euclaise/mathqa_programs huggingface dataset:
Problem: 18 times a positive integer is more than its square by 80 , then the positive integer is
Options: a ) 13 , b ) 10 , c ) 11 , d ) 12 , e ) 14
Rationale: "explanation : let the number be x . then , 18 x = x 2 + 80 = > x 2 - 18 x + 80 = 0 = > ( x - 10 ) ( x - 8 ) = 0 = > x = 10 or 8 answer : b"
Answer: b
Python program:
a = 18 ** 2
b = 80 * 4
c = a - b
d = 18 + c 
e = d / 2
Problem: if | x + 3 | = 15 , what is the sum of all the possible values of x ?
Options: a ) - 16 , b ) - 12 , c ) - 8 , d ) - 3 , e ) 11
Rationale: "there will be two cases x + 3 = 15 or x + 3 = - 15 = > x = 12 or x = - 18 sum of both the values will be - 18 + 15 = - 3 answer : d"
Answer: d
Python program:
a = 3 + 15
Problem: a box has 12 shapes ; 3 circles , 5 squares , and 4 triangles . how many groups of 3 shapes can be made with at least 1 triangle ?
Options: a ) 46
b ) 64
c ) 164
d ) 146
e ) 56
Rationale: the problem asks for a combination , since order does n ' t matter . now , selecting r items from a set of n gives the combination formula : ncr = n ! / r ! ( n - r ) ! n = 12 r = 3 so , total groups is 12 c 3 = 12 ! / ( 3 ! ( 12 - 3 ) ! ) = 220 , and n = 12 - 4 = 8 r = 3 for groups without a triangle is 8 c 3 = 8 ! / ( 3 ! ( 8 - 3 ) ! ) = 56 , so , groups with at least 1 triangle = 220 - 56 = 164 answer : c
Answer: c
Python program:
a = 12 + 12 
b = a + 4 
c = 4 * b
d = 4 + 2 
e = 5 + 3 
f = d * e
g = c + f 
h = g + 4
Problem: how many liters of water must be evaporated from 50 liters of a 3 - percent sugar solution to get a 5 - percent solution ?
Options: a ) 35 , b ) 22.5 , c ) 27 , d ) 16 2 / 3 , e ) 15
Rationale: "how many liters of water must be evaporated from 50 liters of a 3 - percent sugar solution to get a 5 - percent solution ? 3 % of a 50 liter solution is 1.5 l . so you are trying to determine how many liters must a solution be for the 1.5 l to represent 5 % of the solution . set up an inequality and solve for x : 1.5 / x = 1 / 5 x = 7.5 since you need a 15 l solution , you must evaporate 22.5 of the original 50 l solution to get a 5 % solution . answer is b ."
Answer: b
Python program:
a = 50 / 100
b = a * 5
c = 50 - b
Problem: we bought 85 hats at the store . blue hats cost $ 6 and green hats cost $ 7 . the total price was $ 540 . how many green hats did we buy ?
Options: a ) a ) 36 , b ) b ) 30 , c ) c ) 40 , d ) d ) 42 , e ) e ) 44
Rationale: "let b be the number of blue hats and let g be the number of green hats . b + g = 85 . b = 85 - g . 6 b + 7 g = 540 . 6 ( 85 - g ) + 7 g = 540 . 510 - 6 g + 7 g = 540 . g = 540 - 510 = 30 . the answer is b ."
Answer: b
Python program:
a = 85 * 6
b = 540 - a
Problem: if â € œ * â €  is called â € œ + â €  , â € œ / â €  is called â € œ * â €  , â € œ - â €  is called â € œ / â €  , â € œ + â €  is called â € œ - â €  . 80 / 40 â € “ 10 * 20 + 10 = ?
Options: a ) 185 , b ) 160 , c ) 170 , d ) 145 , e ) 225
Rationale: "explanation : given : 80 / 40 â € “ 10 * 20 + 10 = ? substituting the coded symbols for mathematical operations , we get , 80 * 40 / 20 + 20 â € “ 10 = ? 80 * 2 + 20 â € “ 10 = ? 160 + 20 â € “ 10 = ? 180 â € “ 10 = 170 answer : c"
Answer: c
Python program:
a = 10 / 20
b = 80 / 40
c = a * b
d = c + 10
Problem: a , b and c enter into a partnership . a invests 3 times as much as b invests and 2 / 3 of what c invests . at the end of the year , the profit earned is rs . 66000 . what is the share of c ?
Options: a ) rs . 15250 , b ) rs . 13375 , c ) rs . 16750 , d ) rs . 18000 , e ) none of these
Rationale: "explanation : let the investment of c be rs . x . the inverstment of b = rs . ( 2 x / 3 ) the inverstment of a = rs . ( 3 × ( 2 / 3 ) x ) = rs . ( 2 x ) ratio of capitals of a , b and c = 2 x : 2 x / 3 : x = 6 : 2 : 3 c ' s share = rs . [ ( 3 / 11 ) × 66000 ] = rs . 18000 answer : option d"
Answer: d
Python program:
a = 2 / 3
b = 2 / 3
c = b * 3
d = a + c 
e = d + 1 
f = 1/(e)
g = 66000 * f
Problem: a factory has three types of machines , each of which works at its own constant rate . if 7 machine as and 11 machine bs can produce 525 widgets per hour , and if 8 machine as and 22 machine cs can produce 600 widgets per hour , how many widgets could one machine a , one machine b , and one machine c produce in one 8 - hour day ?
Options: a ) 400 , b ) 475 , c ) 550 , d ) 625 , e ) 600
Rationale: "let machine a produce a widgets per hour . b produce b widgets per hour and c produce c widgets per hour . 7 a + 11 b = 525 - - - ( 1 ) 8 a + 22 c = 600 - - - ( 2 ) dividing ( 2 ) by 2 4 a + 11 c = 300 . . . . . ( 3 ) adding ( 1 ) ( 3 ) 11 a + 11 b + 11 c = 825 a + b + c = 75 per hour so for eight hrs = 75 * 8 = 600 = answer = e"
Answer: e
Python program:
a = 600 / 11
b = a * 8
Problem: find number which is 70 % less than 60 .
Options: a ) 18 , b ) 22 , c ) 28 , d ) 26 , e ) 98
Rationale: "explanation : 70 % less is 30 % of the given number therefore , 30 % of 60 is 18 . answer : a"
Answer: a
Python program:
a = 60 * 70
b = a / 100
Problem: a person want to give his money of $ 1000 to his 4 children a , b , c , d in the ratio 2 : 4 : 3 : 1 . what is the a + d share ?
Options: a ) $ 100 , b ) $ 200 , c ) $ 300 , d ) $ 500 , e ) $ 600
Rationale: "a ' s share = 1000 * 2 / 10 = $ 200 d ' s share = 1000 * 1 / 10 = $ 100 a + d = $ 300 answer is c"
Answer: c
Python program:
a = 2 + 3 
b = a + 3 
c = 4 / b
d = c * 1000
Problem: mariah has decided to hire three workers . to determine whom she will hire , she has selected a group of 14 candidates . she plans to have one working interview with 3 of the 14 candidates every day to see how well they work together . how many days will it take her to have working interviews with all the different combinations of job candidates ?
Options: a ) 720 , b ) 120 , c ) 300 , d ) 30 , e ) 333
Rationale: "333 . answer e"
Answer: e
Python program:
a = math.factorial(14)
b = 14 - 3
c = math.factorial(b)
d = a / c
e = math.factorial(3)
f = d / e
g = f / 2
h = g - 14
i = h - 14
j = i - 10
Problem: an athlete runs 200 metres race in 20 seconds . what is his speed ?
Options: a ) 23 , b ) 38 , c ) 37 , d ) 36 , e ) 28
Rationale: "speed = distance / time = 200 / 20 = 10 m / s = 10 * 18 / 5 = 36 km / hr answer : d"
Answer: d
Python program:
a = 200 / 20
b = a * const_3_6
Problem: a certain meter records voltage between 0 and 10 volts inclusive . if the average value of 3 recordings on the meter was 6 volts , what was the smallest possible recording in volts ?
Options: a ) 2 , b ) 3 , c ) 4 , d ) 5 , e ) 6
Rationale: "if average of 3 is 6 so sum of 3 should be 18 3 recording can be from 0 - 10 inclusive to find one smallest other two should be highest so , lets assume three var are a , b , c say a is smallest and give b and c greatest readings say 8 and 8 so a has to be 2 a"
Answer: a
Python program:
a = 3 * 4
b = a - 10
Problem: find the last digit in the product 287 x 287 + 269 x 269 - 2 x 287 x 269 ?
Options: a ) 5 , b ) 6 , c ) 8 , d ) 9 , e ) 4
Rationale: explanation : given exp . = a 2 + b 2 - 2 ab , where a = 287 and b = 269 = ( a - b ) 2 = ( 287 - 269 ) 2 = ( 182 ) = 324 answer is e
Answer: e
Python program:
a = 287 * 287
b = 269 * 269
c = a + b 
d = 2 * 287
e = d * 269
f = c - e
g = 10 * 2
h = 3 * 100
i = g + h 
j = f - i
Problem: at a monthly meeting , 2 / 3 of the attendees were males and 3 / 4 of the male attendees arrived on time . if 5 / 6 of the female attendees arrived on time , what fraction of the attendees at the monthly meeting did not arrive on time ?
Options: a ) 1 / 3 , b ) 1 / 4 , c ) 3 / 8 , d ) 2 / 9 , e ) 5 / 18
Rationale: "males who did not arrive on time are 1 / 4 * 2 / 3 = 1 / 6 of the attendees . females who did not arrive on time are 1 / 6 * 1 / 3 = 1 / 18 of the attendees . the fraction of all attendees who did not arrive on time is 1 / 6 + 1 / 18 = 2 / 9 the answer is d ."
Answer: d
Python program:
a = 5 / 6
b = 1 - a
c = 2 / 3
d = 1 - c
e = b * d
f = 3 / 4
g = 1 - f
h = 2 / 3
i = g * h
j = e + i
Problem: the sum of the ages of 4 children born at the intervals of 4 years each is 36 years . what is the age of the youngest child ?
Options: a ) 3 , b ) 18 , c ) 10 , d ) 99 , e ) 38
Rationale: "let x = the youngest child . each of the other four children will then be x + 4 , x + 8 , x + 12 we know that the sum of their ages is 36 . so , x + ( x + 4 ) + ( x + 8 ) + ( x + 12 ) = 36 therefore the youngest child is 3 years old answer : a"
Answer: a
Python program:
a = 4 / 4
b = 36 / a
c = 4 - 1
d = c * 4
e = b - d
f = e / 4
Problem: a school has 4 section of chemistry in class x having 50 , 35 , 45 and 42 students . the mean marks obtained in chemistry test are 50 , 60 , 55 and 45 respectively for the 4 sections . determine the overall average of marks per student .
Options: a ) 50.12 , b ) 52.12 , c ) 51.12 , d ) 53.12 , e ) none of the above
Rationale: "required average marks = 50 ã — 50 + 35 ã — 60 + 45 ã — 55 + 42 ã — 45 / 50 + 35 + 45 + 42 = 2500 + 2100 + 2475 + 1890 / 172 = 8965 â  „ 172 = 52.12 answer b"
Answer: b
Python program:
a = 50 * 50
b = 35 * 60
c = a + b 
d = 45 * 55
e = c + d 
f = 42 * 45
g = e + f 
h = 50 + 35 
i = h + 45 
j = i + 42 
k = g / j
Problem: what is the least integer that is a sum of 4 different prime numbers each greater than 10 ?
Options: a ) 60 , b ) 62 , c ) 64 , d ) 66 , e ) 68
Rationale: the sum of the four smallest primes greater than 10 is 11 + 13 + 17 + 19 = 60 . the answer is a .
Answer: a
Python program:
a = 10 + 1 
b = 10 + 1 
c = b + 2 
d = a + c 
e = 10 + 1 
f = e + 2 
g = f + 4 
h = d + g 
i = 10 + 1 
j = i + 2 
k = j + 4 
l = k + 2 
m = h + l
Problem: what is the smallest positive integer that can be multiplied by 605 to make it a perfect square ?
Options: a ) 2 , b ) 3 , c ) 5 , d ) 7 , e ) 11
Rationale: "605 is multiplied by 5 gives 3025 its a square root of 55 answer is 5 - option c"
Answer: c
Python program:
a = 3 + 4
Problem: set a consists of the integers from 1 to 12 , inclusive , while set b consists of the integers from 5 to 15 , inclusive . how many distinct integers do belong to the both sets at the same time ?
Options: a ) 8 , b ) 10 , c ) 12 , d ) 15 , e ) 9
Rationale: "a = { 1,2 , 3,4 , 5,6 , 7 , 8 , 9 , 10 , 11 , 12 } b = { 5,6 , 7 , 8 , 9 , 10 , 11 , 12 , 13 , 14 , 15 } common elements = { 5,6 , 7 , 8 , 9 , 10 , 11 , 12 } = 8 elements answer : option a ."
Answer: a
Python program:
a = 5 + 1
Problem: p , q and r have rs . 6000 among themselves . r has two - thirds of the total amount with p and q . find the amount with r ?
Options: a ) 2388 , b ) 3722 , c ) 2400 , d ) 2872 , e ) 1231
Rationale: explanation : let the amount with r be rs . r r = 2 / 3 ( total amount with p and q ) r = 2 / 3 ( 6000 - r ) = > 3 r = 12000 - 2 r = > 5 r = 12000 = > r = 2400 . answer : c
Answer: c
Python program:
a = 2 / 3
b = 1 + a 
c = 6000 / b
d = 2 / 3
e = c * d
Problem: on sunday , bill ran 4 more miles than he ran on saturday . julia did not run on saturday , but she ran twice the number of miles on sunday that bill ran on sunday . if bill and julia ran a total of 32 miles on saturday and sunday , how many miles did bill run on sunday ?
Options: a ) 5 , b ) 6 , c ) 7 , d ) 8 , e ) 9
Rationale: "let bill run x on saturday , so he will run x + 4 on sunday . . julia will run 2 * ( x + 4 ) on sunday . . totai = x + x + 4 + 2 x + 8 = 32 . . 4 x + 12 = 32 . . x = 5 . . ans = x + 4 = 5 + 4 = 9 answer e"
Answer: e
Python program:
a = 2 * 4
b = 4 + a 
c = 32 - b
d = c / 4
e = d + 4
Problem: a man saves 20 % of his monthly salary . if an account of dearness of things he is to increase his monthly expenses by 20 % , he is only able to save rs . 260 per month . what is his monthly salary ?
Options: a ) 5000 , b ) 2999 , c ) 2878 , d ) 2990 , e ) 6500
Rationale: "income = rs . 100 expenditure = rs . 80 savings = rs . 20 present expenditure 80 * ( 20 / 100 ) = rs . 96 present savings = 100 â € “ 96 = rs . 4 100 - - - - - - 4 ? - - - - - - - - - 260 = > 6500 answer : e"
Answer: e
Python program:
a = 260 * 100
b = 100 - 20
c = 100 - 20
d = 20 / 100
e = c * d
f = b + e 
g = 100 - f
h = a / g
Problem: a 160 meter long train crosses a man standing on the platform in 4 sec . what is the speed of the train ?
Options: a ) 176 kmph , b ) 144 kmph , c ) 176 kmph , d ) 134 kmph , e ) 161 kmph
Rationale: "s = 160 / 4 * 18 / 5 = 144 kmph answer : b"
Answer: b
Python program:
a = 160 / 4
b = a * const_3_6
Problem: p and q started a business investing rs 60000 and rs 15000 resp . in what ratio the profit earned after 2 years be divided between p and q respectively .
Options: a ) 7 : 5 , b ) 17 : 3 , c ) 4 : 1 , d ) 17 : 7 , e ) 5 : 8
Rationale: explanation : in this type of question as time frame for both investors is equal then just get the ratio of their investments . p : q = 60000 : 15000 = 60 : 15 = 4 : 1 option c
Answer: c
Python program:
a = 60000 / 15000
Problem: 20 people can write 50 book in 15 days working 8 hour a day . then in how many day 200 can be written by 60 people ?
Options: a ) 200 , b ) 100 , c ) 50 , d ) 70 , e ) 25
Rationale: "work per day epr hour per person = 50 / ( 15 * 8 * 20 ) / / eq - 1 people = 60 ; let suppose day = p ; per day work for 8 hours acc . to condition work per day epr hour per person = 200 / ( p * 8 * 60 ) / / eq - 2 eq - 1 = = eq - 2 ; p = 100 answer : b"
Answer: b
Python program:
a = 50 * 15
b = 60 / 2
c = a / b
Problem: what least number must be added to 1078 , so that the sum is completely divisible by 23 ?
Options: a ) 3 , b ) 2 , c ) 4 , d ) 5 , e ) 6
Rationale: "47 * 23 = 1081 1081 - 1078 = 3 answer : a"
Answer: a
Python program:
a = 4 * 10
b = a + 2 
c = b * 23
d = c - 1078
Problem: find the average marks of all the students in 2 separate classes , if the average marks of students in the first class of 55 students is 60 and that of another class of 48 students is 58
Options: a ) 55.1 , b ) 51.1 , c ) 53.1 , d ) 52.1 , e ) 59.1
Rationale: sum of the marks for the class of 55 students = 55 * 60 = 3300 sum of the marks for the class of 48 students = 48 * 58 = 2784 sum of the marks for the class of 103 students = 3300 + 2784 = 6084 average marks of all the students = 6084 / 103 = 59.1 answer : e
Answer: e
Python program:
a = 55 * 60
b = 48 * 58
c = a + b 
d = 55 + 48 
e = c / d
Problem: a train is 100 meter long and is running at the speed of 30 km per hour . find the time it will take to pass a man standing at a crossing .
Options: a ) 10 seconds , b ) 12 seconds , c ) 14 seconds , d ) 16 seconds , e ) none of these
Rationale: explanation : as we need to get answer in seconds , so never forget to convert speed into meter per second . speed = 30 km / hr = 30 * 5 / 18 m / sec = 25 / 3 m / sec distance = length of train = 100 meter required time = distancespeed = 100253 = 100 ∗ 325 = 12 sec answer : b
Answer: b
Python program:
a = 100 / 1000
b = a / 30
c = 3600 * b
Problem: on a game show , a contestant is given 3 keys , each of which opens exactly one of the 3 identical boxes . the contestant assigns each key to one of the boxes and wins the amount of money contained in any box that is opened by the key assigned to it . the first box contains $ 4 , the second $ 400 , and the third $ 4000 . what is the probability that a contestant will win more than $ 4000 ?
Options: a ) 2 / 6 , b ) 1 / 6 , c ) 1 / 8 , d ) 1 / 3 , e ) 1 / 2
Rationale: let ' s call the boxes that contain $ 4 , $ 400 , and $ 4000 , respectively , box a , box b , box c . these are opened , respectively , by key a , key b , and key c . we want to know the probability of winning more than $ 4000 . notice that if the distribution of keys is : box a = key b box b = key a box c = key c then the contestant wins exactly $ 4000 , not more than $ 4000 . the only configuration that leads to winning more than $ 1000 is : box a = key a box b = key b box c = key c i . e . , getting all three keys correct . that ' s the only way to be more than $ 4000 . so , really , the question can be rephrased : what is the probability of guessing the order of keys so that each key matches the correct box ? well , for a set of three items , the number of possible permutations is 3 ! = 3 * 2 * 1 = 6 . of those 6 possible permutations , only one of them leads to all three keys being paired with the right box . so , the answer is probability = 1 / 6 answer : b
Answer: b
Python program:
a = 3 * 2
b = 1 / a
Problem: for any integer k greater than 1 , the symbol k * denotes the product of all integers between 1 and k , inclusive . if k * is a multiple of 1701 what is the least possible value of k ?
Options: a ) 8 , b ) 10 , c ) 12 , d ) 14 , e ) 16
Rationale: "1701 = 3 * 3 * 3 * 3 * 3 * 7 thus k must include numbers at least up to the number 12 so that there are at least five appearances of 3 ( that is : 3 , 6 , 9 = 3 * 3 , and 12 ) . the answer is c ."
Answer: c
Python program:
a = 1701 / 3
b = a / 3
c = 1 + 4 
d = b / c
Problem: a car traveled 462 miles per tankful of gasoline on the highway and 336 miles per tankful of gasoline in the city . if the car traveled 12 fewer miles per gallon in the city than on the highway , how many miles per gallon did the car travel in the city ?
Options: a ) 14 , b ) 16 , c ) 21 , d ) 22 , e ) 32
Rationale: "i treat such problems as work ones . work = rate * time mileage ( m ) = rate ( mpg ) * gallons ( g ) x gallons is a full tank { 462 = rx { 336 = ( r - 12 ) x solve for r , r = 44 44 - 12 = 32 mpg e"
Answer: e
Python program:
a = 462 - 336
b = a / 12
c = 336 / b
Problem: the side of a rhombus is 25 m and length of one of its diagonals is 10 m . the area of the rhombus is ?
Options: a ) 244.85 , b ) 224.95 , c ) 244.85 , d ) 224.95 , e ) 244.95
Rationale: "area of the rhombus = 1 / 2 * p * √ 4 ( a ) 2 - ( p ) 2 a = 25 ; p = 10 a = 1 / 2 * 10 * √ 4 ( 25 ) 2 - ( 10 ) 2 = 1 / 2 * 10 * √ 2500 - 100 = 1 / 2 * 10 * √ 2400 a = 244.95 answer : e"
Answer: e
Python program:
a = 2 * 25
b = a ** 2
c = 10 ** 2
d = b - c
e = math.sqrt(d)
f = 10 * e
g = f / 2
Problem: two dogsled teams raced across a 300 - mile course in wyoming . team a finished the course in 3 fewer hours than did team b . if team a ’ s average speed was 5 miles per hour greater than that of team b , what was team b ’ s average speed , in miles per hour ?
Options: a ) 12 , b ) 15 , c ) 18 , d ) 20 , e ) 25
Rationale: speed of b = s speed of a = s + 5 time taken by b = 300 / s time taken by a = 300 / ( s + 5 ) difference in their time is 3 hrs . 300 / s - 3 = 300 / ( s + 5 ) plug in the values from the option no need of choosing 12 & 18 it wo n ' t satisfy a ) if we take 15 then t ( b ) = 300 / 15 = 20 t ( a ) = 300 / 20 = 15 . hence from this option difference comes out to be 5 which is not correct b ) if we take 20 then t ( b ) = 300 / 20 = 15 t ( a ) = 300 / 25 = 12 difference in timing is 3 hence option d is correct
Answer: d
Python program:
a = 3 * 5
b = negate + ( 
c = 3 * 5
d = c ** 2
e = 4 * 3
f = 300 * 5
g = e * negate
h = d - g
i = math.sqrt(h)
j = b / i
Problem: a shopkeeper forced to sell at cost price , uses a 700 grams weight for a kilogram . what is his gain percent ?
Options: a ) 10 % , b ) 9 % , c ) 11.11 % , d ) 42.85 % , e ) none of these
Rationale: "shopkeeper sells 700 g instead of 1000 g . so , his gain = 1000 - 700 = 300 g . thus , % gain = ( 300 * 100 ) / 700 = 42.85 % . answer : option d"
Answer: d
Python program:
a = 2 * 100
b = 100 / 2
c = a + b 
d = c / 700
e = d * 100
Problem: a man can do a piece of work in 7 days , but with the help of his son , he can do it in 3 days . in what time can the son do it alone ?
Options: a ) 5 , b ) 7 , c ) 15 / 2 , d ) 21 / 4 , e ) 18 / 5
Rationale: "son ' s 1 day ' s work = ( 1 / 3 ) - ( 1 / 7 ) = 4 / 21 the son alone can do the work in 21 / 4 days answer is d"
Answer: d
Python program:
a = 7 * 3
b = 7 - 3
c = a / b
Problem: what is log 3 ( 4 ) log 4 ( 5 ) . . . log 80 ( 81 ) ?
Options: a ) 1 , b ) 4 , c ) 81 , d ) log 80 243 , e ) e 81
Rationale: recall the change of base formula logb ( a ) = ln ( a ) ln ( b ) : ( alternatively , we can substitute logc for ln on the right , as long as the base is the same on the top and on the bottom . ) using this , we can rewrite the entire expression using natural logarithms , as ln ( 4 ) ln ( 3 ) ln ( 5 ) ln ( 4 ) ln ( 81 ) ln ( 80 ) = ln ( 81 ) ln ( 3 ) = log 3 ( 81 ) = log 3 ( 34 ) = 4 : correct answer b
Answer: b
Python program:
a = math.log(81)
b = math.log(3)
c = a / b
Problem: 0.0005521 / 0.0000110 x 15.05 = ?
Options: a ) 7534 , b ) 255.4 , c ) 756.4 , d ) 755.4 , e ) 752.4
Rationale: "explanation : ? = 0.0005521 / 0.0000110 x 15.05 = 755.4 answer : option d"
Answer: d
Python program:
a = 0 / 5521
Problem: the average of 6 observations is 16 . a new observation is included and the new average is decreased by 1 . the seventh observation is ?
Options: a ) 1 , b ) 3 , c ) 9 , d ) 6 , e ) 7
Rationale: "let seventh observation = x . then , according to the question we have = > ( 96 + x ) / 7 = 15 = > x = 9 hence , the seventh observation is 9 . answer : c"
Answer: c
Python program:
a = 16 - 1
b = 6 + 1 
c = a * b
d = 16 * 6
e = c - d
Problem: the total age of a and b is 16 years more than the total age of b and c . c is how many years younger than a ?
Options: a ) 16 , b ) 24 , c ) c is elder than a , d ) data inadequate , e ) none
Rationale: "solution [ ( a + b ) - ( b + c ) ] = 16 â € ¹ = â € º a - c = 16 . answer a"
Answer: a
Python program:
a = 16 * 1
Problem: keats library purchases a number of new books , all in the category of biography , and the library does not acquire any other books . with the addition of the new biographies , the biography collection of the library amounts to 25 % of the total number of books in the library . if prior to the purchase , only 20 % of the books in keats library were biographies , by what percent has the number of biographies in the library increased ?
Options: a ) 23 % , b ) 28 % , c ) 33 % , d ) 38 % , e ) 43 %
Rationale: "let x be the number of new biographies added to the library . let b be the original number of biographies , so the original number of books was 5 b . 0.25 ( 5 b + x ) = b + x 0.25 b = 0.75 x x = 0.33 b the answer is c ."
Answer: c
Python program:
a = 25 * 100
b = 20 * 100
c = a - b
d = 100 - 25
e = c / d
f = e / 20
g = f * 100
Problem: a train running at the speed of 60 km / hr crosses a pole in 36 seconds . what is the length of the train ?
Options: a ) 186 m , b ) 176 m , c ) 100 m , d ) 600 m , e ) 765 m
Rationale: "speed = ( 60 * 5 / 18 ) m / sec = ( 50 / 3 ) m / sec length of the train = ( speed x time ) = ( 50 / 3 * 36 ) m = 600 m . answer : d"
Answer: d
Python program:
a = 60 * 1000
b = a / 3600
c = b * 36
Problem: the product of three consecutive numbers is 504 . then the sum of the smallest two numbers is ?
Options: a ) 11 , b ) 15 , c ) 20 , d ) 38 , e ) 56
Rationale: "product of three numbers = 504 504 = 7 * 8 * 9 . so , the three numbers are 7 , 8 and 9 . and sum of smallest of these two = 7 + 8 = 15 . answer : option b"
Answer: b
Python program:
a = 2 ** 504
b = math.factorial(4)
c = a * b
Problem: if 3 ^ 20 x 2 ^ 20 = 6 ^ n what is the value of n ?
Options: a ) 18 , b ) 20 , c ) 22 , d ) 24 , e ) 26
Rationale: "3 ^ 20 * 2 ^ 20 = 6 ^ n 6 ^ 20 = 6 ^ n therefore n = 20 b"
Answer: b
Python program:
a = 2 ** 20
b = 3 ** 20
c = a * b
d = math.log(c)
e = math.log(6)
f = d / e
Problem: 20 men can do a work in 40 days . when should 20 men leave the work so that the entire work is completed in 40 days after they leave the work ?
Options: a ) 0 days , b ) 10 days , c ) 20 days , d ) 30 days , e ) 40 days
Rationale: "total work to be done = 20 * 40 = 800 let 20 men leave the work after ' p ' days , so that the remaining work is completed in 40 days after they leave the work . 40 p + ( 20 * 40 ) = 800 40 p = 0 = > p = 0 days answer : a"
Answer: a
Python program:
a = 20 * 40
b = 40 * 20
c = a - b
d = c / 40