euclaise/mathqa_programs huggingface dataset:
Problem: in the storage room of a certain bakery , the ratio of sugar to flour is 5 to 6 , and the ratio of flour to baking soda is 10 to 1 . if there were 60 more pounds of baking soda in the room , the ratio of flour to baking soda would be 8 to 1 . how many pounds of sugar are stored in the room ?
Options: a ) 600 , b ) 1200 , c ) 1500 , d ) 1600 , e ) 2000
Rationale: "sugar : flour = 5 : 6 = 25 : 30 ; flour : soda = 10 : 1 = 30 : 3 ; thus we have that sugar : flour : soda = 25 x : 30 x : 3 x . also given that 30 x / ( 3 x + 60 ) = 8 / 1 - - > x = 80 - - > sugar = 25 x = 2,000 . answer : e ."
Answer: e
Python program:
a = 5 / 6
b = 8 * 60
c = 10 - 8
d = b / c
e = 10 * d
f = a * e
Problem: the h . c . f of two numbers is 19 and their l . c . m is 4263 . if one of the numbers is 399 , then the other is ?
Options: a ) 202 , b ) 203 , c ) 204 , d ) 205 , e ) 206
Rationale: "other number = ( 19 * 4263 ) / 399 = 203 . answer : b"
Answer: b
Python program:
a = 19 * 399
Problem: in a restaurant , the profit is 110 % of the cost . if the cost increases by 12 % but the selling price remains constant , approximately what percentage of the selling price is the profit ?
Options: a ) 30 % , b ) 47 % , c ) 90 % , d ) 100 % , e ) none of these
Rationale: explanation : let c . p . = rs . 100 . then , profit = rs . 110 , s . p . = rs . 210 . new c . p . = 112 % of rs . 100 = rs . 112 new s . p . = rs . 210 . profit = rs . ( 210 - 112 ) = rs . 98 . required percentage = ( 98 / 210 * 100 ) % = 47 % appox answer : b
Answer: b
Python program:
a = 110 / 100
b = 100 * a
c = b + 100 
d = 12 / 100
e = 1 + d 
f = 100 * e
g = c - f
h = 110 / 100
i = 100 * h
j = i + 100 
k = g / j
l = 100 * k
Problem: at a loading dock , each worker on the night crew loaded 3 / 4 as many boxes as each worker on the day crew . if the night crew has 3 / 4 as many workers as the day crew , what fraction of all the boxes loaded by the two crews did the day crew load ?
Options: a ) 3 / 5 , b ) 4 / 5 , c ) 11 / 15 , d ) 16 / 25 , e ) 19 / 25
Rationale: "let x be the number of workers on the day crew . let y be the number of boxes loaded by each member of the day crew . then the number of boxes loaded by the day crew is xy . the number of boxes loaded by the night crew is ( 3 x / 4 ) ( 3 y / 4 ) = 9 xy / 16 the total number of boxes is xy + 9 xy / 16 = 25 xy / 16 the fraction loaded by the day crew is xy / ( 25 xy / 16 ) = 16 / 25 the answer is d ."
Answer: d
Python program:
a = 4 * 4
b = 4 * 4
c = 3 * 3
d = b + c 
e = a / d
Problem: walking 6 / 5 of his usual rate , a boy reaches his school 4 min early . find his usual time to reach the school ?
Options: a ) 22 , b ) 99 , c ) 27 , d ) 24 , e ) 20
Rationale: "speed ratio = 1 : 6 / 5 = 5 : 6 time ratio = 6 : 5 1 - - - - - - - - 6 4 - - - - - - - - - ? 24 m . answer : d"
Answer: d
Python program:
a = 4 * 6
Problem: how many seconds will a 500 m long train take to cross a man walking with a speed of 3 km / hr in the direction of the moving train if the speed of the train is 66 km / hr ?
Options: a ) 11 , b ) 30 , c ) 29 , d ) 88 , e ) 61
Rationale: "speed of train relative to man = 66 - 3 = 63 km / hr . = 63 * 5 / 18 = 35 / 2 m / sec . time taken to pass the man = 500 * 2 / 35 = 28.57 sec . approx . 29 sec answer : c"
Answer: c
Python program:
a = 66 - 3
b = a * const_0_2778
c = 500 / b
Problem: what number times ( 1 ⁄ 4 ) ^ 2 will give the value of 4 ^ 3 ?
Options: a ) 4 , b ) 16 , c ) 64 , d ) 256 , e ) 1024
Rationale: "x * ( 1 / 4 ) ^ 2 = 4 ^ 3 x = 4 ^ 2 * 4 ^ 3 = 4 ^ 5 = 1024 the answer is e ."
Answer: e
Python program:
a = 2 ** 0
b = 4 ** 3
c = a * b
Problem: a vendor bought toffees at 6 for a rupee . how many for a rupee must he sell to gain 25 % ?
Options: a ) 2 , b ) 9 , c ) 6 , d ) 3 , e ) 5
Rationale: "c . p . of 6 toffees = re . 1 s . p . of 6 toffees = 150 % of re . 1 = rs . 3 / 2 for rs . 3 / 2 , toffees sold = 6 . for re . 1 , toffees sold = 6 x 3 / 2 = 9 . answer b"
Answer: b
Python program:
a = 25 / 100
b = 1 + a 
c = 6 * b
Problem: one night 19 percent of the female officers on a police force were on duty . if 152 police officers were on duty that night and half of these were female officers , how many female officers were on the police force ?
Options: a ) 300 , b ) 350 , c ) 400 , d ) 450 , e ) 500
Rationale: "let x be the number of female police officers on the police force . the number of female police officers on duty was 76 . 0.19 x = 76 x = 400 the answer is c ."
Answer: c
Python program:
a = 152 / 2
b = 19 / 100
c = a / b
Problem: a car ferry can hold up to 70 tons of cargo . what is the greatest number of vehicles that the ferry can carry if half the vehicles are cars with an average ( arithmetic mean ) weight of 0.75 tons and half of the vehicles are trucks with an average ( arithmetic mean ) weight of 6 tons ?
Options: a ) 20 , b ) 24 , c ) 28 , d ) 32 , e ) 36
Rationale: "the weight of one car and one truck is 6.75 tons . 70 / 6.75 = 10 plus a remainder the ferry could carry 10 cars and 10 trucks for a total of 20 vehicles . the answer is a ."
Answer: a
Python program:
a = 0 + 75 
b = 70 / a
c = 0 + 75 
d = 70 / c
e = b + d
Problem: a train passes a platform in 35 seconds . the same train passes a man standing on the platform in 20 seconds . if the speed of the train is 54 km / hr , the length of the platform is
Options: a ) 280 meter , b ) 240 meter , c ) 225 meter , d ) 200 meter , e ) none of these
Rationale: "explanation : speed of the train = 54 km / hr = ( 54 × 10 ) / 35 m / s = 15 m / s length of the train = speed × time taken to cross the man = 15 × 20 = 300 m let the length of the platform = l time taken to cross the platform = ( 300 + l ) / 15 = > ( 300 + l ) / 15 = 35 = > 300 + l = 15 × 35 = 525 = > l = 525 - 300 = 225 meter answer : option c"
Answer: c
Python program:
a = const_0_2778 * 54
b = 35 - 20
c = a * b
Problem: a grocer has 400 pounds of coffee in stock , 20 percent of which is decaffeinated . if the grocer buys another 100 pounds of coffee of which 50 percent is decaffeinated , what percent , by weight , of the grocer ’ s stock of coffee is decaffeinated ?
Options: a ) 26 % , b ) 30 % , c ) 32 % , d ) 34 % , e ) 40 %
Rationale: "1 . 20 % of 400 = 80 pounds of decaffeinated coffee 2 . 50 % of 100 = 50 pounds of decaffeinated coffee 3 . wt have 130 pounds of decaffeinated out of 500 pounds , that means 130 / 500 * 100 % = 26 % . the correct answer is a ."
Answer: a
Python program:
a = 20 / 100
b = a * 400
c = 50 / 100
d = 100 * c
e = b + d 
f = 400 + 100 
g = e / f
h = g * 100
Problem: praveen starts business with rs . 3220 and after 5 months , hari joins with praveen as his partner . after a year , the profit is divided in the ratio 2 : 3 . what is hari ’ s contribution in the capital ?
Options: a ) s . 7500 , b ) s . 8000 , c ) s . 8280 , d ) s . 9000 , e ) s . 6000
Rationale: "let hari ’ s capital be rs . x . then , 3220 * 12 / 7 x = 2 / 3 = > 14 x = 115920 = > x = 8280 . answer : c"
Answer: c
Python program:
a = 5 / 12
b = 1 - a
c = 3220 / b
d = 2 / 3
e = c / d
Problem: how many integers from 22 to 160 , inclusive , are divisible by 3 but not divisible by 7 ?
Options: a ) 30 , b ) 35 , c ) 40 , d ) 50 , e ) 60
Rationale: "we should find # of integers divisible by 3 but not by 3 * 7 = 21 . # of multiples of 21 in the range from 22 to 160 , inclusive is ( 147 - 42 ) / 21 + 1 = 6 ; 46 - 6 = 40 . answer : c ."
Answer: c
Python program:
a = 160 / 10
Problem: 8 identical machines , working alone and at their constant rates , take 6 hours to complete a job lot . how long would it take for 4 such machines to perform the same job ?
Options: a ) 2.25 hours , b ) 8.75 hours , c ) 12 hours , d ) 14.25 hours , e ) 16 hours
Rationale: let each machine do 1 unit of work for 1 hour 8 machines - - > 8 units of work in 1 hour for 6 hours = 8 * 6 = 48 units of total work is done . now this 48 units of total work must be done by 4 machines 4 units of work ( 4 machines ) - - - > 1 hour for 48 units of work 4 * 12 - - - > 1 * 12 hours c 12 hours
Answer: c
Python program:
a = 6 * 8
b = a / 4
Problem: a candidate got 35 % of the votes and lost to the rival by 2100 votes . how many votes were cast ?
Options: a ) 7000 , b ) 7200 , c ) 7400 , d ) 7600 , e ) 7800
Rationale: "35 % - - - - - - - - - - - l 65 % - - - - - - - - - - - w - - - - - - - - - - - - - - - - - - 30 % = 2100 10 % = 700 100 % of the votes = 7000 answer : a"
Answer: a
Python program:
a = 35 / 100
b = 1 - a
c = 35 / 100
d = b - c
e = 2100 / d
Problem: if you write down all the numbers from 1 to 25 , then how many times do you write 3 ?
Options: a ) a ) 11 , b ) b ) 3 , c ) c ) 2 , d ) d ) 1 , e ) e ) 6
Rationale: "explanation : explanation : clearly , from 1 to 25 , there are ten numbers with 3 as the unit ' s digit - 3 , 13 , 23 so , required number = 3 answer : b"
Answer: b
Python program:
a = 25 - 1
b = a / 3
Problem: what is the square root of 81 , divided by 3 ?
Options: a ) 9 , b ) 36 , c ) 122 , d ) 3 , e ) 1
Rationale: "square root is a number times itself square root of 81 = 6 , 9 / 3 = 3 ( d ) 3"
Answer: d
Python program:
a = math.sqrt(81)
b = a / 3
Problem: the mean of 30 values was 250 . it was detected on rechecking that one value 165 was wrongly copied as 135 for the computation of the mean . find the correct mean .
Options: a ) 151 , b ) 149 , c ) 152 , d ) 251 , e ) none of the above
Rationale: "corrected mean = 250 × 30 − 135 + 165 / 30 = 7500 − 135 + 165 / 30 = 7530 / 30 = 251 answer d"
Answer: d
Python program:
a = 30 * 250
b = 165 - 135
c = a + b 
d = c / 30
Problem: a cyclist rides a bicycle 9 km at an average speed of 11 km / hr and again travels 11 km at an average speed of 9 km / hr . what is the average speed for the entire trip ?
Options: a ) 9.3 , b ) 9.6 , c ) 9.8 , d ) 10.1 , e ) 10.3
Rationale: "distance = 20 km time = 9 / 11 + 11 / 9 = ( 81 + 121 ) / 99 = 202 / 99 hours average speed = ( 20 * 99 ) / 202 = 9.8 km / h the answer is c ."
Answer: c
Python program:
a = 9 + 11 
b = 9 / 11
c = 11 / 9
d = b + c 
e = a / d
Problem: a man can row upstream at 26 kmph and downstream at 30 kmph , and then find the speed of the man in still water ?
Options: a ) 29 , b ) 28 , c ) 30 , d ) 32 , e ) 23
Rationale: "us = 26 ds = 30 m = ( 30 + 26 ) / 2 = 28 answer : b"
Answer: b
Python program:
a = 26 + 30 
b = a / 2
Problem: in a group of 60 people , 35 have visited iceland and 23 have visited norway . if 31 people have visited both iceland and norway , how many people have visited neither country ?
Options: a ) 30 , b ) 31 , c ) 32 , d ) 33 , e ) 34
Rationale: this is an example of a standard overlapping sets question . it has no ' twists ' to it , so you ' ll likely find using the overlapping sets formula to be a fairly easy approach . if you ' re not familiar with it , then here is the formula : 60 = 35 + 23 - 31 + ( # in neither group ) = 33 the prompt gives you all of the numbers you need to get to the correct answer . just plug in and solve . d
Answer: d
Python program:
a = 35 + 23 
b = a - 31
c = 60 - b
Problem: a reduction of 5 % in the price of oil enables a house wife to obtain 10 kgs more for rs . 5000 , what is the reduced price for kg ?
Options: a ) 23 , b ) 27 , c ) 25 , d ) 35 , e ) 15
Rationale: "5000 * ( 5 / 100 ) = 250 - - - - 10 ? - - - - 1 = > rs . 25 answer : c"
Answer: c
Python program:
a = 5000 * 5
b = a / 100
c = b / 10
Problem: if a 2 - b 2 = 10 and a * b = 8 , find a 4 + b 4 .
Options: a ) 200 , b ) 228 , c ) 182 , d ) 102 , e ) 128
Rationale: "a 2 - b 2 = 10 : given a 4 + b 4 - 2 a 2 b 2 = 102 : square both sides and expand . a * b = 8 : given a 2 b 2 = 82 : square both sides . a 4 + b 4 - 2 ( 64 ) = 100 : substitute a 4 + b 4 = 228 correct answer b"
Answer: b
Python program:
a = 10 ** 2
b = 8 ** 2
c = b * 2
d = a + c
Problem: find the sum of first 80 odd numbers
Options: a ) 6400 , b ) 8000 , c ) 5000 , d ) 4980 , e ) 4960
Rationale: "explanation : n 2 = 802 = 6400 answer : option a"
Answer: a
Python program:
a = 80 / 2
b = a / 2
c = b / 2
d = c / 2
e = d / 2
f = 80 / e
g = f / 2
h = 80 / 2
i = h / 2
j = i / 2
k = j / 2
l = k / 2
m = 80 / l
n = m / 2
o = math.sqrt(n)
p = 1 + o 
q = g + p
Problem: of 58 players on a cricket team , 37 are throwers . the rest of the team is divided so one third are left - handed and the rest are right handed . assuming that all throwers are right handed , how many right - handed players are there total ?
Options: a ) 51 , b ) 55 , c ) 59 , d ) 71 , e ) 92
Rationale: total = 58 thrower = 37 rest = 58 - 37 = 21 left handed = 21 / 3 = 7 right handed = 14 if all thrower are right handed then total right handed is 37 + 14 = 51 so a . 51 is the right answer
Answer: a
Python program:
a = 1 / 3
b = 1 - a
c = 58 - 37
d = b * c
e = 37 + d
Problem: the amount of principal rs . 8000 at compound interest at the ratio of 5 % p . a . for 6 years is
Options: a ) s . 9621 , b ) s . 6921 , c ) s . 10721 , d ) s . 6261 , e ) s . 6361
Rationale: "c . i = p ( 1 + r / 100 ) ^ n = 8000 ( 1 + 5 / 100 ) ^ 6 = rs 10721 answer : c"
Answer: c
Python program:
a = 5 / 100
b = 1 + a 
c = b ** 6
d = 8000 * c
Problem: angelo and isabella are both salespersons . in any given week , angelo makes $ 590 in base salary plus 8 percent of the portion of his sales above $ 1,000 for that week . isabella makes 10 percent of her total sales for any given week . for what amount of weekly sales would angelo and isabella earn the same amount of money ?
Options: a ) 23,500 , b ) 24,500 , c ) 25,500 , d ) 26,500 , e ) 27,500
Rationale: let the weekly sales of both = x 590 + ( x − 1000 ) 8 / 100 = 10 / 100 x x = 25500 answer : c
Answer: c
Python program:
a = 8 / 100
b = 1000 * a
c = 590 - b
d = 10 / 100
e = 8 / 100
f = d - e
g = c / f
h = g / 1000
i = math.floor(h)
Problem: the product of the squares of two positive integers is 1600 . how many pairs of positive integers satisfy this condition ?
Options: a ) 0 , b ) 1 , c ) 2 , d ) 3 , e ) 4
Rationale: "ans : e - 4 pairs ( x ˆ 2 ) ( y ˆ 2 ) = 1600 [ square root both sides ] xy = 40 40 = 1 x 40 , 4 x 10 , 40 x 1 , 10 x 4 , 5 x 8 , 8 x 5 , 20 x 2 , 2 x 20 cancel the repeats this leaves us with exactly 4 options . hence , e"
Answer: e
Python program:
a = 2 + 3 
b = a - 2
Problem: what percent is 20 % of 25 % ?
Options: a ) 20 % , b ) 30 % , c ) 50 % , d ) 60 % , e ) 80 %
Rationale: required percentage = 20 % / 25 % * 100 = 20 / 25 * 100 = 80 % answer is e
Answer: e
Python program:
a = 20 / 25
b = a * 100
Problem: walking at 40 % of his usual speed a man takes 24 minutes more to cover a distance . what is his usual time to cover this distance ?
Options: a ) 16 , b ) 36 , c ) 42 , d ) 48 , e ) 54
Rationale: speed is inversly proprtional to time walking at 40 % of speed meand 2 / 5 s takes 5 / 2 t . it takes 24 minutes extra to cover the distance . then 5 / 2 t = t + 24 5 t = 2 t + 48 3 t = 48 t = 16 . option a is correct
Answer: a
Python program:
a = 40 / 100
b = 1 / a
c = b - 1
d = 24 / c
Problem: there are 660 male and female participants in a meeting . half the female participants and one - quarter of the male participants are democrats . one - third of all the participants are democrats . how many of the democrats are female ?
Options: a ) 75 , b ) 110 , c ) 125 , d ) 175 , e ) 225
Rationale: "female = x male = 660 - x x / 2 + 660 - x / 4 = 1 / 3 * ( 660 ) = 220 x = 220 x / 2 = 110 is supposed to be the answer m is missing something correct option b"
Answer: b
Python program:
a = 660 / 3
b = a * 4
c = b - 660
d = c / 2
Problem: the speed of a train is 70 kmph . what is the distance covered by it in 10 minutes ?
Options: a ) 10.66 kmph , b ) 11.66 kmph , c ) 21.66 kmph , d ) 12.66 kmph , e ) 11.96 kmph
Rationale: "70 * 10 / 60 = 11.66 kmph answer : b"
Answer: b
Python program:
a = 10 / const_60
b = a * 70
Problem: what is the ratio e of the surface area of a cube to the surface area of a rectangular solid identical to the cube in all ways except that its length has been doubled ?
Options: a ) 1 / 4
b ) 3 / 8
c ) 1 / 2
d ) 3 / 5
e ) 2
Rationale: one side surface area of a cube = x * x = x ^ 2 total 6 sides = 6 x ^ 2 as for the rectangular , height ( h ) and width ( w ) are same as cube , x . only length = 2 x . l x h = 2 x * x = 2 x ^ 2 - - - - > 4 sides = 2 x ^ 2 * 4 = 8 x ^ 2 w * h = x * x = x ^ 2 - - - - - - > 2 sides = x ^ 2 * 2 = 2 x ^ 2 total 6 sides = 8 x ^ 2 + 2 x ^ 2 = 10 x ^ 2 ratio of cube area to rectangular area e = 6 x ^ 2 / 10 x ^ 2 - - - - > 6 / 10 - - - - > 3 / 5 ( d )
Answer: d
Python program:
a = 1 * 1
b = 2 * 3
c = a * b
d = 1 * 1
e = d * 2
f = 1 * 2
g = f * 4
h = e + g 
i = c / h
Problem: if the operation @ is defined for all a and b by the equation a @ b = ( a ^ b ) / 2 , then ( 3 @ 2 ) = ?
Options: a ) 4 , b ) 2 , c ) 9 / 2 , d ) - 9 / 2 , e ) - 8 / 2
Rationale: work within the parenthesis first so solve ( 3 @ 2 ) first ( 3 @ 2 ) = ( 3 ^ 2 ) / 2 = 9 / 2 so 9 / 2 is the answer . . . . this question is merely testing order of operations remember pemdas answer : c
Answer: c
Python program:
a = 3 ** 2
b = a / 2
Problem: a boat can travel with a speed of 10 km / hr in still water . if the speed of the stream is 8 km / hr , find the time taken by the boat to go 54 km downstream .
Options: a ) 4.25 hr , b ) 5.25 hr , c ) 3 hr , d ) 2.25 hr , e ) 2.50 hr
Rationale: "speed of boat in still water = 10 km / hr speed of the stream = 8 km / hr speed downstream = ( 10 + 8 ) = 18 km / hr time taken to travel 68 km downstream = 54 â  „ 18 = 17 â  „ 4 = 3 hours answer is c"
Answer: c
Python program:
a = 10 + 8 
b = 54 / a
Problem: there is enough provisions for 9600 women in an army camp for 400 days . if there were 4800 men less , how long will the provision last ?
Options: a ) 799 , b ) 800 , c ) 801 , d ) 802 , e ) 803
Rationale: we have , m 1 d 1 = m 2 d 2 9600 * 400 = 4800 * d 2 d 2 = 9600 * 400 / 4800 = 800 days . answer : b
Answer: b
Python program:
a = 9600 * 400
b = a / 4800
Problem: if a * b * c = ( √ ( a + 2 ) ( b + 3 ) ) / ( c + 1 ) , find the value of 6 * 15 * 3 .
Options: a ) 8 , b ) 5 , c ) 11 , d ) 3 , e ) 4
Rationale: "6 * 15 * 3 = ( √ ( 6 + 2 ) ( 15 + 3 ) ) / ( 3 + 1 ) = ( √ 8 * 18 ) / 4 = ( √ 144 ) / 4 = 12 / 4 = 3 . answer is d ."
Answer: d
Python program:
a = 6 + 2 
b = 15 + 3 
c = a * b
d = math.sqrt(c)
e = 3 + 1 
f = d / e
Problem: shannon and maxine work in the same building and leave work at the same time . shannon lives due north of work and maxine lives due south . the distance between maxine ' s house and shannon ' s house is 60 miles . if they both drive home at the rate 2 r miles per hour , maxine arrives home 60 minutes after shannon . if maxine rider her bike home at the rate of r per hour and shannon still drives at a rate of 2 r miles per hour , shannon arrives home 2 hours before maxine . how far does maxine live from work ?
Options: a ) 20 , b ) 34 , c ) 38 , d ) 40 , e ) 48
Rationale: "nice question + 1 we have that x / 24 - ( 60 - x ) / 2 r = 40 also x / r - ( 60 - x ) / 2 r = 120 so we get that 2 x - 60 = 80 r 3 x - 60 = 240 r get rid of r 120 = 3 x x = 48 hence answer is e"
Answer: e
Python program:
a = 3 * 60
b = a - 60
c = b / 3
Problem: a and b began business with rs . 6000 and rs . 4000 after 8 months , a withdraws rs . 1000 and b advances rs . 1000 more . at the end of the year , their profits amounted to rs . 630 find the share of a .
Options: a ) 240 , b ) 288 , c ) 277 , d ) 357 , e ) 361
Rationale: "( 6 * 8 + 5 * 4 ) : ( 4 * 8 + 5 * 4 ) 17 : 13 17 / 30 * 630 = 357 answer : d"
Answer: d
Python program:
a = 6000 * 8
b = 6000 - 1000
c = 12 - 8
d = b * c
e = a + d 
f = 4000 * 8
g = 4000 + 1000 
h = 12 - 8
i = g * h
j = f + i 
k = e + j 
l = 630 / k
m = 6000 * 8
n = 6000 - 1000
o = 12 - 8
p = n * o
q = m + p 
r = l * q
Problem: a , b and c rents a pasture for rs . 950 . a put in 12 horses for 8 months , b 16 horses for 9 months and 18 horses for 6 months . how much should c pay ?
Options: a ) 295 , b ) 199 , c ) 676 , d ) 156 , e ) 122
Rationale: "12 * 8 : 16 * 9 = 18 * 6 8 : 12 : 9 9 / 29 * 950 = 295 answer : a"
Answer: a
Python program:
a = 12 * 8
b = 16 * 9
c = a + b 
d = 18 * 6
e = c + d 
f = 950 / e
g = 16 * 9
h = f * g
Problem: in what ratio p : q should the mixture p of milk and water in the ratio of 2 : 1 be mixed with another mixture q of milk and water in the ratio 1 : 5 so that the resultant mixture contains equal quantities of milk and water ?
Options: a ) 3 : 2 , b ) 2 : 1 , c ) 4 : 3 , d ) 3 : 5 , e ) 3 : 1
Rationale: "( 2 / 3 ) * p + ( 1 / 6 ) * q = ( 1 / 3 ) * p + ( 5 / 6 ) * q 2 p = 4 q p / q = 2 / 1 the answer is b ."
Answer: b
Python program:
a = 1 + 5 
b = 2 + 2 
c = a - b
d = c + 1
Problem: at the wholesale store you can buy an 8 - pack of hot dogs for $ 1.55 , a 20 - pack for $ 3.05 , and a 350 - pack for $ 22.95 . what is the greatest number of hot dogs you can buy at this store with $ 200 ?
Options: a ) 1,108 , b ) 2,900 , c ) 2,108 , d ) 2,124 , e ) 2,256
Rationale: "we have $ 200 and we have to maximize the number of hot dogs that we can buy with this amount . let ' s try to find out what is the maximum number of hot dogs that we can buy for a lesser amount of money , which in this case is 350 for $ 22.95 . for the sake of calculation , let ' s take $ 23 . 23 x 8 gives 184 , i . e . a total of 350 x 8 = 2800 hot dogs . we are left with ~ $ 16 . similarly , let ' s use $ 3 for calculation . we can buy 5 20 - pack hot dogs ( 3 x 5 ) , a total of 20 x 5 = 100 hot dogs . so we have 2900 hot dogs . 2108 looks far - fetched ( since we are not likely to be left with > $ 1.55 ) . hence , ( b ) 2900 ( answer b )"
Answer: b
Python program:
a = 200 / 22
b = a * 350
Problem: ifaequals the sum of the even integers from 2 to 80 , inclusive , andbequals the sum of the odd integers from 1 to 79 , inclusive , what is the value of a - b ?
Options: a ) 1 , b ) 10 , c ) 19 , d ) 40 , e ) 21
Rationale: "this is a solution from beatthegmat : even numbers : ( 80 - 2 ) / 2 + 1 = 40 even integers . ( 80 + 2 ) / 2 = 41 is the average of the even set . sum = avg * ( # of elements ) = 41 * 40 = 1640 = a odd numbers : ( 79 - 1 ) / 2 + 1 = 40 odd integers . ( 79 + 1 ) / 2 = 40 is the average of the odd set . sum = avg * ( # of elements ) = 40 * 40 = 1600 = b a - b = 1640 - 1600 = 40 . answer : d"
Answer: d
Python program:
a = 80 / 2
b = 80 / 2
c = b + 1 
d = a * c
e = 79 + 1 
f = e / 2
g = 79 - 1
h = g / 2
i = h + 1 
j = f * i
k = d - j
Problem: if 31 % of a number is 46.5 , the number is ?
Options: a ) 150 , b ) 155 , c ) 160 , d ) 165 , e ) none
Rationale: "answer let 31 % of a = 46.5 ⇒ ( 31 x a ) / 100 = 46.5 ∴ a = ( 46.5 x 100 ) / 31 = 150 correct option : a"
Answer: a
Python program:
a = 46 / 5
b = 31 / 100
c = a / b
Problem: if an average hard drive had a capacity of 0.6 tb in 2000 , and average hard drive capacities double every 5 years , what will be the average hard drive capacity in 2050 ?
Options: a ) 256 , b ) 512 , c ) 768 , d ) 6144 , e ) 1536
Rationale: "0.6 * 2 ^ 10 = 0.6 * 1024 = 614.4 the answer is d ."
Answer: d
Python program:
a = 0 * 6
b = a * 2
c = b * 2
d = c * 2
e = d * 2
f = e * 2
g = f * 2
h = g * 2
i = h * 2
j = i * 2
k = j + 0 
l = k * 10
Problem: two digits in father ' s age are the same as the digit in the son ' s age , but in reverse order . in 5 years father will be twice as old as son will be then . what is the difference in their current age ?
Options: a ) 18 , b ) 16 , c ) 34 , d ) 25 , e ) 12
Rationale: father ' s age = 10 x + y so son ' s age = 10 y + x . . after 5 years , 10 x + y + 5 = 2 * ( 10 y + x + 5 ) . . . . so 5 + 19 y = 8 x . . . check for odd values of y , y = 1 satisfies the eqn with x = 3 . . . so ages are 31 and 13 and ans as found correctly by u is a . . 18
Answer: a
Python program:
a = 5 * 4
b = a - 2
Problem: a train running at the speed of 60 km / hr crosses a pole in 18 seconds . what is the length of the train ?
Options: a ) 187 m , b ) 278 m , c ) 300 m , d ) 150 m , e ) 267 m
Rationale: "speed = ( 60 * 5 / 18 ) m / sec = ( 50 / 3 ) m / sec length of the train = ( speed x time ) = ( 50 / 3 * 18 ) m = 300 m . answer : c"
Answer: c
Python program:
a = 60 * 1000
b = a / 3600
c = b * 18