidates in an election . winner candidate received 62 % of votes and won the election by 288 votes . find the number of votes casted to the winning candidate ?
Options: a ) 456 , b ) 744 , c ) 912 , d ) 1200 , e ) 1400
Rationale: w = 62 % l = 38 % 62 % - 38 % = 24 % 24 % - - - - - - - - 288 62 % - - - - - - - - ? = > 744 answer : b
Answer: b
Python program:
a = 100 - 62
b = 62 - a
c = b / 100
d = 288 / c
e = d * 62
f = e / 100
Problem: there are 17 teams in the hockey league , and each team faces all the other teams 10 times each . how many games are played in the season ?
Options: a ) 980 , b ) 1150 , c ) 1360 , d ) 1540 , e ) 1720
Rationale: "the number of ways to choose two teams is 17 c 2 = 17 * 16 / 2 = 136 the total number of games in the season is 10 * 136 = 1360 . the answer is c ."
Answer: c
Python program:
a = 17 - 1
b = 17 * a
c = b * 10
d = c / 2
Problem: in how many ways can 7 boys be seated in a circular order ?
Options: a ) 110 , b ) 230 , c ) 720 , d ) 420 , e ) 680
Rationale: "number of arrangements possible = ( 7 − 1 ) ! = 6 ! = 6 x 5 x 4 x 3 x 2 x 1 = 720 answer : c"
Answer: c
Python program:
a = 7 / 1
b = a / 3
c = b - 3
Problem: if n = 8 ^ 9 – 8 , what is the units digit of n ?
Options: a ) 4 , b ) 0 , c ) 1 , d ) 2 , e ) 3
Rationale: "8 ^ 9 - 8 = 8 ( 8 ^ 8 - 1 ) = = > 8 ( 2 ^ 24 - 1 ) last digit of 2 ^ 24 is 6 based on what explanation livestronger is saying . 2 ^ 24 - 1 yields 6 - 1 = 5 as the unit digit . now on multiply this with 8 , we get unit digit as 0 answer : b"
Answer: b
Python program:
a = math.log(8)
b = 8 ** 9
c = math.log(b)
d = a / c
Problem: a , b , c subscribe rs . 50,000 for a business . if a subscribes rs . 4000 more than b and b rs . 5000 more than c , out of a total profit of rs . 40,000 , what will be the amount a receives ?
Options: a ) 14700 , b ) 14500 , c ) 16800 , d ) 14300 , e ) 14000
Rationale: "total amount invested = 50000 assume that investment of c = x . then investment of b = 5000 + x , investment of a = 4000 + 5000 + x = 9000 + x x + 5000 + x + 9000 + x = 50000 ⇒ 3 x + 14000 = 50000 ⇒ 3 x = 50000 – 14000 = 36000 ⇒ x = 36000 / 3 = 12000 investment of c = x = 12000 investment of b = 5000 + x = 17000 investment of a = 9000 + x = 21000 ratio of the investment of a , b and c = 21000 : 17000 : 12000 = 21 : 17 : 12 share of a = total profit × 21 / 50 = 40000 × 21 / 50 = 16,800 answer is c"
Answer: c
Python program:
a = 5000 * 10
b = 4000 + 5000 
c = b + 5000 
d = a - c
e = d / 3
f = 4000 + 5000 
g = e + f 
h = 3 * 12
i = h * 1000
j = 5000 * 10
k = i / j
l = g * k
Problem: 30 carrots on a scale weigh 5.94 kg . when 3 carrots are removed from the scale , the average weight of the 27 carrots is 200 grams . what is the average weight ( in grams ) of the 3 carrots which were removed ?
Options: a ) 165 , b ) 170 , c ) 175 , d ) 180 , e ) 185
Rationale: 27 * 200 = 5400 . the other 3 carrots weigh a total of 540 grams . the average weight is 540 / 3 = 180 grams . the answer is d .
Answer: d
Python program:
a = 27 * 200
b = a / 1000
c = 5 - 94
d = c / 3
e = d * 1000
Problem: two trains start at same time from two stations and proceed towards each other at the rate of 20 km / hr and 25 km / hr respectively . when they meet , it is found that one train has traveled 75 km more than the other . what is the distance between the two stations ?
Options: a ) 540 km , b ) 675 km , c ) 276 km , d ) 178 km , e ) 176 km
Rationale: "explanation : let us assume that trains meet after ' x ' hours distance = speed * time distance traveled by two trains = 20 x km and 25 x km resp . as one train travels 75 km more than the other , 25 x â € “ 20 x = 75 5 x = 75 x = 15 hours as the two trains are moving towards each other , relative speed = 20 + 25 = 45 km / hr therefore , total distance = 45 * 15 = 675 km . answer : b"
Answer: b
Python program:
a = 20 + 25 
b = 25 - 20
c = 75 / b
d = a * c
Problem: what is the smallest positive integer x such that 120 - x is the cube of a positive integer ?
Options: a ) 10 , b ) 6 , c ) 5 , d ) 0 , e ) 1
Rationale: "given 130 - x is a perfect cube so we will take 125 = 5 * 5 * 5 130 - x = 125 x = 130 - 125 = 5 correct option is c"
Answer: c
Python program:
a = 3 + 4
Problem: two ants , arthur and amy , have discovered a picnic and are bringing crumbs back to the anthill . amy makes twice as many trips and carries one and a half times as many crumbs per trip as arthur . if arthur carries a total of c crumbs to the anthill , how many crumbs will amy bring to the anthill , in terms of c ?
Options: a ) x / 2 , b ) x , c ) 3 x / 2 , d ) 2 x , e ) 3 x
Rationale: "lets do it by picking up numbers . let arthur carry 2 crumbs per trip , this means amy carries 3 crumbs per trip . also let arthur make 2 trips and so amy makes 4 trips . thus total crumbs carried by arthur ( c ) = 2 x 2 = 4 , total crumbs carried by amy = 3 x 4 = 12 . 12 is 3 times 4 , so e"
Answer: e
Python program:
a = 1 / 2
b = 1 + a 
c = 2 * b
Problem: a shopkeeper forced to sell at cost price , uses a 850 grams weight for a kilogram . what is his gain percent ?
Options: a ) 17.65 % , b ) 9 % , c ) 11.11 % , d ) 12 % , e ) none of these
Rationale: "shopkeeper sells 850 g instead of 1000 g . so , his gain = 1000 - 850 = 150 g . thus , % gain = ( 150 * 100 ) / 850 = 17.65 % . answer : option a"
Answer: a
Python program:
a = 2 * 100
b = 100 / 2
c = a + b 
d = c / 850
e = d * 100
Problem: in a mayoral election , candidate x received 2 / 3 more votes than candidate y , and candidate y received 1 / 3 fewer votes than z . if z received 27,000 votes how many votes did candidate x received ?
Options: a ) 18000 , b ) 22000 , c ) 24000 , d ) 26000 , e ) 30000
Rationale: "z = 27 - - > y received 2 / 3 fewer votes than z - - > y = z - 1 / 3 * z = 18 ; x received 2 / 3 more votes than y - - > x = y + 2 / 3 * y = 30 . answer : e ."
Answer: e
Python program:
a = 3 / 3
b = 2 - a
c = const_0_25 * 100
d = c * 100
e = d * 10
f = b * e
g = 2 / 3
h = g + 2 
i = f * h
Problem: a cubical block of metal weighs 4 pounds . how much will another cube of the same metal weigh if its sides are twice as long ?
Options: a ) 48 , b ) 32 , c ) 24 , d ) 18 , e ) 12
Rationale: "for example our cube have a side 1 meter , so we have 1 cubical meter in this cube and this cubical meter weigth 4 pounds if we take cube with side 2 meters we will have 8 cubical meters in this cube 8 meters * 4 pounds = 32 pounds so answer is b and similar but more theoretical approach : if we have sides a and b than they have equal ration with their areas : a / b = a ^ 2 / b ^ 2 and they have equal ration with their volumes : a / b = a ^ 3 / b ^ 3 we have two sides 1 / 2 so their volume will be in ratio 1 / 8 weight of one cube * volume of another cube 4 * 8 = 32 so answer is b"
Answer: b
Python program:
a = 2 * 4
b = 4 * a
Problem: the price of a coat in a certain store is $ 500 . if the price of the coat is to be reduced by $ 200 , by what percent is the price to be reduced ?
Options: a ) 10 % , b ) 15 % , c ) 20 % , d ) 25 % , e ) 40 %
Rationale: "price of a coat in a certain store = $ 500 the price of the coat is to be reduced by $ 200 % change = ( final value - initial value ) * 100 / initial value % reduction = ( reduction in price ) * 100 / initial value i . e . % reduction = ( 200 ) * 100 / 500 = 40 % answer : option e"
Answer: e
Python program:
a = 200 / 500
b = a * 100
Problem: bob wants to run a mile in the same time as his sister . if bob ’ s time for a mile is currently 10 minutes 40 seconds and his sister ’ s time is currently 10 minutes 8 seconds , by what percent does bob need to improve his time in order run a mile in the same time as his sister ?
Options: a ) 3 % , b ) 5 % , c ) 8 % , d ) 10 % , e ) 12 %
Rationale: "bob ' s time = 640 secs . his sis ' time = 608 secs . percent increase needed = ( 640 - 608 / 640 ) * 100 = 32 / 640 * 100 = 5 % . ans ( b ) ."
Answer: b
Python program:
a = 10 * 10
b = 10 * const_60
c = b + 8 
d = 10 * const_60
e = d + 40 
f = c / e
g = 1 - f
h = a * g
Problem: when a mobile is sold for rs . 24000 , the owner loses 40 % . at what price must that mobile be sold in order to gain 40 % ?
Options: a ) 54,000 , b ) 56,000 , c ) 58,000 , d ) 60,000 , e ) 62,000
Rationale: "60 : 24000 = 140 : x x = ( 24000 x 140 ) / 60 = 56000 . hence , s . p . = rs . 56,000 . answer : option b"
Answer: b
Python program:
a = 24000 * 100
b = 100 - 40
c = a / b
d = 100 + 40 
e = c * d
f = e / 100
g = f / 100
h = g / 40
i = h * 2
j = math.floor(i)
Problem: bella is taking a trip in her car from new york ( point a ) chicago , illinois ( point b ) . she is traveling at an average speed of 50 miles per hour , if the total distance from point a to point b is 790 miles , in approximately how long will bella reach her destination ?
Options: a ) 10 hours , b ) 12.50 hours , c ) 15.80 hours , d ) 25 hours , e ) 1 day
Rationale: answer is ( c ) . if she is traveling at a speed of 50 miles per hour and her trip is a total of 790 miles , 790 miles divided by 50 miles per hours would equal 15.80 hours , just shy of 16 hours .
Answer: c
Python program:
a = 790 / 50
Problem: because he ’ s taxed by his home planet , mork pays a tax rate of 10 % on his income , while mindy pays a rate of 20 % on hers . if mindy earned 3 times as much as mork did , what was their combined tax rate ?
Options: a ) 32.5 % , b ) 17.5 % , c ) 20 % , d ) 36 % , e ) 37.5 %
Rationale: "say morks income is - 100 so tax paid will be 10 say mindys income is 3 * 100 = 300 so tax paid is 20 % * 300 = 60 total tax paid = 10 + 60 = 70 . combined tax % will be 70 / 100 + 300 = 15.5 %"
Answer: b
Python program:
a = 10 / 100
b = 20 / 100
c = 3 * b
d = a + c 
e = 1 + 3 
f = d / e
g = 100 * f
Problem: three numbers are in the ratio 4 : 5 : 6 and their average is 36 . the largest number is :
Options: a ) 28 , b ) 32 , c ) 43.2 , d ) 42 , e ) 45
Rationale: "explanation : let the numbers be 4 x , 5 x and 6 x . therefore , ( 4 x + 5 x + 6 x ) / 3 = 36 15 x = 108 x = 7.2 largest number = 6 x = 43.2 . answer c"
Answer: c
Python program:
a = 4 * 6
b = a * 100
c = 5 * 6
d = b + c
Problem: the probability that event a occurs is 0.4 , and the probability that events a and b both occur is 0.25 . if the probability that either event a or event b occurs is 0.6 , what is the probability that event b will occur ?
Options: a ) 0.05 , b ) 0.15 , c ) 0.45 , d ) 0.5 , e ) 0.55
Rationale: p ( a or b ) = p ( a ) + p ( b ) - p ( a n b ) 0.6 = 0.4 + p ( b ) - 0.25 p ( b ) = 0.45 answer : c
Answer: c
Python program:
a = 0 + 6 
b = a - 0
Problem: there are 437 doctors and nurses in a hospital . if the ratio of the doctors to the nurses is 8 : 11 , then how many nurses are there in the hospital ?
Options: a ) 152 , b ) 253 , c ) 57 , d ) 171 , e ) 181
Rationale: "given , the ratio of the doctors to the nurses is 8 : 11 number of nurses = 11 / 19 x 437 = 253 answer : b"
Answer: b
Python program:
a = 11 - 8
b = 8 * a
c = b * 11
Problem: two passenger trains start at the same hour in the day from two different stations and move towards each other at the rate of 14 kmph and 21 kmph respectively . when they meet , it is found that one train has traveled 60 km more than the other one . the distance between the two stations is ?
Options: a ) 477 , b ) 420 , c ) 279 , d ) 276 , e ) 291
Rationale: "1 h - - - - - 5 ? - - - - - - 60 12 h rs = 14 + 21 = 35 t = 12 d = 35 * 12 = 420 . answer : b"
Answer: b
Python program:
a = 21 - 14
b = 60 / a
c = b * 14
d = 21 - 14
e = 60 / d
f = e * 21
g = c + f
Problem: if the length of the sides of two cubes are in the ratio 4 : 1 , what is the ratio of their total surface area ?
Options: a ) 4 : 1
b ) 6 : 1
c ) 8 : 1
d ) 16 : 1
e ) 64 : 1
Rationale: let x be the length of the small cube ' s side . the total surface area of the small cube is 6 x ^ 2 . the total surface area of the large cube is 6 ( 4 x ) ^ 2 = 96 x ^ 2 . the ratio of surface areas is 16 : 1 . the answer is d .
Answer: d
Python program:
a = 4 * 4
Problem: how many integers from 0 to 50 inclusive have a remainder of 3 when divided by 8 ?
Options: a ) 5 , b ) 6 , c ) 7 , d ) 8 , e ) 9
Rationale: "the numbers should be of the form 8 c + 3 . the minimum is 3 when c = 0 . the maximum is 43 when c = 5 . there are six such numbers . the answer is b ."
Answer: b
Python program:
a = 50 / 10
Problem: two brothers took the gmat exam , the higher score is x and the lower one is y . if the difference between the two scores is 1 / 5 , what is the value of x / y ?
Options: a ) 3 . , b ) 5 , c ) 1 / 2 . , d ) 1 / 3 . , e ) there is n ' t enough data to answer the question .
Rationale: "answer is b : 5 x - y = ( x + y ) / 2 solving for x / y = 5"
Answer: b
Python program:
a = 5 * 1
b = a / 5
c = 5 + b
Problem: how much interest will $ 10,000 earn in 9 months at an annual rate of 3 % ?
Options: a ) $ 250 , b ) $ 350 , c ) $ 450 , d ) $ 550 , e ) $ 225
Rationale: "soln : - 9 months = 3 / 4 of year ; 3 % = 3 / 100 = 3 / 100 ; $ 10,000 ( principal ) * 3 / 100 ( interest rate ) * 3 / 4 ( time ) = $ 225 . answer : e"
Answer: e
Python program:
a = 100 ** 2
b = 3 / 100
c = a * b
d = 3 / 3
e = c * d
Problem: the average weight of 20 persons sitting in a boat had some value . a new person added to them whose weight was 47 kg only . due to his arrival , the average weight of all the persons decreased by 5 kg . find the average weight of first 20 persons ?
Options: a ) 55 , b ) 56 , c ) 57 , d ) 58 , e ) 59
Rationale: "20 x + 47 = 21 ( x – 5 ) x = 58 answer : d"
Answer: d
Python program:
a = 20 + 1 
b = a * 5
c = b - 47
Problem: p can do a work in 24 days . q can do the samework in 9 days & r can do the same work in 12 days . q & r start the work and leave after 3 days . p finishes the remaining work in how many days .
Options: a ) 8 , b ) 10 , c ) 14 , d ) 16 , e ) 19
Rationale: work done by p in 1 day = 1 / 24 work done by q in 1 day = 1 / 9 work done by r in 1 day = 1 / 12 work done by q and r in 1 day = 1 / 9 + 1 / 12 = 7 / 36 work done by q and r in 3 days = 3 × 7 / 36 = 7 / 12 remaining work = 1 – 7 / 12 = 5 / 12 number of days in which p can finish the remaining work = ( 5 / 12 ) / ( 1 / 24 ) = 10 b
Answer: b
Python program:
a = 1 / 12
b = 1 / 9
c = a + b 
d = c * 3
e = 1 - d
f = 1 / 24
g = e / f