euclaise/mathqa_programs huggingface dataset:
Problem: on multiplying a number a by 153 , the result obtained was 102325 . however , it is found that both the 2 ' s are wrong . find the correct result .
Options: a ) 104345 , b ) 107375 , c ) 108385 , d ) 109395 , e ) 105355
Rationale: the only thing you actually know about the correct number a is that it is divisible by 153 and has 5 as a factor . you should immediately try to find the factors of 153 and look for them in the options . 153 = 9 * 17 divisibility by 9 is easy to check . only ( d ) satisfies .
Answer: d
Python program:
a = 4 + 3 
b = a * 10
c = 4 + 3 
d = 100 * 10
e = c * d
f = b + e 
g = f + 102325
Problem: andrew purchased 11 kg of grapes at the rate of 98 per kg and 7 kg of mangoes at the rate of 50 per kg . how much amount did he pay to the shopkeeper ?
Options: a ) 1000 , b ) 1055 , c ) 1428 , d ) 1500 , e ) 1080
Rationale: "cost of 11 kg grapes = 98 × 11 = 1078 . cost of 7 kg of mangoes = 50 × 7 = 350 . total cost he has to pay = 1078 + 350 = 1428 c"
Answer: c
Python program:
a = 11 * 98
b = 7 * 50
c = a + b
Problem: two numbers are in the ratio of 3 : 4 . if 12 be subtracted from each , they are in the ratio of 9 : 8 . find the numbers ?
Options: a ) 6,9 , b ) 3,8 , c ) 6,7 , d ) 3,5 , e ) 3,4
Rationale: "( 3 x - 12 ) : ( 4 x - 12 ) = 9 : 8 x = 1 = > 3,4 answer : e"
Answer: e
Python program:
a = 3 * 12
Problem: in an election a candidate who gets 60 % of the votes is elected by a majority of 1380 votes . what is the total number of votes polled ?
Options: a ) a ) 4500 , b ) b ) 5200 , c ) c ) 6900 , d ) d ) 7520 , e ) e ) 6000
Rationale: "let the total number of votes polled be x then , votes polled by other candidate = ( 100 - 60 ) % of x = 40 % of x 60 % of x - 40 % of x = 1380 20 x / 100 = 1380 x = 1380 * 100 / 20 = 6900 answer is c"
Answer: c
Python program:
a = 100 - 60
b = 60 - a
c = b / 100
d = 1380 / c
Problem: rounded to 3 decimal places , 1.003 ^ 4 =
Options: a ) 1.004 , b ) 1.006 , c ) 1.008 , d ) 1.012 , e ) 1.016
Rationale: as compared to 1 , 0.003 is a very small quantity . thus , we can write ( 1 + 0.003 ) ^ 4 is nearly equal to ( 1 + 4 * 0.003 ) = 1.012 . as the question asks for approximation to three decimal places , the further terms will anyways not come into picture . d .
Answer: d
Python program:
a = 3 / 1000
b = a * 3
c = 1 + 3
Problem: the banker ' s gain of a certain sum due 2 years hence at 10 % per annum is rs . 24 . what is the present worth ?
Options: a ) rs . 600 , b ) rs . 500 , c ) rs . 400 , d ) rs . 300 , e ) none of these
Rationale: "explanation : t = 2 years r = 10 % td = ( bg × 100 ) / tr = ( 24 × 100 ) / ( 2 × 10 ) = 12 × 10 = rs . 120 td = ( pw × tr ) / 100 ⇒ 120 = ( pw × 2 × 10 ) / 100 ⇒ 1200 = pw × 2 pw = 1200 / 2 = rs . 600 answer : option a"
Answer: a
Python program:
a = 24 * 100
b = 2 * 10
c = a / b
d = 100 * c
e = 2 * 10
f = d / e
Problem: in a certain pond , 50 fish were caught , tagged , and returned to the pond . a few days later , 50 fish were caught again , of which 2 were found to have been tagged . if the percent of tagged fish in the second catch approximates the percent of tagged fish in the pond , what is the approximate number of fish in the pond ?
Options: a ) 400 , b ) 625 , c ) 1,250 , d ) 2,500 , e ) 10,000
Rationale: "total fish = x percentage of second catch = ( 2 / 50 ) * 100 = 4 % so , x * 4 % = 50 x = 1250 answer : c"
Answer: c
Python program:
a = 2 / 50
b = 50 / a
Problem: at a certain restaurant , the ratio of the number of cooks to the number of waiters is 3 to 10 . when 12 more waiters are hired , the ratio of the number of cooks to the number of waiters changes to 3 to 14 . how many cooks does the restaurant have ?
Options: a ) 4 , b ) 6 , c ) 9 , d ) 12 , e ) 15
Rationale: "originally there were 3 k cooks and 10 k waiters . 14 k = 10 k + 12 k = 3 there are 9 cooks . the answer is c ."
Answer: c
Python program:
a = 12 / 4
b = 12 / 14
c = a * b
Problem: the profit earned by selling an article for 912 is equal to the loss incurred when the same article is sold for 448 . what should be the sale price of the article for making 50 per cent profit ?
Options: a ) 960 , b ) 1060 , c ) 1,200 , d ) 1020 , e ) none of these
Rationale: "let the profit or loss be x and 912 – x = 448 + x or , x = 464 ⁄ 2 = 232 \ cost price of the article = 912 – x = 448 + x = 680 \ sp of the article = 680 × 150 ⁄ 100 = 1020 answer d"
Answer: d
Python program:
a = 912 + 448 
b = a / 2
c = 50 / 100
d = 1 + c 
e = b * d
Problem: working individually , julie can peel potatoes in 10 hours and ted can peel potatoes in 8 hours . if julie and ted work together but independently at the task for 4 hours , at which point ted leaves , how many remaining hours will it take julie to complete the task alone ?
Options: a ) 3 / 15 , b ) 2 / 11 , c ) 1 / 4 , d ) 1 / 3 , e ) 1
Rationale: in first 4 hrs ted will finish 4 / 8 = 1 / 2 of work and julie will finish 4 / 10 work so total 1 / 2 + 2 / 5 = 9 / 10 work is finished and 1 - 9 / 10 = 1 / 10 work remaining . now julie will take ( 1 / 10 ) * 10 = 1 hrs to finish it . so answer is e .
Answer: e
Python program:
a = 1 / 10
b = 1 / 8
c = a + b 
d = 4 * c
e = 1 - d
f = 1 / 10
g = e / f
Problem: x is able to do a piece of work in 8 days and y can do the same work in 12 days . if they can work together for 3 days , what is the fraction of work left ?
Options: a ) 8 / 5 , b ) 6 / 5 , c ) 7 / 5 , d ) 3 / 5 , e ) 4 / 5
Rationale: "explanation : amount of work x can do in 1 day = 1 / 8 amount of work y can do in 1 day = 1 / 12 amount of work x and y can do in 1 day = 1 / 8 + 1 / 12 = 5 / 24 amount of work x and y can together do in 3 days = 3 × ( 5 / 24 ) = 5 / 8 fraction of work left = 1 – 5 / 8 = 3 / 5 answer : option d"
Answer: d
Python program:
a = 8 * 12
b = 8 + 12 
c = a / b
d = 3 / c
Problem: an article is bought for rs . 1450 and sold for rs . 1420 , find the loss percent ?
Options: a ) 2 % , b ) 4 % , c ) 6 % , d ) 8 % , e ) 12 %
Rationale: "1450 - - - - 30 100 - - - - ? = > 2 % answer : a"
Answer: a
Python program:
a = 1420 * 100
b = a / 1450
c = 100 - b
Problem: in a group of 28 junior high school students , 7 take french , 9 take spanish , and 4 take both languages . the students taking both french and spanish are not counted with the 7 taking french or the 10 taking spanish . how many students are not taking either french or spanish ?
Options: a ) 7 , b ) 6 , c ) 9 , d ) 4 , e ) 8
Rationale: "e 8 add 7 + 9 + 4 to get 20 . then subtract 21 from the total students ⇒ 28 – 20 = 8 . answer is e"
Answer: e
Python program:
a = 7 + 9 
b = 28 - a
Problem: when working alone , painter w can paint a room in 2 hours , and working alone , painter x can paint the same room in r hours . when the two painters work together and independently , they can paint the room in 3 / 4 of an hour . what is the value of r ?
Options: a ) 3 / 4 , b ) 1 [ 1 / 5 ] , c ) 1 [ 2 / 5 ] , d ) 1 [ 3 / 4 ] , e ) 2
Rationale: "rate * time = work let painter w ' s rate be w and painter x ' s rate be x r * t = work w * 2 = 1 ( if the work done is same throughout the question then the work done can be taken as 1 ) = > w = 1 / 2 x * r = 1 = > x = 1 / z when they both work together then their rates get added up combined rate = ( w + x ) r * t = work ( w + x ) * 3 / 4 = 1 = > w + x = 4 / 3 = > 1 / 2 + 1 / r = 4 / 3 = > 1 / r = ( 8 - 3 ) / 6 = 5 / 6 = > r = 6 / 5 = 1 [ 1 / 5 ] answer b"
Answer: b
Python program:
a = 4 - 2
b = 2 + 3 
c = 1 / b
d = a + c
Problem: if 36 men can do a piece of work in 15 hours , in how many hours will 15 men do it ?
Options: a ) 22 , b ) 36 , c ) 60 , d ) 88 , e ) 72
Rationale: "explanation : let the required no of hours be x . then less men , more hours ( indirect proportion ) \ inline \ fn _ jvn \ therefore 15 : 36 : : 15 : x \ inline \ fn _ jvn \ leftrightarrow ( 15 x x ) = ( 36 x 15 ) \ inline \ fn _ jvn \ leftrightarrow \ inline \ fn _ jvn x = \ frac { 36 \ times 15 } { 15 } = 36 hence , 15 men can do it in 36 hours . answer : b ) 36"
Answer: b
Python program:
a = 36 * 15
b = a / 15
Problem: buses a and b start from a common bus stop x . bus a begins to travel in a straight line away from bus b at a constant rate of 60 miles per hour . one hour later , bus b begins to travel in a straight line in the exact opposite direction at a constant rate of 80 miles per hour . if both buses travel indefinitely , what is the positive difference , in minutes , between the amount of time it takes bus b to cover the exact distance that bus a has covered and the amount of time it takes bus b to cover twice the distance that bus a has covered ?
Options: a ) 36 , b ) 72 , c ) 132 , d ) 144 , e ) 180
Rationale: "1 st part : - in 1 hr , bus a covers 30 miles . relative speed of bus abus b is ( 80 - 30 ) = 50 mph . so time required for bus b to cover the exact distance as a is 50 * t = 30 t = 3 / 5 = 36 min 2 nd part 80 * t = 2 d - b has to cover twice the distance 30 * ( t + 1 ) = d - a traveled 1 hr more and has to travel only only d so d / 30 - 2 d / 80 = 1 d = 120 t = 3 hrs = 180 min question asks for + ve difference between part 1 and part 2 in minutes = 180 - 36 = 180 min e"
Answer: e
Python program:
a = 2 * 60
b = 2 * 60
c = 80 - b
d = a / c
e = 80 - 60
f = 60 / e
g = d - f
h = g * const_60
Problem: dawson is going with 14 friends on a trip to washington d . c for spring break . airfare and hotel costs a total of $ 13500.00 for the group of 15 friends . how much does each person have to pay for their hotel and airfare ?
Options: a ) $ 900 , b ) $ 800 , c ) $ 850 , d ) $ 950 , e ) $ 920
Rationale: answer = a the total cost of the trip ( $ 13500.00 ) divided by 15 equals $ 900.00 .
Answer: a
Python program:
a = 13500 / 15
Problem: the batting average of a particular batsman is 60 runs in 46 innings . if the difference in his highest and lowest score is 190 runs and his average excluding these two innings is 58 runs , find his highest score .
Options: a ) 179 , b ) 367 , c ) 269 , d ) 177 , e ) 199
Rationale: "explanation : total runs scored by the batsman = 60 * 46 = 2760 runs now excluding the two innings the runs scored = 58 * 44 = 2552 runs hence the runs scored in the two innings = 2760 â € “ 2552 = 208 runs . let the highest score be x , hence the lowest score = x â € “ 190 x + ( x - 190 ) = 208 2 x = 398 x = 199 runs answer : e"
Answer: e
Python program:
a = 60 * 46
b = 46 - 2
c = 58 * b
d = a - c
e = 190 + d 
f = e / 2
Problem: the point a and point b is 30 miles apart , the point b and point c is 25 miles apart . a car travels from point a to point b in 30 min and point b to point c in 40 min . what is the average speed of the car ?
Options: a ) 34.15 , b ) 40.35 , c ) 47.14 , d ) 50.12 , e ) 56.66
Rationale: average speed = total distance covered / total time taken = 55 miles / 70 min = 0.79 miles / min = 47.14 miles / hour answer : c
Answer: c
Python program:
a = 30 / 30
b = 25 / 40
c = a + b 
d = c / 2
e = d * const_60
Problem: 0.009 / x = 0.025 . find the value of x
Options: a ) 0.0003 , b ) 0.36 , c ) 0.3 , d ) 36 , e ) 90
Rationale: "x = 0.009 / 0.36 = 0.25 answer : c"
Answer: c
Python program:
a = 0 / 9
Problem: at the moment there are 54210 tagged birds in a certain wildlife refuge . if exactly 30 percent of all birds in the refuge are tagged , what percent of the untagged birds must be tagged so that half of all birds in the refuge are tagged ?
Options: a ) 66.67 , b ) 66 , c ) 67 , d ) 65.99 , e ) 67.26
Rationale: all birds = 54210 currently tagged = 54210 * 30 / 100 = 16263 so untagged birds = 54210 - 16263 = 37947 half of all birds = 27105 the number of birds to be tagged to make half of all birds tagged = 27105 - 16263 = 10842 so now the question remains - 10842 is how much percentage of untagged birds ( 16263 ) = 10842 * 100 / 16263 = 66.67 answer ( a )
Answer: a
Python program:
a = 100 - 30
Problem: find the cost of fencing around a circular field of diameter 70 m at the rate of rs . 1 a meter ?
Options: a ) 288 , b ) 132 , c ) 220 , d ) 592 , e ) 261
Rationale: "2 * 22 / 7 * 35 = 220 220 * 1 = rs . 220 answer : c"
Answer: c
Python program:
a = 70 / 2
b = circumface * (
Problem: a train takes 10 sec to pass a signal post and covers a distance of 10 km in 15 min . find the length of train ?
Options: a ) 100.1 m , b ) 223.1 m , c ) 111.1 m , d ) 120.3 m , e ) 133.4 m
Rationale: explanation : we know , speed = distance / time speed = 10 / 50 x 60 = 40 x 5 / 18 m / sec = 11.1 m / sec length of train = ( speed x time ) = ( 11.11 x 10 ) = 111.1 m answer is c
Answer: c
Python program:
a = 1000 * 10
b = const_60 * 15
c = a / b
d = c * 10
Problem: an amount of money is to be distributed among faruk , vasim and ranjith in the ratio 3 : 5 : 6 . if vasims share is rs . 1500 , what is the difference between faruk ' s and ranjith ' s shares ?
Options: a ) s 1200 , b ) s 1500 , c ) s 1600 , d ) s 1900 , e ) s 900
Rationale: explanation : let p = faruk , q = vasim , r = ranjith let p = 3 x , q = 5 x and r = 6 x . then , 5 x = 1500 ? x = 300 . p = 900 , q = 1500 and r = 1800 . hence , ( r - p ) = ( 1800 - 900 ) = 900 answer : e
Answer: e
Python program:
a = 1500 / 5
b = 6 - 3
c = a * b
Problem: a farmer spent $ 34 on feed for chickens and goats . he spent 40 % money on chicken feed , which he bought at a 20 % discount off the full price , and spent the rest on goat feed , which he bought at full price . if the farmer had paid full price for both the chicken feed and the goat feed , what amount would he have spent on the chicken feed and goat feed combined ?
Options: a ) $ 37.40 , b ) $ 38.50 , c ) $ 39.20 , d ) $ 39.50 , e ) $ 40.60
Rationale: "a farmer spent 40 % money on chicken feed , so he spent 0.4 * $ 34 = $ 13.6 on chicken feed , thus he spent the remaining 34 - 13.6 = $ 20.4 on goat feed . now , since he bought chicken feed at a 20 % discount then the original price of it was x * 0.8 = $ 13.6 - - > x = $ 17 . therefore if the farmer had paid full price for both the chicken feed and the goat feed , then he would he have spent 17 + 20.4 = $ 37.4 . answer : a ."
Answer: a
Python program:
a = 40 / 100
b = 34 * a
c = b + 34
Problem: a sum of rs . 312 was divided among 100 boys and girls in such a way that each boy gets rs . 3.60 and each girl rs . 2.40 .
Options: a ) 45 , b ) 49 , c ) 52 , d ) 60 , e ) 74
Rationale: let number of boys = x then number of girls = ( 100 - x ) 3.60 x + 2.40 ( 100 - x ) = 312 ¡ ê 1.2 x = 312 - 240 = 72 ¡ ê x = 60 answer : d
Answer: d
Python program:
a = 2 * 4
b = 312 - a
c = 3 - 6
d = b / c
Problem: according to the direction on a can of frozen orange juice concentrate is to be mixed with 3 cans of water to make orange juice . how many 6 - ounce cans of the concentrate are required to prepare 200 6 - ounce servings of orange juice ?
Options: a ) 25 , b ) 34 , c ) 50 , d ) 67 , e ) 50
Rationale: "orange juice concentrate : water : : 1 : 3 total quantity of orange juice = 200 * 6 = 1200 oz so orange juice concentrate : water : : 300 oz : 900 oz no . of 6 oz can = 300 oz / 6 oz = 50 answer e , 50 cans"
Answer: e
Python program:
a = 6 * 200
b = 200 / 10
c = a / b
Problem: if the average ( arithmetic mean ) of a and b is 30 and the average of b and c is 60 , what is the value of c − a ?
Options: a ) 25 , b ) 60 , c ) 90 , d ) 140 , e ) it can not be determined from the information given .
Rationale: - ( a + b = 60 ) b + c = 120 c - a = 60 b . 60
Answer: b
Python program:
a = 60 * 2
b = 30 * 2
c = a - b
Problem: on june 1 a bicycle dealer noted that the number of bicycles in stock had decreased by 4 for each of the past 5 months . if the stock continues to decrease at the same rate for the rest of the year , how many fewer bicycles will be in stock on november 1 than were in stock on january 1 ?
Options: a ) 8 , b ) 12 , c ) 40 , d ) 32 , e ) 36
Rationale: "jan 1 = c feb 1 = c - 4 march 1 = c - 8 april 1 = c - 12 may 1 = c - 16 june 1 = c - 20 july 1 = c - 24 aug 1 = c - 28 sept 1 = c - 32 oct 1 = c - 36 nov 1 = c - 40 difference between stock on november 1 than were in stock on january 1 will be - c - ( c - 40 ) = 40 hence answer will be ( c )"
Answer: c
Python program:
a = 10 - 1
b = a * 4
Problem: the volumes of two cones are in the ratio 1 : 12 and the radii of the cones are in the ratio of 1 : 3 . what is the ratio of their heights ?
Options: a ) a ) 3 : 4
b ) b ) 2 : 7
c ) c ) 2 : 2
d ) d ) 2 : 1
e ) e ) 2 : 9
Rationale: the volume of the cone = ( 1 / 3 ) π r 2 h only radius ( r ) and height ( h ) are varying . hence , ( 1 / 3 ) π may be ignored . v 1 / v 2 = r 12 h 1 / r 22 h 2 = > 1 / 12 = ( 1 ) 2 h 1 / ( 3 ) 2 h 2 = > h 1 / h 2 = 3 / 4 i . e . h 1 : h 2 = 3 : 4 answer : a
Answer: a
Python program:
a = 3 / 4
Problem: two numbers are 35 % and 42 % are less than a third number . how much percent is the second number less than the first ?
Options: a ) 11.769 % , b ) 10.769 % , c ) 12.769 % , d ) 11.69 % , e ) 11.89 %
Rationale: "explanation : i ii iii 65 58 100 65 - - - - - - - - 7 100 - - - - - - ? = > 10.769 % answer b"
Answer: b
Python program:
a = 100 - 35
b = 100 - 42
c = a - b
d = 100 - 35
e = c / d
f = e * 100
Problem: john and roger can finish the work 24 days if they work together . they worked together for 16 days and then roger left . john finished the remaining work in another 16 days . in how many days john alone can finish the work ?
Options: a ) 30 days , b ) 48 days , c ) 70 days , d ) 80 days , e ) 90 days
Rationale: amount of work done by john and roger in 1 day = 1 / 24 amount of work done by john and roger in 16 days = 16 ã — ( 1 / 24 ) = 2 / 3 remaining work â € “ 1 â € “ 2 / 3 = 1 / 3 john completes 1 / 3 work in 16 days amount of work john can do in 1 day = ( 1 / 3 ) / 16 = 1 / 48 = > john can complete the work in 48 days answer : b
Answer: b
Python program:
a = 16 / 24
b = 1 - a
c = 16 / b
Problem: there are 43 stations between ernakulam and chennai . how many second class tickets have to be printed , so that a passenger can travel from one station to any other station ?
Options: a ) 1980 , b ) 1920 , c ) 1990 , d ) 1890 , e ) 1900
Rationale: "the total number of stations = 45 from 45 stations we have to choose any two stations and the direction of travel ( ernakulam to chennai is different from chennai to ernakulam ) in 45 p 2 ways . 45 p 2 = 45 * 44 = 870 answer : a"
Answer: a
Python program:
a = 43 + 2 
b = 43 + 2 
c = b - 1
d = a * c
Problem: if x and y are sets of integers , x # y denotes the set of integers that belong to set x or set y , but not both . if x consists of 12 integers , y consists of 18 integers , and 6 of the integers are in both x and y , then x # y consists of how many integers ?
Options: a ) 6 , b ) 16 , c ) 18 , d ) 30 , e ) 174
Rationale: "the number of integers that belong to set x only is 12 - 6 = 6 ; the number of integers that belong to set y only is 18 - 6 = 12 ; the number of integers that belong to set x or set y , but not both is 6 + 12 = 18 . answer : c ."
Answer: c
Python program:
a = 18 - 6
b = 12 - 6
c = a + b
Problem: when a certain tree was first planted , it was 4 feet tall , and the height of the tree increased by a constant amount each year for the next 6 years . at the end of the 6 th year , the tree was 1 / 6 taller than it was at the end of the 4 th year . by how many feet did the height of the tree increase each year ?
Options: a ) 3 / 10 , b ) 2 / 5 , c ) 1 / 2 , d ) 2 / 3 , e ) 6 / 5
Rationale: "say , the tree grows by x feet every year . then , 4 + 6 x = ( 1 + 1 / 6 ) ( 4 + 4 x ) or , x = 1 / 2 answer c"
Answer: c
Python program:
a = 6 - 4
b = a * 6
c = b - 4
d = 4 / c
Problem: with a uniform speed a car covers the distance in 8 hours . had the speed been increased by 3 km / hr , the same distance could have been covered in 7 1 / 2 hours . what is the distance covered ?
Options: a ) 360 km , b ) 480 km , c ) 278 km , d ) 297 km , e ) 671 km
Rationale: let the distance be x km . then , x / ( 7 1 / 2 ) - x / 8 = 3 2 x / 15 - x / 8 = 3 = > x = 360 km . answer : a
Answer: a
Python program:
a = 1 / 2
Problem: for any integer n greater than 1 , # n denotes the product of all the integers from 1 to n , inclusive . how many prime numbers q are there between # 6 + 2 and # 6 + 6 , inclusive ?
Options: a ) none , b ) one , c ) two , d ) three , e ) four
Rationale: "none is the answer . a . because for every k 6 ! + k : : k , because 6 ! : : k , since k is between 2 and 6 . a"
Answer: a
Python program:
a = 1 + 1
Problem: a dishonest dealer professes to sell goods at the cost price but uses a weight of 500 grams per kg , what is his percent ?
Options: a ) 20 % , b ) 25 % , c ) 29 % , d ) 55 % , e ) 100 %
Rationale: "500 - - - 500 100 - - - ? = > 100 % answer : e"
Answer: e
Python program:
a = 100 / 500
b = 3 + 2 
c = b * 2
d = 100 * c
e = a * d
f = e - 100
Problem: ( 7895632 x 881 ) = ?
Options: a ) 6846381250 , b ) 6584638130 , c ) 6584638135 , d ) 6584638140 , e ) 6956051792
Rationale: 7895632 x 881 = 6956051792 ans e
Answer: e
Python program:
a = 4 + 1 
b = a ** 4
c = 7895632 * b
Problem: solve the equation for x : 8 x - 40 + 2 x = 5 + 10 - x
Options: a ) 4 , b ) 10 , c ) 7 , d ) 5 , e ) 3
Rationale: "d 5 10 x + x = 15 + 40 11 x = 55 = > x = 5"
Answer: d
Python program:
a = 40 + 5 
b = 8 + 8 
c = a / b
Problem: a waitress ' s income consists of her salary and tips . during one week , her tips were 9 / 4 of her salary . what fraction of her income for the week came from tips ?
Options: a ) 9 / 13 , b ) 1 / 6 , c ) 1 / 3 , d ) 4 / 9 , e ) 5 / 9
Rationale: her tips were 9 / 4 of her salary . let ' s say her salary = $ 4 this mean her tips = ( 9 / 4 ) ( $ 4 ) = $ 9 so , her total income = $ 4 + $ 9 = $ 13 what fraction of her income for the week came from tips $ 9 $ 13 = 9 / 13 = a
Answer: a
Python program:
a = 9 + 4 
b = 9 / a
Problem: a can do a piece of work in 8 days . b can do it in 12 days . with the assistance of c they completed the work in 4 days . find in how many days can c alone do it ?
Options: a ) 87 days , b ) 20 days , c ) 16 days , d ) 24 days , e ) 36 days
Rationale: "c = 1 / 4 - 1 / 8 - 1 / 12 = 1 / 24 = > 24 days answer : d"
Answer: d
Python program:
a = 8 * 12
b = 8 * 12
c = 8 * 12
d = c / 8
e = 8 * 12
f = e / 12
g = d + f 
h = g * 4
i = b - h
j = i / 4
k = a / j
Problem: find the value of m 62519 x 9999 = m ?
Options: a ) 724533811 , b ) 625127481 , c ) 545463251 , d ) 725117481 , e ) 677899932
Rationale: "62519 x 9999 = 62519 x ( 10000 - 1 ) = 62519 x 10000 - 62519 x 1 = 625190000 - 62519 = 625127481 b"
Answer: b
Python program:
a = 9999 - 4
b = a * 62519
Problem: the difference between compound interest and simple interest on a sum for 3 years at 10 % p . a . is rs . 124 find the sum .
Options: a ) rs . 5000 , b ) rs . 4000 , c ) rs . 6000 , d ) rs . 8000 , e ) rs . 7000
Rationale: "for 3 years , we know c . i - s . i = p ( r / 100 ) ^ 3 + 3 ( r / 100 ) ^ 2 so , putting all values we have , 124 = p ( ( 10 / 100 ) ^ 3 + 3 ( 10 / 100 ) ^ 2 ) = 4000 answer : b"
Answer: b
Python program:
a = 3 / 100
b = 1 + a 
c = b ** 10
d = 3 / 100
e = 10 * d
f = 1 + e 
g = c - f
h = 124 / g
Problem: an italian sausage is 8 inches long . how many pieces of sausage can be cut from the 8 - inch piece of sausage if each piece is to be 2 / 3 of an inch ?
Options: a ) 12 , b ) 32 , c ) 22 , d ) 15 , e ) 20
Rationale: number of pieces = italian sausage ÷ 2 / 3 of an inch = 8 ÷ 2 / 3 = 8 / 1 ÷ 2 / 3 = 8 / 1 * 3 / 2 = 24 / 2 = 12 . answer is a .
Answer: a
Python program:
a = 2 / 3
b = 8 / a
Problem: a is a working partner and b is a sleeping partner in the business . a puts in rs . 3500 and b rs . 2500 , a receives 10 % of the profit for managing the business the rest being divided in proportion of their capitals . out of a total profit of rs . 9600 , money received by a is ?
Options: a ) 1978 , b ) 2707 , c ) 7728 , d ) 4200 , e ) 6000
Rationale: "35 : 25 = > 7 : 5 9600 * 10 / 100 = 960 9600 - 960 = 8640 8640 * 7 / 12 = 5040 + 960 = 6000 answer : e"
Answer: e
Python program:
a = 10 / 100
b = 1 - a
c = 9600 * b
d = 3500 + 2500 
e = 2500 / d
f = c * e
g = 9600 - f
Problem: what is the dividend . divisor 20 , the quotient is 8 and the remainder is 6
Options: a ) a ) 145 , b ) b ) 148 , c ) c ) 150 , d ) d ) 153 , e ) e ) 166
Rationale: "d = d * q + r d = 20 * 8 + 6 d = 160 + 6 d = 166 answer : e"
Answer: e
Python program:
a = 20 * 8
b = a + 6