euclaise/mathqa_programs huggingface dataset:
Problem: by weight , liquid x makes up 0.8 percent of solution a and 1.8 percent of solution b . if 300 grams of solution a are mixed with 700 grams of solution b , then liquid x accounts for what percent of the weight of the resulting solution ?
Options: a ) 1.5 % , b ) 1.9 % , c ) 10 % , d ) 15 % , e ) 19 %
Rationale: "i think there is a typo in question . it should have been ` ` by weight liquid ' x ' makes up . . . . . ` ` weight of liquid x = 0.8 % of weight of a + 1.8 % of weight of b when 300 gms of a and 700 gms of b is mixed : weight of liquid x = ( 0.8 * 300 ) / 100 + ( 1.8 * 700 ) / 100 = 15 gms % of liquid x in resultant mixture = ( 15 / 1000 ) * 100 = 1.5 % answer : 1.5 % answer : a"
Answer: a
Python program:
a = 300 * 0
b = 700 * 1
c = a + b 
d = c / 1000
Problem: two pipes a and b can fill a tank in 10 hour and 15 hours respectively . if both the pipes are opened simultaneously , how much time will be taken to fill the tank ?
Options: a ) 2 hrs , b ) 6 hrs , c ) 5 hrs , d ) 4 hrs , e ) 1 hr
Rationale: "part filled by a in 1 hour = 1 / 10 part filled by b in 1 hour = 1 / 15 part filled by a + b in 1 hour = 1 / 10 + 1 / 15 = 1 / 6 both the pipes will together will fill the tank in 6 hours . answer is b"
Answer: b
Python program:
a = 1 / 10
b = 1 / 15
c = a + b 
d = 1 / c
Problem: if x # y is defined to equal x ^ 2 / y for all x and y , then ( - 1 # 3 ) # 3 =
Options: a ) 4 / 3 , b ) 1 / 3 , c ) 1 / 27 , d ) - 1 / 12 , e ) - 4 / 3
Rationale: "( - 1 ) ^ 2 / 3 = 1 / 3 ( 1 / 3 ) ^ 2 / 3 = 1 / 27 so c is my answer"
Answer: c
Python program:
a = negate ** (
b = a / 2
c = b ** 2
d = c / 2
Problem: how many integers between 362,855 and 852,755 have tens digit 1 and units digit 3 ?
Options: a ) 4,888 , b ) 4,898 , c ) 4,889 , d ) 4,869 , e ) 4,896
Rationale: "there is one number in hundred with 1 in the tens digit and 3 in the units digit : 13 , 113 , 213 , 313 , . . . the difference between 362,855 and 852,755 is 852,755 - 362,855 = 489,900 - one number per each hundred gives 133,900 / 100 = 4,889 numbers . answer : c ."
Answer: c
Python program:
a = 2 * 100
b = 3 + 4 
c = b * 10
d = a + c 
e = d + 2 
f = 852 - 755
Problem: a train covers a distance of 12 km in 10 min . if it takes 15 sec to pass a telegraph post , then the length of the train is ?
Options: a ) 250 m , b ) 300 m , c ) 120 m , d ) 200 m , e ) 166 m
Rationale: "speed = ( 12 / 10 * 60 ) km / hr = ( 72 * 5 / 18 ) m / sec = 20 m / sec . length of the train = 20 * 15 = 300 m . answer : b"
Answer: b
Python program:
a = 12 / 10
b = a - 15
c = 12 / b
Problem: two right circular cylinders of equal volumes have their heights in the ratio 1 : 2 . find the ratio of their radii .
Options: a ) √ 3 : 1
b ) √ 7 : 1
c ) √ 2 : 1
d ) 2 : 1
e ) 3 : 1
Rationale: explanation : let their heights be h and 2 h and radii be r and r respectively then . π r 2 h = π r 2 ( 2 h ) = > r 2 / r 2 = 2 h / h = 2 / 1 = > r / r = √ 2 / 1 = > r : r = √ 2 : 1 answer is c
Answer: c
Python program:
a = math.sqrt(2)
Problem: a certain country had a total annual expenditure of $ 4.8 x 10 ^ 11 last year . if the population of the country was 240 million last year , what was the per capita expenditure ?
Options: a ) $ 500 , b ) $ 1,000 , c ) $ 2,000 , d ) $ 3,000 , e ) $ 5,000
Rationale: "total expenditure / population = per capita expenditure hence , ( 4,8 x 10 ^ 11 ) / 240 000 000 = ( 4,8 x 10 ^ 11 ) / ( 2,4 x 10 ^ 8 ) = 2 x 10 ^ ( 11 - 8 ) = 2 x 10 ^ 3 = 2000 . answer is c ."
Answer: c
Python program:
a = 10 ** 11
b = 4 * 8
c = 4 + 2 
d = 10 ** c
e = 240 * d
f = b / e
Problem: a waitress ' s income consists of her salary and tips . during one week , her tips were 2 / 4 of her salary . what fraction of her income for the week came from tips ?
Options: a ) 1 / 9 , b ) 1 / 6 , c ) 1 / 3 , d ) 4 / 9 , e ) 5 / 9
Rationale: "her tips were 2 / 4 of her salary . let ' s say her salary = $ 4 this mean her tips = ( 2 / 4 ) ( $ 4 ) = $ 2 so , her total income = $ 4 + $ 2 = $ 6 what fraction of her income for the week came from tips $ 2 / $ 6 = 1 / 3 = c"
Answer: c
Python program:
a = 2 + 4 
b = 2 / a
Problem: what is the sum of all even numbers from 1 to 601 ?
Options: a ) 122821 , b ) 281228 , c ) 90300 , d ) 122850 , e ) 128111
Rationale: "explanation : 600 / 2 = 300 300 * 301 = 90300 answer : c"
Answer: c
Python program:
a = 1 * 601
b = a / 4
Problem: 60 percent of movie theatres in town x have 3 screens or less . 20 % of those theatres sell an average of more than $ 200 worth of popcorn per showing . 56 percent of all the movie theatres in town x sell $ 300 or less of popcorn per showing . what percent of all the stores on the street have 4 or more screens and sell an average of more than $ 300 worth of popcorn per day ?
Options: a ) 12 , b ) 18 , c ) 32 , d ) 40 , e ) 44
Rationale: "lets take numbers here . assume that the total number of movie theaters in the town = 100 then number of movie theaters with 3 screens or less = 60 = > number of movie theaters with 4 screens or more = 40 movie theaters with 3 screens or less selling popcorn at more than $ 200 = 20 % of 60 = 12 number of movie theaters selling popcorn at $ 300 or less = 56 = > number of movie theaters selling popcorn at more than $ 300 = 100 - 56 = 44 of these 44 theaters , 12 are those with 3 screens or less therefore 18 ( 44 - 12 ) must be those with four screens or more b is the answer"
Answer: b
Python program:
a = 20 / 300
b = 20 / 100
c = b * 200
d = a * c
Problem: in a certain pond , 70 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 ) 1,750 , d ) 2,500 , e ) 10,000
Rationale: "this is a rather straight forward ratio problem . 1 . 70 fish tagged 2 . 2 out of the 50 fish caught were tagged thus 2 / 50 2 / 50 = 70 / x thus , x = 1750 think of the analogy : 2 fish is to 50 fish as 50 fish is to . . . ? you ' ve tagged 50 fish and you need to find what that comprises as a percentage of the total fish population - we have that information with the ratio of the second catch . c"
Answer: c
Python program:
a = 2 / 50
b = 70 / a
Problem: there are 990 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 ) 100 , c ) 125 , d ) 175 , e ) 165
Rationale: "female = x male = 990 - x x / 2 + 990 - x / 4 = 1 / 3 * ( 990 ) = 330 x = 330 x / 2 = 165 is supposed to be the answer m is missing something correct option e"
Answer: e
Python program:
a = 990 / 3
b = a * 4
c = b - 990
d = c / 2
Problem: 5 years ago amith was 3 times as old as his daughter and 10 years hence , he will be two times as old as his daughter . then amith ’ s current age is ,
Options: a ) 10 , b ) 50 , c ) 40 , d ) 20 , e ) 60
Rationale: d 20 amith ’ s age = a and daughter ’ s age = b then , a – 5 = 3 ( b – 5 ) = > a – 3 b + 10 = 0 … … ( 1 ) and , a + 10 = 2 ( a + 10 ) = > a – 2 b – 10 = 0 … … ( 2 ) solving the 2 eqns , we will get a = 50 , b = 20 . therefore , amith ’ s age is 50 and his daughter ’ s age is 20
Answer: d
Python program:
a = 5 * 3
b = a + 5
Problem: at a tanning salon , customers are charged $ 10 for their first visit in a calendar month and $ 7 for each visit after that in the same calendar month . in the last calendar month , 100 customers visited the salon , of which 30 made a second visit , and 10 made a third visit . all other customers made only one visit . if those visits were the only source of revenue for the salon , what was the revenue for the last calendar month at the salon ?
Options: a ) $ 1220 , b ) $ 1280 , c ) $ 1300 , d ) $ 1340 , e ) $ 1880
Rationale: "i get b . this question seems too straightforward for 600 + . am i missing something ? 100 first - time visits - - > 100 ( 10 ) = $ 1000 30 + 10 = 40 subsequent visits - - > 40 ( 7 ) = $ 280 total revenue : 1000 + 280 = $ 1280 the answer is b ."
Answer: b
Python program:
a = 10 + 7 
b = a * 30
c = 100 - 30
d = c * 10
e = b + d
Problem: a retailer buys a radio for rs 232 . his overhead expenses are rs 15 . he sellis the radio for rs 300 . the profit percent of the retailer is
Options: a ) 10 % , b ) 50 % , c ) 21.4 % , d ) 52 % , e ) none of these
Rationale: explanation : cost price = ( 232 + 15 ) = 247 sell price = 300 gain = ( 53 / 247 ) * 100 = 21.4 % . answer : c
Answer: c
Python program:
a = 232 + 15 
b = 300 / a
c = b * 100
d = c - 100
Problem: a batch of cookies was divided among 3 tins : 2 / 3 of all the cookies were placed in either the blue tin or the green tin , and the rest were placed in the red tin . if 1 / 4 of all the cookies were placed in the blue tin , what fraction q of the cookies that were placed in the other tins were placed in the green tin ?
Options: a ) 15 / 2 , b ) 9 / 4 , c ) 5 / 9 , d ) 7 / 5 , e ) 9 / 7
Rationale: blue tin or red tin : 2 / 3 ( n ) red tin : ( 1 / 3 ) n blue tin : ( 1 / 4 ) n what the last statment meant , is it wants this fraction : ( # of cookies in green tin ) / ( # of cookies in red and green tin ) # of cookies in green tin = 2 n / 3 - n / 4 = 8 n - 3 n / 12 = 5 n / 12 # of cookies in red and green tin = n / 3 + 5 n / 12 = 9 n / 12 fraction q = 5 n / 12 * 12 / 9 n = 5 / 9 ( c )
Answer: c
Python program:
a = 2 / 3
b = 1 / 4
c = a - b
d = c * 12
e = 12 / 3
f = 2 / 3
g = 1 / 4
h = f - g
i = h * 12
j = e + i 
k = d / j
Problem: aaron will jog from home at 3 miles per hour and then walk back home by the same route at 6 miles per hour . how many miles from home can aaron jog so that he spends a total of 3 hours jogging and walking ?
Options: a ) 3 , b ) 6 , c ) 2 , d ) 5 , e ) 8
Rationale: "xyt / ( x + y ) x = 3 , y = 6 , t = 3 3 * 6 * 3 / 3 + 6 = 54 / 9 = 6 answer : b"
Answer: b
Python program:
a = 3 * 6
b = a * 3
c = 3 * 6
d = b / c
Problem: a man engaged a servant on the condition that he would pay him rs . 710 and a uniform after a year service . he served only for 8 months and got rs . 460 and a uniform . find the price of the uniform ?
Options: a ) rs . 40 , b ) rs . 30 , c ) rs . 25 , d ) rs . 20 , e ) rs . 45
Rationale: "8 / 12 = 2 / 3 * 710 = 473.33 460.00 - - - - - - - - - - - - - - - 13.33 1 / 3 uniform 13.33 1 - - - - - - - - - - - - - - - ? = > rs . 40 answer : a"
Answer: a
Python program:
a = 8 * 710
b = 3 * 4
c = b * 460
d = a - c
e = 3 * 4
f = e * 1
g = d / f
h = g * 4
Problem: the cricket team of 11 members is 26 yrs old & the wicket keeper is 3 yrs older . if the ages ofthese 2 are excluded , the average age of theremaining players is 1 year less than the average age of the whole team . what is the average age of the team ?
Options: a ) 19 , b ) 21 , c ) 23 , d ) 25 , e ) 27
Rationale: "let the average age of the whole team be x years . 11 x - ( 26 + 29 ) = 9 ( x - 1 ) = > 11 x - 9 x = 46 = > 2 x = 46 = > x = 23 . so , average age of the team is 23 years . c"
Answer: c
Python program:
a = 26 + 3 
b = a + 26 
c = 11 - 2
d = b - c
e = 11 - 2
f = 11 - e
g = d / f
Problem: a student has to obtain 33 % of the total marks to pass . he got 125 marks and failed by 73 marks . the maximum marks are ?
Options: a ) 450 , b ) 300 , c ) 500 , d ) 600 , e ) 175
Rationale: "let the maximum marks be x then , 33 % of x = 125 + 73 33 x / 100 = 198 x = 600 answer is d"
Answer: d
Python program:
a = 125 + 73 
b = 33 / 100
c = a / b
Problem: a ratio between two numbers is 3 : 4 and their l . c . m . is 180 . the first number is
Options: a ) 60 , b ) 45 , c ) 20 , d ) 15 , e ) none
Rationale: "sol . let the required numbers be 3 x and 4 x . then , their l . c . m . is 12 x . ∴ 12 x = 180 ⇔ x = 15 . hence , the first number is 45 . answer b"
Answer: b
Python program:
a = 3 * 4
b = 180 / a
c = b * 3
Problem: mike , jim and bob are all professional fisherman . mike can catch 30 fish in one hour , jim can catch twice as much and bob can catch 50 % more than jim . if the 3 started to fish together and after 40 minutes mike and bob left , how many fish did the 3 fishermen catch in one hour ?
Options: a ) 110 , b ) 120 , c ) 140 , d ) 130 , e ) 112
Rationale: all of them catch fishes in relation to number 30 . . . . 2 / 3 * 30 + 2 * 30 + 2 * 1.5 * 30 * 2 / 3 = 140 answer is c
Answer: c
Python program:
a = 3 * 40
b = a + 50 
c = b - 30
Problem: in a certain game of dice , the player ’ s score is determined as a sum of two throws of a single die . the player with the highest score wins the round . if more than one player has the highest score , the winnings of the round are divided equally among these players . if john plays this game against 22 other players , what is the probability of the minimum score that will guarantee john some monetary payoff ?
Options: a ) 41 / 50 , b ) 1 / 221 , c ) 1 / 216 , d ) 1 / 36 , e ) 1 / 42
Rationale: "to guarantee that john will get some monetary payoff he must score the maximum score of 6 + 6 = 12 , because if he gets even one less than that so 11 , someone can get 12 and john will get nothing . p ( 12 ) = 1 / 6 ^ 2 = 1 / 36 . answer : d ."
Answer: d
Python program:
a = 22 / 3
b = a - 1
c = b ** 2
d = 1 / c
Problem: it was calculated that 75 men could complete a piece of work in 10 days . when work was scheduled to commence , it was found necessary to send 25 men to another project . how much longer will it take to complete the work ?
Options: a ) 10 days . , b ) 20 days . , c ) 25 days . , d ) 12.5 days . , e ) 15 days .
Rationale: "one day work = 1 / 10 one man ’ s one day work = 1 / ( 10 * 75 ) now : no . of workers = 50 one day work = 50 * 1 / ( 10 * 75 ) the total no . of days required to complete the work = ( 75 * 10 ) / 50 = 15 answer : e"
Answer: e
Python program:
a = 75 / 25
b = 10 * a
Problem: two equally sized jugs full of water are each emptied into two separate unequally sized empty jugs , x and y . now , jug x is 1 / 7 full , while jug y is 2 / 3 full . if water is poured from jug x into jug y until jug y is filled , what fraction of jug x then contains water ?
Options: a ) 0 , b ) 1 / 14 , c ) 2 / 15 , d ) 1 / 10 , e ) 2 / 10
Rationale: suppose the water in each jug is l liters cx x ( 1 / 7 ) = l cx = 7 l liters cx is capacity of x cy x ( 2 / 3 ) = l cy = 3 l / 2 liters cy is capacity of y now , y is 3 l / 2 - l empty = l / 2 empty so , we can put only l / 2 water in jug y from jug x jug x ' s remaining water = l - l / 2 = l / 2 fraction of x which contains water = water / cx = ( l / 2 ) / 7 l = 1 / 14 answer will be b
Answer: b
Python program:
a = 1 / 7
b = 2 / 3
c = 1 - b
d = 2 / 3
e = c / d
f = a * e
Problem: a grocery store bought some mangoes at a rate of 4 for a dollar . they were separated into two stacks , one of which was sold at a rate of 3 for a dollar and the other at a rate of 6 for a dollar . what was the ratio of the number of mangoes in the two stacks if the store broke even after having sold all of its mangoes ?
Options: a ) 1 : 4 , b ) 1 : 5 , c ) 2 : 3 , d ) 1 : 2 , e ) 1 : 2
Rationale: "the cost price of a mango = 1 / 4 dollars . the selling price of a mango from the first stack = 1 / 3 dollars - - > the profit from one mango = 1 / 3 - 1 / 4 = 1 / 12 dollars . the selling price of a mango from the second stack = 1 / 6 dollars - - > the loss from one mango = 1 / 3 - 1 / 6 = 1 / 6 dollars . the profit from one mango from the first stack is 4 times the loss from one mango from the second stack . the ratio is 1 / 12 * 6 / 1 = 1 / 2 = 1 : 2 e"
Answer: e
Python program:
a = 1 / 3
b = 1 / 4
c = a - b
d = 1 / 4
e = 2 * 4
f = 1 / e
g = d - f
h = c / g
Problem: if the weight of 13 meters long rod is 13.4 kg . what is the weight of 6 meters long rod ?
Options: a ) 7.2 kg . , b ) 10.8 kg . , c ) 12.4 kg . , d ) 6.18 kg , e ) none
Rationale: answer ∵ weight of 13 m long rod = 13.4 kg ∴ weight of 1 m long rod = 13.4 / 13 kg ∴ weight of 6 m long rod = 13.4 x 6 / 13 = 6.18 kg option : d
Answer: d
Python program:
a = 6 * 13
b = a / 13
Problem: if each side of a rectangle is increased by 50 % with the length being double the width , find the percentage change in its area ?
Options: a ) 284 % , b ) 276 % , c ) 265.25 % , d ) 284.5 % , e ) 275 %
Rationale: "area = 2 a x a new length = 250 a / 100 = 5 a / 2 new width = 150 a / 100 = 3 a / 2 new area = ( 5 a x 3 a ) / ( 2 x 2 ) = ( 15 a ² / 4 ) increased area = = ( 15 a ² / 4 ) - a ² increase % = [ ( 11 a ² / 4 ) x ( 1 / a ² ) x 100 ] % = 275 % answer : e"
Answer: e
Python program:
a = 50 / 50
b = a * 2
c = b ** 2
d = c - 1
e = d * 100
Problem: the length of a room is 5.5 m and width is 3.75 m . find the cost of paying the floor by slabs at the rate of rs . 800 per sq . metre
Options: a ) 22488 , b ) 16500 , c ) 27889 , d ) 23778 , e ) 29982
Rationale: "explanation : area = 5.5 × 3.75 sq . metre . cost for 1 sq . metre . = rs . 800 hence total cost = 5.5 × 3.75 × 800 = 5.5 × 3000 = rs . 16500 answer : b ) rs . 16500"
Answer: b
Python program:
a = 5 * 5
b = 800 * a
Problem: if the area of a circle decreases by 25 % , then the radius of a circle decreases by
Options: a ) 13 % , b ) 18 % , c ) 36 % , d ) 64 % , e ) none of these
Rationale: "if area of a circle decreased by x % then the radius of a circle decreases by ( 100 − 10 √ 100 − x ) % = ( 100 − 10 √ 100 − 25 ) % = ( 100 − 10 √ 75 ) % = 100 - 87 = 13 % answer a"
Answer: a
Python program:
a = 100 - 25
b = a / 100
c = math.sqrt(b)
d = 1 - c
e = d * 100
Problem: alfred buys an old scooter for $ 4700 and spends $ 1000 on its repairs . if he sells the scooter for $ 5800 , his gain percent is ?
Options: a ) 5.45 % , b ) 6.23 % , c ) 1.75 % , d ) 8.12 % , e ) 10 %
Rationale: "c . p . = 4700 + 1000 = $ 5700 s . p . = $ 5800 gain = 5800 - 5700 = $ 100 gain % = 100 / 5700 * 100 = 1.75 % answer is c"
Answer: c
Python program:
a = 4700 + 1000 
b = 5800 - a
c = 4700 + 1000 
d = b / c
e = d * 100
Problem: find the average of all the numbers between 11 and 36 which are divisible by 5 .
Options: a ) 25 , b ) 77 , c ) 20 , d ) 28 , e ) 10
Rationale: "explanation : average = ( 15 + 20 + 25 + 30 + 35 ) / 5 = 125 / 5 = 25 answer : a"
Answer: a
Python program:
a = 11 + 4 
b = 36 - 4
c = a + b 
d = c / 2
Problem: how many e ways can jason sit with his 5 friends in a row of 6 seats with an aisle on either side of the row , if jason insists on sitting next to one of the aisles ?
Options: a ) 120 , b ) 240 , c ) 360 , d ) 540 , e ) 720
Rationale: jason can select his seat in 2 ways ( two aisles ) his 1 st of 4 friends have 5 seats to select = > his 2 nd of remaining 3 friends will have 4 seat to chose from . . . and so on total ways e = > 2 * 5 * 4 * 3 * 2 * 1 = 240 . b
Answer: b
Python program:
a = math.factorial(5)
b = a * 2
Problem: 56 : 65 : : 68 : ?
Options: a ) 49 , b ) 84 , c ) 86 , d ) 64 , e ) 56
Rationale: "ans 86 reverse of 68 answer : c"
Answer: c
Python program:
a = 56 / 65
b = 68 * a
Problem: in the biology lab of ` ` jefferson ' ' high school there are 0.037 * 10 ^ 5 germs , equally divided among 148000 * 10 ^ ( - 3 ) petri dishes . how many germs live happily in a single dish ?
Options: a ) 10 , b ) 25 , c ) 35 , d ) 40 , e ) 55
Rationale: "0.037 * 10 ^ 5 can be written as 3700 148000 * 10 ^ ( - 3 ) can be written as 148 required = 3700 / 148 = 25 answer : b"
Answer: b
Python program:
a = 1000 * 100
b = a * 0
c = 148000 / 1000
d = b / c
Problem: the sum of ages of 5 children born 1.5 years different each is 50 years . what is the age of the elder child ?
Options: a ) 8 , b ) 9 , c ) 10 , d ) 16 , e ) 13
Rationale: "let the ages of children be x , ( x + 1.5 ) , ( x + 3 ) , ( x + 4.5 ) and ( x + 6 ) years . then , x + ( x + 1.5 ) + ( x + 3 ) + ( x + 4.5 ) + ( x + 6 ) = 50 5 x = 35 x = 7 . x + 6 = 7 + 6 = 13 answer : e"
Answer: e
Python program:
a = 1 + 5 
b = 1 + 5 
c = a + b 
d = 4 + 4 
e = c + d 
f = e + 50 
g = f / 5
Problem: what is the average ( arithmetic mean ) of all multiples of 10 from 10 to 100 inclusive ?
Options: a ) 190 , b ) 195 , c ) 200 , d ) 205 , e ) 55
Rationale: "this question can be solved with the average formula and ' bunching . ' we ' re asked for the average of all of the multiples of 10 from 10 to 100 , inclusive . to start , we can figure out the total number of terms rather easily : 1 ( 10 ) = 10 2 ( 10 ) = 20 . . . 10 ( 10 ) = 100 so we know that there are 10 total numbers . we can now figure out the sum of those numbers with ' bunching ' : 10 + 100 = 110 20 + 90 = 110 30 + 80 = 110 etc . since there are 10 total terms , this pattern will create 5 ' pairs ' of 110 . thus , since the average = ( sum of terms ) / ( number of terms ) , we have . . . ( 5 ) ( 110 ) / ( 10 ) = 55 answer : e"
Answer: e
Python program:
a = 10 + 100 
b = 100 - 10
c = b / 10
d = c + 1 
e = a * d
f = e / 2
g = 100 - 10
h = g / 10
i = h + 1 
j = f / i
Problem: a cistern can be filled by a tap in 4 hours while it can be emptied by another tap in 5 hours . if both the taps are opened simultaneously , then after how much time will the cistern get filled ?
Options: a ) 7.5 , b ) 20 , c ) 30 , d ) 32 , e ) 40
Rationale: "net part filled in 1 hour = ( 1 / 4 - 1 / 5 ) = 1 / 20 the cistern will be filled in 20 / 1 hrs i . e . , 20 hrs . answer : b"
Answer: b
Python program:
a = 1 / 4
b = 1 / 5
c = a - b
d = 1 / c
Problem: what is the sum of all 3 digit numbers that leave a remainder of ' 2 ' when divided by 4 ?
Options: a ) 123,750 , b ) 164,850 , c ) 164,749 , d ) 149,700 , e ) 156,720
Rationale: "find the number , upon sum of 3 digits of a number gives a reminder 2 when it is divided by 4 seeing the options after dividing and finding the reminder of 2 my answer was a"
Answer: a
Python program:
a = 1000 - 3
b = 3 * 3
c = b * 10
d = 3 * 3
e = c + d 
f = e + 3 
g = a - f
h = g / 4
i = h + 1 
j = i / 2
k = 1000 - 3
l = 3 * 3
m = l * 10
n = 3 * 3
o = m + n 
p = o + 3 
q = k + p 
r = j * q
Problem: in an election a candidate who gets 60 % of the votes is elected by a majority of 1200 votes . what is the total number of votes polled ?
Options: a ) 4500 , b ) 5200 , c ) 6900 , d ) 7520 , 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 = 1200 20 x / 100 = 1200 x = 1200 * 100 / 20 = 6000 answer is e"
Answer: e
Python program:
a = 100 - 60
b = 60 - a
c = b / 100
d = 1200 / c
Problem: if money is invested at r percent interest , compounded annually , the amount of investment will double in approximately 70 / r years . if pat ' s parents invested $ 5000 in a long term bond that pays 8 percent interest , compounded annually , what will be the approximate total amount of investment 18 years later , when pat is ready for college ?
Options: a ) $ 20000 , b ) $ 15000 , c ) $ 12000 , d ) $ 10000 , e ) $ 9000
Rationale: "since investment doubles in 70 / r years then for r = 8 it ' ll double in 70 / 8 = ~ 9 years ( we are not asked about the exact amount so such an approximation will do ) . thus in 18 years investment will double twice and become ( $ 5,000 * 2 ) * 2 = $ 20,000 ( after 9 years investment will become $ 5,000 * 2 = $ 10,000 and in another 9 years it ' ll become $ 10,000 * 2 = $ 20,000 ) . answer : a ."
Answer: a
Python program:
a = 5000 * 2
b = a * 2
Problem: tomeka is playing a dice game . if she rolls the same number on her second roll as she rolls on her first , she wins . each roll is with two , fair , 6 - sided dice . if tomeka rolled a 7 on her first roll , what is the probability that she will win on her second roll ?
Options: a ) 1 / 4 , b ) 1 / 5 , c ) 1 / 6 , d ) 1 / 9 , e ) 1 / 12
Rationale: there are 6 ways to roll a seven : 1 and 6 , 6 and 1 , 2 and 5 , 5 and 2 , 3 and 4 , 4 and 3 . there are 6 * 6 = 36 ways to roll two six - sided dice . thus the probability of winning by rolling a seven on the second roll given a seven on the first roll is 6 / 36 = 1 / 6 c
Answer: c
Python program:
a = 6 * 6
b = 6 / a