euclaise/mathqa_programs huggingface dataset:
Problem: two persons a and b can complete a piece of work in 15 days and 30 days respectively . if they work together , what part of the work will be completed in 5 days ?
Options: a ) 1 / 8 , b ) 1 / 3 , c ) 1 / 6 , d ) 1 / 2 , e ) 5 / 3
Rationale: "a ' s one day ' s work = 1 / 15 b ' s one day ' s work = 1 / 30 ( a + b ) ' s one day ' s work = 1 / 15 + 1 / 30 = 1 / 10 the part of the work completed in 5 days = 5 ( 1 / 10 ) = 1 / 2 . answer : d"
Answer: d
Python program:
a = 1 / 15
b = 1 / 30
c = a + b 
d = 5 * c
Problem: the temperature of a certain cup of coffee 10 minutes after it was poured was 120 degrees fahrenheit . if the temperature f of the coffee t minutes after it was poured can be determined by the formula f = 120 ( 2 ^ - at ) + 60 , where f is in degrees fahrenheit and a is a constant . then the temperature of the coffee 50 minutes after it was poured was how many degrees fahrenheit ?
Options: a ) 63.75 , b ) 75 , c ) 80 , d ) 85 , e ) 90
Rationale: "answer : b the temperature of coffee 10 minutes after it was poured ( 120 f ) will help in solving the constant “ a ” . 120 = 120 ( 2 ^ 10 a ) + 60 2 ^ - 1 = 2 ^ 10 a a = - 1 / 10 the temperature of coffee 50 minutes after it was poured is : f = 120 ( 2 ^ - 50 / 10 ) + 60 f = 120 * 1 / 32 + 60 f = 15 / 4 + 60 f = 255 / 4 = 63.75 a"
Answer: a
Python program:
a = 60 / 10
b = 1 - 2
c = a * b
d = 2 ** c
e = d * 120
f = e + 60
Problem: water boils at 212 ° f or 100 ° c and ice melts at 32 ° f or 0 ° c . if the temperature of a pot of water is 40 ° c , what is the temperature of the pot of water in ° f ?
Options: a ) 85 ° f , b ) 92 ° f , c ) 96 ° f , d ) 99 ° f , e ) 104 ° f
Rationale: "let f and c denote the temperature in fahrenheit and celsius respectively . ( f - 32 ) / ( 212 - 32 ) = ( c - 0 ) / ( 100 - 0 ) f = 9 c / 5 + 32 f = 9 ( 40 ) / 5 + 32 = 104 ° f the answer is e ."
Answer: e
Python program:
a = 212 - 32
b = a / 100
c = b * 40
d = c + 32
Problem: the number of natural numbers n such that ( n + 1 ) ^ 2 / ( n + 7 ) is an integer , is ?
Options: a ) 4 , b ) 5 , c ) 6 , d ) 7 , e ) 8
Rationale: we can use ( n + 1 ) ^ 2 greater than ( n + 7 ) which gives n > 2 , - 3 . . . . . . . . now there are four integers - 2 . - 1 , 01 in between - 3 and 2 . so answer is 4 . answer : a
Answer: a
Python program:
a = 7 - 3
Problem: total dinning bill of 8 people was $ 139.00 and 10 % tip divided the bill evenly ? what is the bill amount each person shared .
Options: a ) 11.84 , b ) 12.84 , c ) 23.84 , d ) 19.11 , e ) 10.12
Rationale: "dinner bill of 8 person = 139 + 10 % tip so , 10 % of 139 = ( 139 * 10 ) / 100 = 13.9 so , the actual total amount = 139 + 13.9 = $ 152.9 so per head bill = 152.9 / 8 = $ 19.11 answer : d"
Answer: d
Python program:
a = 1 / 10
b = a + 1 
c = 139 * 0
d = c / 8
Problem: positive integer y is 50 percent of 50 percent of positive integer x , and y percent of x equals 100 . what is the value of x ?
Options: a ) 50 , b ) 100 , c ) 200 , d ) 1,000 , e ) 2,000
Rationale: "y = 50 % of 50 % 0 f x = x / 4 and y / 100 of x = 100 y / 100 * 4 y = 100 y = 50 and x = 200 answer - c"
Answer: c
Python program:
a = 50 / 100
b = 50 / 100
c = a * b
d = c * 1000
Problem: 3 / 4 of 1 / 2 of 2 / 5 of 5060 = ?
Options: a ) 392 , b ) 759 , c ) 753 , d ) 493 , e ) 540
Rationale: "b 759 ? = 5060 * ( 2 / 5 ) * ( 1 / 2 ) * ( 3 / 4 ) = 759"
Answer: b
Python program:
a = 3 / 4
b = 1 / 2
c = a * b
d = 2 / 5
e = c * d
f = e * 5060
Problem: the average of 10 numbers is 40.2 . later it is found that two numbers have been wrongly copied . the first is 18 greater than the actual number and the second number added is 13 instead of 31 . find the correct average .
Options: a ) 40.2 , b ) 40.4 , c ) 40.6 , d ) 40.8 , e ) none of the above
Rationale: sum of 10 numbers = 402 corrected sum of 10 numbers = 402 – 13 + 31 – 18 = 402 hence , new average = 402 ⁄ 10 = 40.2 answer a
Answer: a
Python program:
a = 40 * 2
b = 13 + 18 
c = a + b 
d = c - 31
e = d / 10
Problem: how many integers between 100 and 190 , inclusive , can not be evenly divided by 3 nor 5 ?
Options: a ) 42 , b ) 44 , c ) 46 , d ) 48 , e ) 50
Rationale: "the total numbers between 100 and 190 , inclusive , is 91 . 3 * 34 = 102 and 3 * 63 = 189 so the number of multiples of 3 is 30 . 5 * 20 = 100 and 5 * 38 = 190 so the number of multiples of 5 is 19 . however , the multiples of 15 have been counted twice . 15 * 7 = 105 and 15 * 12 = 180 so the number of multiples of 15 is 6 . thus the total number is 91 - 30 - 19 + 6 = 48 . the answer is d ."
Answer: d
Python program:
a = 2 * 100
b = 3 + 4 
c = b * 10
d = a + c 
e = d + 2 
f = 190 - e
Problem: $ 300 is divided amongst a , b and c so that a may get 2 / 3 as much as b and c together , b may get 6 / 9 as much as a and c together , then the share of a is
Options: a ) $ 100 , b ) $ 150 , c ) $ 125 , d ) $ 120 , e ) $ 250
Rationale: "a : ( b + c ) = 2 : 3 a ' s share = 300 * 2 / 5 = $ 120 answer is d"
Answer: d
Python program:
a = 2 / 3
b = a + 1 
c = 300 / b
d = 2 / 3
e = c * d
Problem: what is the cp of rs 100 stock at 4 discount , with 1 / 5 % brokerage ?
Options: a ) 96.9 , b ) 96.3 , c ) 96.2 , d ) 96.7 , e ) 96.21
Rationale: explanation : use the formula , cp = 100 – discount + brokerage % cp = 100 - 4 + 1 / 5 96.2 thus the cp is rs 96.2 . answer : c
Answer: c
Python program:
a = 100 - 4
b = 1 / 5
c = a + b
Problem: if an article is sold at 18 % profit instead of 11 % profit , then the profit would be $ 63 more . what is the cost price ?
Options: a ) $ 600 , b ) $ 900 , c ) $ 1200 , d ) $ 1500 , e ) $ 1800
Rationale: "7 % * cost price = $ 63 1 % * cost price = $ 63 / 7 = $ 9 the cost price is $ 900 . the answer is b ."
Answer: b
Python program:
a = 63 / 11
b = a * 100
Problem: how many x ways can you group 3 people from 4 sets of twins if no two people from the same set of twins can be chosen ?
Options: a ) 3 , b ) 16 , c ) 28 , d ) 32 , e ) 56
Rationale: ways to select 3 people from 8 people ( 4 twins x 2 ) = 8 c 3 = 56 ways to select 1 twin + 1 people = 4 c 1 * 6 c 1 = 24 ways to select a group 3 people from 4 sets of twins if no two people from the same set of twins can be chosen x = 56 - 24 = 32 ans : d
Answer: d
Python program:
a = 2 ** 3
b = a * 4
Problem: in the game of dubblefud , yellow chips , blue chips and green chips are each worth 2 , 4 and 5 points respectively . in a certain selection of chips , the product of the point values of the chips is 16000 . if the number of blue chips in this selection equals the number of green chips , how many yellow chips are in the selection ?
Options: a ) 1 , b ) 2 , c ) 3 , d ) 4 , e ) 5
Rationale: this is equivalent to : - 2 x * 4 y * 5 z = 16000 y = z ( given ) 2 x * 4 y * 5 y = 16000 2 x * y ^ 2 = 16000 / 20 2 x * y ^ 2 = 800 now from options given we will figure out which number will divide 800 and gives us a perfect square : - which gives us x = 4 as 2 * 4 * y ^ 2 = 800 y ^ 2 = 100 y = 10 number of yellow chips = 4 hence d
Answer: d
Python program:
a = 2 * 4
b = a * 5
c = 16000 / b
d = 10 ** 2
e = c / d
Problem: if a light flashes every 10 seconds , how many times will it flash in 2 / 3 of an hour ?
Options: a ) 152 , b ) 241 , c ) 345 , d ) 451 , e ) 542
Rationale: "there are 60 minutes in an hour . in 2 / 3 of an hour there are ( 60 * 2 / 3 ) minutes = 40 minutes . in 2 / 3 of an hour there are ( 60 * 40 ) seconds = 2400 seconds . light flashed for every 10 seconds . in 2400 seconds 2400 / 10 = 240 times . the count start after the first flash , the light will flashes 241 times in 2 / 3 of an hour . answer : b"
Answer: b
Python program:
a = 3600 / 4
b = a * 3
c = b / 10
Problem: john can complete a given task in 20 days . jane will take only 12 days to complete the same task . john and jane set out to complete the task by beginning to work together . however , jane was indisposed 5 days before the work got over . in how many days did the work get over from the time john and jane started to work on it together ?
Options: a ) 95 / 8 , b ) 93 / 8 , c ) 90 / 8 , d ) 12 , e ) 10
Rationale: "in such questions , you need to start from the end . last 4 days john works alone and completes 5 * ( 1 / 20 ) = 1 / 4 of the work . so 3 / 4 of the work should have been completed by the two of them together before jane left . their combined rate of work is 1 / 20 + 1 / 12 = 8 / 60 time taken to complete 3 / 4 of the work = ( 3 / 4 ) / ( 8 / 60 ) = 45 / 8 days . so total number of days taken to complete the work = 45 / 8 + 5 = 95 / 8 days . a"
Answer: a
Python program:
a = 20 * 12
b = 12 * 5
c = a - b
d = 12 + 20 
e = c / d
f = 5 + e
Problem: if the wheel is 18 cm then the number of revolutions to cover a distance of 1056 cm is ?
Options: a ) 18 , b ) 26 , c ) 14 , d ) 12 , e ) 9.3
Rationale: "2 * 22 / 7 * 18 * x = 1056 = > x = 9.3 answer : e"
Answer: e
Python program:
a = 3 * 100
b = 1 * 10
c = a + b 
d = c + 4 
e = d / 100
f = 2 * e
g = f * 18
h = 1056 / g
Problem: if a large pizza has a radius that is 60 % larger that that of a medium pizza , what is the percent increase in area between a medium and a large pizza ?
Options: a ) 30 % , b ) 60 % , c ) 98 % , d ) 120 % , e ) 156 %
Rationale: "let the radius of medium pizza be r . then the radius of large pizza is 1.6 r . the area of the medium pizza is pi * r ^ 2 the area of the large pizza is pi * ( 1.6 * r ) ^ 2 = 2.56 * pi * r ^ 2 , an increase of 156 % . the answer is e ."
Answer: e
Python program:
a = 60 / 100
b = 1 + a 
c = b ** 2
d = c - 1
e = d * 100
Problem: if a - b = 3 and a ( power 2 ) + b ( power 2 ) = 25 , find the value of ab .
Options: a ) 5 , b ) 8 , c ) 4 , d ) 10 , e ) 3
Rationale: 2 ab = ( a ( power 2 ) + b ( power 2 ) - ( a - b ) ( power 2 ) = 25 - 9 = 16 ab = 8 . answer is b .
Answer: b
Python program:
a = 3 ** 2
b = 25 - a
c = b / 2
Problem: on a certain day , orangeade was made by mixing a certain amount of orange juice with an equal amount of water . on the next day , orangeade was made by mixing the same amount of orange juice with four times the amount of water . on both days , all the orangeade that was made was sold . if the revenue from selling the orangeade was the same for both days and if the orangeade was sold at $ 0.40 per glass on the first day , what was the price per glass on the second day ?
Options: a ) $ 0.16 , b ) $ 0.20 , c ) $ 0.30 , d ) $ 0.40 , e ) $ 0.45
Rationale: "on the first day 1 unit of orange juice and 1 unit of water was used to make 2 units of orangeade ; on the second day 1 unit of orange juice and 4 units of water was used to make 5 units of orangeade ; so , the ratio of the amount of orangeade made on the first day to the amount of orangeade made on the second day is 2 to 5 . naturally the ratio of the # of glasses of orangeade made on the first day to the # of glasses of orangeade made on the second day is 2 to 5 . we are told thatthe revenue from selling the orangeade was the same for both daysso the revenue from 2 glasses on the first day equals to the revenue from 5 glasses on the second day . say the price of the glass of the orangeade on the second day was $ x then 2 * 0.4 = 5 * x - - > x = $ 0.16 . answer : a ."
Answer: a
Python program:
a = 1 + 1 
b = a * 0
c = 1 + 2 
d = b / c
Problem: a car takes 6 hours to cover a distance of 144 km . how much should the speed in kmph be maintained to cover the same direction in 3 / 2 th of the previous time ?
Options: a ) 50 kmph , b ) 60 kmph , c ) 65 kmph , d ) 16 kmph , e ) none
Rationale: "time = 6 distence = 144 3 / 2 of 6 hours = 6 * 3 / 2 = 9 hours required speed = 144 / 9 = 16 kmph d )"
Answer: d
Python program:
a = 6 * 3
b = a / 2
c = 144 / b
Problem: a man purchased 3 blankets @ rs . 100 each , 5 blankets @ rs . 150 each and two blankets at a certain rate which is now slipped off from his memory . but he remembers that the average price of the blankets was rs . 140 . find the unknown rate of two blankets ?
Options: a ) 350 , b ) 550 , c ) 490 , d ) 450 , e ) 457
Rationale: "10 * 140 = 15 = 1400 3 * 100 + 5 * 150 = 1050 1400 – 1050 = 350 answer : a"
Answer: a
Python program:
a = 10 * 150
b = 3 * 100
c = 5 * 150
d = b + c 
e = a - d
Problem: how long will it take a train travelling at 78 kmph to pass an electric pole if the train is 110 meters in lenght ?
Options: a ) 2.07 , b ) 3.07 , c ) 5.07 , d ) 4.07 , e ) 2
Rationale: sol . speed = [ 78 x 5 / 18 ] m / sec = 21.7 m / sec . time taken = ( 110 / 21.7 ) sec = 5.07 sec . answer c
Answer: c
Python program:
a = 110 / 1000
b = a / 78
c = b * 3600
Problem: find the least number which when divided by 20,25 , 35,40 leaves remainder 14,19 , 29,34 respectively .
Options: a ) 1394 , b ) 1450 , c ) 1245 , d ) 2564 , e ) 1256
Rationale: "the difference of 20 - 14 = 6 , 25 - 19 = 6 , 35 - 29 = 6 , 40 - 34 = 6 lcm of 20,25 , 35,40 = 1400 required number = 1400 - 6 = 1394 answer is a"
Answer: a
Python program:
a = math.lcm(20, 25)
b = 14 + 19
Problem: the cash realised on selling a 14 % stock is rs . 106.25 , brokerage being 1 / 4 % is
Options: a ) 123 , b ) 106 , c ) 100 , d ) 156 , e ) 240
Rationale: explanation : cash realised = rs . ( 106.25 - 0.25 ) = rs . 106 . answer : b
Answer: b
Python program:
a = 1 / 4
b = 106 - 25
Problem: if a car went the first third of the distance at 80 kmh , the second third at 24 kmh , and the last third at 54 kmh , what was the average speed of the car for the entire trip ?
Options: a ) 36 kmh , b ) 40 kmh , c ) 41 kmh , d ) 44 kmh , e ) 50 kmh
Rationale: "assume d / 3 = 2160 ( this number is convenient because it is divisible by 80 , 24 and 54 ) so : 2160 = 80 * t 1 = 27 hrs 2160 = 24 * t 2 = 90 hrs 2160 = 54 * t 3 = 40 hrs t = t 1 + t 2 + t 3 = 157 hrs d = rt ( 240 * 3 ) = r * 157 r = 41.27 answer : c"
Answer: c
Python program:
a = 1 / 80
b = 1 / 24
c = a + b 
d = 1 / 54
e = c + d 
f = 3 / e
Problem: one side of a rectangle is 3 cm shorter than the other side . if we increase the length of each side by 1 cm , then the area of the rectangle will increase by 22 cm 2 . find the lengths of all sides .
Options: a ) 10 and 3 , b ) 7 and 10 , c ) 10 and 7 , d ) 3 and 10 , e ) 12 and 9
Rationale: "let x be the length of the longer side x > 3 , then the other side ' s length is x − 3 cm . then the area is s 1 = x ( x - 3 ) cm 2 . after we increase the lengths of the sides they will become ( x + 1 ) and ( x − 3 + 1 ) = ( x − 2 ) cm long . hence the area of the new rectangle will be a 2 = ( x + 1 ) ⋅ ( x − 2 ) cm 2 , which is 22 cm 2 more than the first area . therefore a 1 + 22 = a 2 x ( x − 3 ) + 22 = ( x + 1 ) ( x − 2 ) x 2 − 3 x + 22 = x 2 + x − 2 x − 2 2 x = 24 x = 12 . so , the sides of the rectangle are 12 cm and ( 12 − 3 ) = 9 cm long . so answer is e ."
Answer: e
Python program:
a = 22 / 2
b = a + 1 
c = b - 3
Problem: rice weighing 25 / 4 pounds was divided equally and placed in 4 containers . how many ounces of rice were in each container ? ( note that 1 pound = 16 ounces )
Options: a ) 22 , b ) 25 , c ) 28 , d ) 31 , e ) 34
Rationale: "25 / 4 ÷ 4 = 25 / 16 pounds in each container 25 / 16 pounds * 16 ounces / pound = 25 ounces in each container the answer is b ."
Answer: b
Python program:
a = 25 / 4
b = a * 16
c = b / 4
Problem: a towel , when bleached , lost 20 % of its length and 20 % of its breadth . what is the percentage decrease in area ?
Options: a ) 24 % , b ) 36 % , c ) 32 % , d ) 54 % , e ) 64 %
Rationale: "percentage change in area = ( − 20 − 20 + ( 20 × 20 ) / 100 ) % = − 36 % i . e . , area is decreased by 36 % answer : b"
Answer: b
Python program:
a = 100 * 100
b = 100 - 20
c = 100 - 20
d = b * c
e = a - d
f = e / 100
Problem: sara bought both german chocolate and swiss chocolate for some cakes she was baking . the swiss chocolate cost $ 3.6 per pound , and german chocolate cost $ 3 per pound . if the total the she spent on chocolate was $ 36 and both types of chocolate were purchased in whole number of pounds , how many total pounds of chocolate she purchased ?
Options: a ) 7 , b ) 8 , c ) 10 , d ) 15 , e ) 36 / 3
Rationale: "if there were all the expensive ones , 3.6 . . . there would be 36 / 3.6 or 10 of them but since 3 $ ones are also there , answer has to be > 10 . . . . . if all were 3 $ ones , there will be 36 / 3 ans e"
Answer: e
Python program:
a = 3 + 6 
b = a / 2
c = 36 / b
Problem: a business finds that their ratio of spending to income is 5 to 9 . their total profit is $ 48000 . what is their total income ?
Options: a ) $ 90000 , b ) $ 108000 , c ) $ 119000 , d ) $ 126000 , e ) $ 140000
Rationale: let x equal the amount of spending , and y equal the amount of income . we know that x = 5 / 9 y we also know that x = y - 48000 therefore we can simplify to : y - 48000 = 5 / 9 y we isolate y , and get : 4 / 9 y = 48000 and to solve for y , we get : y = 48000 answer : b
Answer: b
Python program:
a = 9 - 5
b = 48000 / a
c = b * 9
Problem: in a certain animal population , for each of the first 3 months of life , the probability that an animal will die during that month is 1 / 10 . for a group of 300 newborn members of the population , approximately how many would be expected to survive the first 3 months of life ?
Options: a ) 219 , b ) 246 , c ) 252 , d ) 262 , e ) 270
Rationale: "number of newborns that can die in first month = 1 / 10 * 300 = 30 survived = 270 number of newborns that can die in second month = 1 / 10 * 270 = 27 survived = 243 number of newborns that can die in third month = 1 / 10 * 243 = 24 survived = 219 answer : a"
Answer: a
Python program:
a = 1 / 10
b = 1 - a
c = 300 * b
d = 1 / 10
e = 1 - d
f = c * e
g = 1 / 10
h = 1 - g
i = f * h
Problem: what is the range of all the roots of | x ^ 2 - 6 | = x ?
Options: a ) 4 , b ) 3 , c ) 2 , d ) 1 , e ) 5
Rationale: "we get 2 quadratic equations here . . 1 ) x ^ 2 - x - 2 = 0 . . . . . . . roots 2 , - 1 2 ) x ^ 2 + x - 2 = 0 . . . . . . . . roots - 2 , 1 inserting each root in given equation , it can be seen that - 1 and - 2 do not satisfy the equations . so value of x for given equation . . . . x = 6 or x = 1 i guess range is 6 - 1 = 5 e"
Answer: e
Python program:
a = math.sqrt(6)
Problem: if 6 spiders make 3 webs in 7 days , then how many days are needed for 1 spider to make 1 web ?
Options: a ) 10 , b ) 12 , c ) 14 , d ) 15 , 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 ) 6 : 1 ( webs ) 1 : 7 } : : x : 3 â ‡ ’ 6 ã — 1 ã — 7 = 1 ã — 3 ã — x â ‡ ’ x = 14 answer : option c"
Answer: c
Python program:
a = 1 * 6
Problem: how many seconds will a train 100 meters long take to cross a bridge 200 meters long if the speed of the train is 36 kmph ?
Options: a ) 22 sec , b ) 27 sec , c ) 30 sec , d ) 24 sec , e ) 11 sec
Rationale: "explanation : d = 100 + 200 = 300 s = 36 * 5 / 18 = 10 mps t = 300 / 10 = 10 sec answer : option c"
Answer: c
Python program:
a = 200 + 100 
b = 36 * const_0_2778
c = a / b
Problem: a water tank is three - fifths full . pipe a can fill a tank in 15 minutes and pipe b can empty it in 6 minutes . if both the pipes are open , how many minutes will it take to empty or fill the tank completely ?
Options: a ) 2 , b ) 4 , c ) 6 , d ) 8 , e ) 10
Rationale: "the combined rate of filling / emptying the tank = 1 / 15 - 1 / 6 = - 1 / 10 since the rate is negative , the tank will be emptied . a full tank would take 10 minutes to empty . since the tank is only three - fifths full , the time is ( 3 / 5 ) * 10 = 6 minutes the answer is c ."
Answer: c
Python program:
a = 2 + 3 
b = 4 / a
c = 1/(6)
d = 1/(15)
e = c - d
f = b / e
Problem: in a bag , there are 5 green , 6 black and 7 red pens . one pen is picked up randomly . what is the probability that it is neither red nor green ?
Options: a ) 5 / 18 , b ) 7 / 18 , c ) 1 / 3 , d ) 1 / 2 , e ) 1 / 5
Rationale: explanation : neither red nor green means the pen drawn is black . total number of outcomes = ( 5 + 6 + 7 ) = 18 . number of favourable outcomes = 6 = number of black pens . hence , probability of the event = 6 / 18 = 1 / 3 . answer : c
Answer: c
Python program:
a = 5 + 6 
b = a + 7 
c = 6 / b
Problem: if ( c - a ) / ( c - b ) = 1 , then ( 5 b + 5 a ) / ( c - a ) =
Options: a ) 10 , b ) 1 , c ) 1.5 , d ) 2 , e ) 2.5
Rationale: "let ' s say c = 2 , b = 1 , a = 1 so that our 1 st expression holds true . now , ibsert those numbers in the second expression and we ' ll get 10 answer a ( hopefully ) ) )"
Answer: a
Python program:
a = 5 - 2
b = a * 5
Problem: the marks obtained by polly and sandy are in the ratio 5 : 6 and those obtained by sandy and willy are in the ratio of 9 : 7 . the marks obtained by polly and willy are in the ratio of . . . ?
Options: a ) 9 : 8 , b ) 11 : 10 , c ) 13 : 12 , d ) 15 : 14 , e ) 17 : 16
Rationale: polly : sandy = 5 : 6 = 15 : 18 sandy : willy = 9 : 7 = 18 : 14 polly : sandy : willy = 15 : 18 : 14 polly : willy = 15 : 14 the answer is d .
Answer: d
Python program:
a = 5 * 9
b = 6 * 7
c = a / b
Problem: x can finish a work in 36 days . y can finish the same work in 24 days . y worked for 12 days and left the job . how many days does x alone need to finish the remaining work ?
Options: a ) 12 , b ) 13 , c ) 16 , d ) 17 , e ) 18
Rationale: "work done by x in 1 day = 1 / 36 work done by y in 1 day = 1 / 24 work done by y in 12 days = 12 / 24 = 1 / 2 remaining work = 1 – 1 / 2 = 1 / 2 number of days in which x can finish the remaining work = ( 1 / 2 ) / ( 1 / 36 ) = 18 e"
Answer: e
Python program:
a = 1 / 24
b = 12 * a
c = 1 - b
d = 1 / 36
e = c / d
Problem: a ( 4 , w ^ 2 ) is the ( x , y ) coordinate of point located on the parabola y = x ^ 2 + 9 . what is the value of w ?
Options: a ) 3 . , b ) 4 . , c ) 5 . , d ) 6 . , e ) 9 .
Rationale: "y = x ^ 2 + 9 w ^ 2 = 4 ^ 2 + 9 w ^ 2 = 25 w = 5 answer c"
Answer: c
Python program:
a = 4 ** 2
b = a - 9
c = 9 / 4
d = b ** c
Problem: two cars started at the same time , from the same point , driving along the same road . the rate of the first car is 50 mph and the rate of the second car is 60 mph . how long will it take for the distance between the two cars to be 30 miles ?
Options: a ) 1 hrs , b ) 2 hrs , c ) 3 hrs , d ) 4 hrs , e ) 5 hrs
Rationale: car 1 50 50 50 total = 150 car 2 60 60 60 total = 180 differece = 30 miles after 3 hrs . answer : c
Answer: c
Python program:
a = 60 - 50
b = 30 / a
Problem: a train 240 m long passes a pole in 24 seconds . how long will it take to pass a platform 650 m long ?
Options: a ) 65 , b ) 80 , c ) 85 , d ) 82 , e ) 89
Rationale: speed = ( 240 / 24 ) m / sec = 10 m / sec . therefore , required time = ( 240 + 650 ) / 10 sec = 89 sec . answer is e .
Answer: e
Python program:
a = 240 + 650 
b = a / speed
Problem: a feed store sells two varieties of birdseed : brand a , which is 40 % millet and 60 % sunflower , and brand b , which is 65 % millet and 35 % safflower . if a customer purchases a mix of the two types of birdseed that is 50 % millet , what percent of the mix is brand a ?
Options: a ) 40 % , b ) 45 % , c ) 50 % , d ) 60 % , e ) 55 %
Rationale: "another method to solve this question using equations : 1 kg of brand a will have 400 g millet and 600 g sunflower . 1 kg of brand b will gave 650 g millet and 350 g sunflower . suppose , x kg of brand a and y kg of brand b are in the mixture . then total weight of millet = 400 x + 650 y g total weight of mixture = 1000 x + 1000 y g given that millet is 500 % hence ( 400 x + 650 y ) / ( 1000 x + 1000 y ) = 1 / 2 or , 800 x + 1300 y = 1000 x + 1000 y or 300 y = 200 x or , x / y = 3 / 2 % of brand a = ( 3 / ( 3 + 2 ) ) * 100 = 60 % hence answer is d"
Answer: d
Python program:
a = 3 + 2 
b = 3 / a
c = b * 100
Problem: a contractor is engaged for 30 days on the condition thathe receives rs . 25 for each day he works & is fined rs . 7.50 for each day is absent . he gets rs . 360 in all . for how many days was he absent ?
Options: a ) 8 , b ) 12 , c ) 15 , d ) 17 , e ) 19
Rationale: "30 * 25 = 750 360 - - - - - - - - - - - 380 25 + 7.50 = 32.5 390 / 32.5 = 12 b"
Answer: b
Python program:
a = 7 * 50
b = a + 360 
c = 7 + 50 
d = b / c
e = 30 - d