euclaise/mathqa_programs huggingface dataset:
Problem: one half of a two digit number exceeds its one third by 6 . what is the sum of the digits of the number ?
Options: a ) 7 , b ) 9 , c ) 11 , d ) 12 , e ) 15
Rationale: "explanation : x / 2 – x / 3 = 6 = > x = 6 3 + 6 = 9 b )"
Answer: b
Python program:
a = 6 * 4
b = reminder + (
Problem: a box contains 5 pairs of shoes ( 10 shoes in total ) . if two shoes are selected at random , what it is the probability that they are matching shoes ?
Options: a ) 1 / 190 , b ) 1 / 20 , c ) 1 / 9 , d ) 1 / 10 , e ) 1 / 92
Rationale: "the problem with your solution is that we do n ' t choose 1 shoe from 20 , but rather choose the needed one after we just took one and need the second to be the pair of it . so , the probability would simply be : 1 / 1 * 1 / 9 ( as after taking one at random there are 9 shoes left and only one is the pair of the first one ) = 1 / 9 answer : c ."
Answer: c
Python program:
a = 10 - 1
b = 1 / a
Problem: in a company of 16 employees , 8 employees earn $ 38,000 , 4 employees earn $ 42,000 , and the 4 highest - paid employees earn the same amount . if the average annual salary for the 16 employees is $ 44,000 , what is the annual salary for each of the highest - paid employees ?
Options: a ) $ 54,000 , b ) $ 55,000 , c ) $ 56,000 , d ) $ 57,000 , e ) $ 58,000
Rationale: "8 * 38,000 + 4 * 42,000 + 4 x = 16 * 44,000 4 x = 704,000 - 304,000 - 168,000 4 x = 232,000 x = 58,000 the answer is e ."
Answer: e
Python program:
a = 4 * 4
b = 4 + 1 
c = a * b
d = c + 2 
e = 1 / 2
f = d + e 
g = f * 16
h = 16 * 4
i = 4 + 1 
j = h * i
k = g - j
l = 4 * 4
m = 4 + 1 
n = l * m
o = n * 4
p = k - o
q = p / 4
r = q * 1000
s = r / 1000
t = s - 8
Problem: if the price of petrol increases by 32 , by how much must a user cut down his consumption so that his expenditure on petrol remains constant ?
Options: a ) 25 % , b ) 20 % , c ) 24.2 % , d ) 33.33 % , e ) none of these
Rationale: explanation : let us assume before increase the petrol will be rs . 100 . after increase it will be rs ( 100 + 32 ) i . e 132 . now , his consumption should be reduced to : - = ( 132 − 100 ) / 132 ∗ 100 . hence , the consumption should be reduced to 24.2 % . answer : c
Answer: c
Python program:
a = 100 + 32 
b = 100 / a
c = 1 - b
d = c * 100
Problem: 108 . triangle a ’ s base is 7 % greater than the base of triangle b , and a ’ s height is 7 % less than the height of triangle b . the area of triangle a is what percent less or more than the area of triangle b ?
Options: a ) 9 % less , b ) 1 % less , c ) equal to each other , d ) 1 % more , e ) 2.1 % more
Rationale: "wish the question specified that we are talking about corresponding height . base of a = 8 / 7 * base of b height of a = 6 / 7 * height of b area of a = ( 1 / 2 ) * base of a * height of a = 8 / 7 * 6 / 7 * area of b = 48 / 49 * area of b area of a is 2.1 % more than the area of b . answer ( e )"
Answer: e
Python program:
a = 100 * 100
b = 100 + 7 
c = 100 - 7
d = b * c
e = a - d
f = 100 / e
Problem: if 2 / z = 2 / ( z + 1 ) + 2 / ( z + 64 ) which of these integers could be the value of z ?
Options: a ) 0 , b ) 1 , c ) 2 , d ) 5 , e ) 8
Rationale: "solving for z algebraically in this problem would not be easy . instead , we can follow the hint in the question ( “ which of these integers … ” ) and test each answer choice : a . 2 / 0 = 2 / 1 + 2 / 64 incorrect ( division by zero ) b . 2 / 1 = 2 / 2 + 2 / 65 incorrect c . 2 / 2 = 2 / 3 + 2 / 66 incorrect d . 2 / 3 = 2 / 4 + 2 / 69 incorrect e . 2 / 4 = 2 / 5 + 2 / 72 correct the correct answer is e , because it contains the only value that makes the equation work . notice how quickly this strategy worked in this case"
Answer: e
Python program:
a = 2 + 2 
b = a + 1 
c = 64 / b
Problem: praveen starts business with rs . 3360 and after 5 months , hari joins with praveen as his partner . after a year , the profit is divided in the ratio 2 : 3 . what is hari ’ s contribution in the capital ?
Options: a ) s . 7500 , b ) s . 8640 , c ) s . 8500 , d ) s . 9000 , e ) s . 6000
Rationale: let hari ’ s capital be rs . x . then , 3360 * 12 / 7 x = 2 / 3 = > 14 x = 120960 = > x = 8640 . answer : b
Answer: b
Python program:
a = 5 / 12
b = 1 - a
c = 3360 / b
d = 2 / 3
e = c / d
Problem: the average ( arithmetic mean ) of 10 , 20 , and 60 is 5 more than the average of 10 , 40 , and what number ?
Options: a ) 25 , b ) 60 , c ) 50 , d ) 30 , e ) 40
Rationale: "a 1 = 90 / 3 = 30 a 2 = a 1 - 5 = 25 sum of second list = 25 * 3 = 75 therefore the number = 75 - 50 = 25 a"
Answer: a
Python program:
a = 10 + 20 
b = a + 60 
c = 5 * 3
d = c + 10 
e = d + 40 
f = b - e
Problem: jill invests $ 10000 in an account that pays an annual rate of 3.96 % , compounding semi - annually . approximately how much does she have in her account after two years ?
Options: a ) $ 10079.44 , b ) $ 10815.83 , c ) $ 12652.61 , d ) $ 14232.14 , e ) $ 20598.11
Rationale: solution : first of all , notice the magic word “ approximately ” — the test - writer is letting us know estimation is perfectly fine . furthermore , the answer choices are nicely spread out , which will facilitate estimating . ok , get ready for some fast & furious estimation . the interest rate 3.96 % is an ugly number , so i ’ m going to approximate that as 4 % . it compounds semiannually , so that means that there ’ s 2 % every six months , and that happens four times in two years . well , 2 % of $ 10000 is $ 200 . if you get $ 200 , or a little more , on four occasions , that ’ s a little more than $ 800 in interest . we expect an answer slightly higher than $ 10800 , so of course ( b ) is just right . notice , i estimated so that everything up until the last sum was single - digit math . single - digit calculations are a good standard for which to strive when you are practicing estimation . by the way , if you find the bank that will do answer ( e ) , double your money in only two years , that ’ s terrific , but it probably is something wildly illegal , a ponzi scheme or worse ! in the real world , that just doesn ’ t happen . on word problems , especially in financial situations , you should always have your antenna up for what ’ s realistic or unrealistic . answer ( b )
Answer: b
Python program:
a = 3 / 96
b = a / 2
c = 1 + b 
d = c ** 4
e = 10000 * d
Problem: 250 men work for 16 days and finish a work . how many men would do a job 3 times the previous one in 20 days ?
Options: a ) 700 , b ) 666 , c ) 600 , d ) 400 , e ) 800
Rationale: number of men needed to finish the required work ( variation , proportion method ) = 3 * 16 * 250 / 20 = 600 answer : c
Answer: c
Python program:
a = 250 * 16
b = 3 * a
c = b / 20
Problem: solution for 1.35 + . 123 + . 321
Options: a ) 2.91 , b ) 1.794 , c ) 1.338 , d ) 1.986 , e ) 1.999
Rationale: "1.35 + . 123 + . 321 = 0 0 = 0 - 1.35 - 0.123 - 0.321 0 = - 1.794 answer : b"
Answer: b
Python program:
a = 123 / 1000
b = 1 + 35 
c = 321 / 1000
d = b + c
Problem: the population of a town increases 25 % and 15 % respectively in two consecutive years . after the growth the present population of the town is 1150 . then what is the population of the town 2 years ago ?
Options: a ) a ) 400 , b ) b ) 500 , c ) c ) 600 , d ) d ) 700 , e ) e ) 800
Rationale: explanation : formula : ( after = 100 denominator ago = 100 numerator ) 1150 * 100 / 125 * 100 / 115 = 800 answer : option e
Answer: e
Python program:
a = 25 / 100
b = 1 + a 
c = 15 / 100
d = 1 + c 
e = b * d
f = 1150 / e
Problem: if 16 machine can finish a job in 45 days , then how many more machines would be needed to finish the job in one - third less time ?
Options: a ) a . 3 , b ) b . 8 , c ) c . 10 , d ) d . 12 , e ) e . 16
Rationale: "you might think of this in a management context - we can use the principle of ' person - hours ' to solve any problem where we have identical workers . so , using simpler numbers , suppose you know that 6 identical employees , working simultaneously , would finish a job in 5 hours . then that job requires 6 * 5 = 30 total hours of person - work . if instead you wanted the job done in 3 hours , you ' d assign 30 / 3 = 10 employees to do the job , because you want to get a total of 30 hours of work from the employees . we can solve this problem identically . if 16 machines ( identical ones , i assume ) work simultaneously for 45 days , they will do a total of 16 * 45 machine - days of work . so the job requires 16 * 45 days of machine work in total . we instead want the job done in 1 / 3 less time , so in 30 days . so we ' ll need 16 * 36 / 30 = 19.2 ~ = 19 machines , or 3 additional machines . a"
Answer: a
Python program:
a = 16 * 45
b = 3 / 4
c = b * 45
d = a / c
e = d - 16
Problem: two trains start simultaneously from opposite ends of a 160 - km route and travel toward each other on parallel tracks . train x , traveling at a constant rate , completes the 160 - km trip in 5 hours . train y , travelling at a constant rate , completes the 160 - km trip in 3 hours . how many kilometers had train x traveled when it met train y ?
Options: a ) 56 , b ) 58 , c ) 60 , d ) 62 , e ) 64
Rationale: if the two trains cover a total distance d , then train x travels ( 3 / 8 ) * d while train y travels ( 5 / 8 ) * d . if the trains travel 160 km to the meeting point , then train x travels ( 3 / 8 ) * 160 = 60 km . the answer is c .
Answer: c
Python program:
a = 160 / 5
b = 160 / 5
c = 160 / 3
d = b + c 
e = 160 / d
f = a * e
Problem: a , b and c invested rs . 6300 , rs . 4200 and rs . 10500 respectively , in a partnership business . find the total share of a & b in profit of rs . 12100 after a year ?
Options: a ) rs . 6030 , b ) rs . 4050 , c ) rs . 6050 , d ) rs . 7050 , e ) rs . 6080
Rationale: "6300 : 4200 : 10500 3 : 2 : 5 a ' share = 3 / 10 * 12100 = 3630 b ' s share = 2 / 10 * 12100 = 2420 required total share = 3630 + 2420 = 6050 answer : c"
Answer: c
Python program:
a = 6300 + 4200 
b = a + 10500 
c = 6300 / b
d = c * 12100
Problem: an athlete runs 200 metres race in 40 seconds . what is his speed ?
Options: a ) 23 , b ) 38 , c ) 18 , d ) 30 , e ) 28
Rationale: "speed = distance / time = 200 / 40 = 5 m / s = 5 * 18 / 5 = 3618 km / hr answer : c"
Answer: c
Python program:
a = 200 / 40
b = a * const_3_6
Problem: company p had 15 percent more employees in december than it had in january . if company p had 490 employees in december , how many employees did it have in january ?
Options: a ) 391 , b ) 426 , c ) 410 , d ) 423 , e ) 445
Rationale: "d = number of employees in december j = number of employees in january j x 1.15 = d j x 1.15 = 490 j = 490 / 1.15 j = 49,000 / 115 = 426 thus b is the correct answer ."
Answer: b
Python program:
a = 15 / 100
b = 1 + a 
c = 490 / b
Problem: the present worth of rs . 1404 due in two equal half - yearly instalments at 8 % per annum simple interest is :
Options: a ) rs . 1325 , b ) rs . 1300 , c ) rs . 1350 , d ) rs . 1500 , e ) none
Rationale: solution required sum = p . w . of rs . 702 due 6 month hence + p . w . of rs . 702 due 1 year hence = rs . [ ( 100 x 702 / 100 + 8 x 1 / 2 ) + ( 100 x 702 / 100 + ( 8 x 1 ) ) ] = rs . ( 675 + 650 ) = rs . 1325 . answer a
Answer: a
Python program:
a = 1404 / 2
b = 100 + 8 
c = b / 100
d = a / c
e = 1404 / 2
f = 8 / 2
g = 100 + f 
h = g / 100
i = e / h
j = d + i
Problem: the weight of every type a widget is the same , the weight of every type b widget is the same , and the weight of every type c widget is the same . if the weight of 7 type a widgets is equal to the weight of 3 type b widgets , and the weight of 5 type b widgets is equal to the weight of 7 type c widgets . what is the ratio of the total weight of 1 type a widget and 1 type b widget , to the total weight of 1 type b widget and 1 type c widget ?
Options: a ) 1 : 2 , b ) 2 : 3 , c ) 3 : 4 , d ) 4 : 5 , e ) 5 : 6
Rationale: "5 b = 7 c and so b = 7 c / 5 7 a = 3 b and so a = 3 b / 7 = 3 c / 5 a + b = 3 c / 5 + 7 c / 5 = 10 c / 5 b + c = 7 c / 5 + c = 12 c / 5 the ratio of a + b : b + c = 10 : 12 = 5 : 6 the answer is e ."
Answer: e
Python program:
a = 7 / 3
b = 1 + a 
c = 7 / 3
d = 5 / 3
e = c + d 
f = b / e
Problem: a shopkeeper buys mangoes at the rate of 6 a rupee and sells them at 4 a rupee . find his net profit or loss percent ?
Options: a ) 34 % , b ) 39 % , c ) 50 % , d ) 35 % , e ) 33 %
Rationale: "the total number of mangoes bought by the shopkeeper be 24 . if he buys 6 a rupee , his cp = 4 he selling at 4 a rupee , his sp = 6 profit = sp - cp = 6 - 4 = 2 profit percent = 2 / 4 * 100 = 50 % answer : c"
Answer: c
Python program:
a = 4 * 100
b = a / 6
Problem: in the graduating class of a certain college , 48 percent of the students are male and 52 percent are female . in this class 60 percent of the male and 20 percent of the female students are 25 years old or older . if one student in the class is randomly selected , approximately what is the probability that he or she will be less than 25 years old ?
Options: a ) a ) 0.9 , b ) b ) 0.6 , c ) c ) 0.45 , d ) d ) 0.3 , e ) e ) 0.25
Rationale: "percent of students who are 25 years old or older is 0.6 * 48 + 0.2 * 52 = ~ 39 , so percent of people who are less than 25 years old is 100 - 39 = 61 . answer : b ."
Answer: b
Python program:
a = 60 / 100
b = 100 - 20
c = b / 100
d = a * c
e = 1 - d
Problem: the cross - section of a cannel is a trapezium in shape . if the cannel is 15 m wide at the top and 4 m wide at the bottom and the area of cross - section is 1900 sq m , the depth of cannel is ?
Options: a ) 150 , b ) 200 , c ) 140 , d ) 240 , e ) 145
Rationale: "1 / 2 * d ( 15 + 4 ) = 1900 d = 200 answer : b"
Answer: b
Python program:
a = 15 + 4 
b = a / 2
c = 1900 / b
d = c / 4
e = d / 2
Problem: 20 percent of andrea ' s living room floor is covered by a carpet that is 4 feet by 9 feet . what is the area of her living room floor ?
Options: a ) 14.4 , b ) 180 , c ) 50.4 , d ) 60 , e ) 90
Rationale: "20 % of area of the floor = 4 * 9 square feet = 36 square feet i . e . 100 % area of floor = ( 36 / 20 ) * 100 = 180 square feet answer : option b"
Answer: b
Python program:
a = 4 * 9
b = 20 / 100
c = a / b
Problem: a student scored an average of 60 marks in 3 subjects : physics , chemistry and mathematics . if the average marks in physics and mathematics is 90 and that in physics and chemistry is 70 , what are the marks in physics ?
Options: a ) 86 , b ) 160 , c ) 76 , d ) 140 , e ) 26
Rationale: "given m + p + c = 60 * 3 = 180 - - - ( 1 ) m + p = 90 * 2 = 180 - - - ( 2 ) p + c = 70 * 2 = 140 - - - ( 3 ) where m , p and c are marks obtained by the student in mathematics , physics and chemistry . p = ( 2 ) + ( 3 ) - ( 1 ) = 180 + 140 - 180 = 140 answer : d"
Answer: d
Python program:
a = 90 * 2
b = 70 * 2
c = a + b 
d = 60 * 3
e = c - d
Problem: if m is an integer such that ( - 2 ) ^ 2 m = 2 ^ ( 21 - m ) then m = ?
Options: a ) 5 , b ) 6 , c ) 7 , d ) 8 , e ) 9
Rationale: "2 m = 21 - m 3 m = 21 m = 7 the answer is c ."
Answer: c
Python program:
a = 2 + 1 
b = 21 / a
Problem: each of the dogs in a certain kennel is a single color . each of the dogs in the kennel either has long fur or does not . of the 45 dogs in the kennel , 29 have long fur , 17 are brown , and 8 are neither long - furred nor brown . how many long - furred dogs are brown ?
Options: a ) 26 , b ) 19 , c ) 11 , d ) 8 , e ) 9
Rationale: no of dogs = 45 long fur = 29 brown = 17 neither long fur nor brown = 8 therefore , either long fur or brown = 45 - 8 = 37 37 = 29 + 17 - both both = 9 answer e
Answer: e
Python program:
a = 29 + 17 
b = 45 - 8
c = a - b
Problem: set a contains all the even numbers between 42 and 90 inclusive . set b contains all the even numbers between 62 and 110 inclusive . what is the difference between the sum of elements of set b and the sum of the elements of set a ?
Options: a ) 300 , b ) 350 , c ) 400 , d ) 450 , e ) 500
Rationale: "each term in set b is 20 more than the corresponding term in set a . the difference of the sums = 25 * 20 = 500 . the answer is e ."
Answer: e
Python program:
a = 62 - 42
b = 90 - 42
c = b / 2
d = c + 1 
e = a * d
Problem: of the 3,600 employees of company x , 1 / 3 are clerical . if the clerical staff were to be reduced by 1 / 6 , what percent of the total number of the remaining employees would then be clerical ?
Options: a ) 25 % , b ) 22.2 % , c ) 20 % , d ) 29.4 % , e ) 11.1 %
Rationale: "welcome , just post the question and the choices let ' s see , the way i did it was 1 / 3 are clerical out of 3600 so 1200 are clerical 1200 reduced by 1 / 6 is 1200 * 1 / 6 so it reduced 200 people , so there is 1000 clerical people left but since 200 people left , it also reduced from the total of 3600 so there are 3400 people total since 1000 clerical left / 3400 people total you get ( a ) 29.4 % answer : d"
Answer: d
Python program:
a = 1 / 3
b = 1 / 6
c = 1 - b
d = a * c
e = 1 / 3
f = 1 / 6
g = 1 - f
h = e * g
i = 1 / 3
j = 1 - i
k = h + j 
l = d / k
m = l * 100
Problem: an artist wishes to paint a circular region on a square poster that is 5 feet on a side . if the area of the circular region is to be 1 / 2 the area of the poster , what must be the radius of the circular region in feet ?
Options: a ) 1 / pi , b ) sqrt ( 2 / pi ) , c ) 2 / sqrt ( pi ) , d ) sqrt ( 12.5 / pi ) , e ) pi / 2
Rationale: "area of the poster is 5 x 5 = 25 1 / 2 the area = 12.5 pi * r ^ 2 = 12.5 r ^ 2 = 12.5 / pi r = sqrt ( 12.5 / pi ) answer ( d )"
Answer: d
Python program:
a = square_area / (
b = a / 2
c = math.sqrt(b)
Problem: the tax on a commodity is diminished by 17 % and its consumption increased by 15 % . the effect on revenue is ?
Options: a ) 2 % , b ) 8 % , c ) 4.5 % , d ) 6.5 % , e ) 1.5 %
Rationale: "100 * 100 = 10000 83 * 115 = 9545 - - - - - - - - - - - 10000 - - - - - - - - - - - 455 100 - - - - - - - - - - - ? = > 4.55 % decrease answer : c"
Answer: c
Python program:
a = 15 / 100
b = 1 + a 
c = 17 / 100
d = 1 - c
e = b * d
f = e * 100
g = 100 - f
Problem: if x is 20 percent greater than 80 , then x =
Options: a ) 68 , b ) 70.4 , c ) 96 , d ) 105.6 , e ) 108
Rationale: "x is 20 % greater than 80 means x is 1.2 times 80 ( in other words 80 + 20 / 100 * 80 = 1.2 * 80 ) therefore , x = 1.2 * 80 = 96.00 answer : c"
Answer: c
Python program:
a = 20 / 100
b = a * 80
c = 80 + b
Problem: a pet groomer has 7 animals to groom for the day ( 2 cats and 5 dogs ) . if she randomly selects 4 animals to groom before lunch , what is the probability she will finish all the cats before lunch ?
Options: a ) 3 / 7 , b ) 2 / 7 , c ) 12 / 13 , d ) 5 / 11 , e ) 4 / 7
Rationale: combination probability formula : ncr = n ! / [ r ! ( n - r ) ! ] total possible , select 4 animals from 7 animals = 7 c 4 = 7 ! / [ 4 ! ( 7 - 4 ) ! ] = 35 . to finish all 2 cats there must be 2 dogs , select 2 dogs from 5 = 5 c 2 = 10 . and , select 2 cats from 2 = 2 c 2 = 1 . 2 cats and 2 dogs = ( 1 ) ( 10 ) = 10 probability = ( number outcomes favorable ) / ( total number outcomes ) = 10 / 735 = 2 / 7 answer : b
Answer: b
Python program:
a = 2 / 7
Problem: at the wholesale store you can buy an 8 - pack of hot dogs for $ 1.75 , a 20 - pack for $ 3.05 , and a 250 - pack for $ 22.95 . what is the greatest number of hot dogs you can buy at this store with $ 250 ?
Options: a ) 1,108 , b ) 2,100 , c ) 2,108 , d ) 2,628 , e ) 2,256
Rationale: "to maximize number of hot dogs with 250 $ total number of hot dogs bought in 250 - pack = 22.95 * 10 = 229.5 $ amount remaining = 250 - 229.5 = 20.5 $ total number of hot dogs bought in 20 - pack = 3.05 * 6 = 18.3 $ amount remaining = 20.5 - 18.3 = 2.2 $ total number of hot dogs bought in 8 - pack = 1.55 * 1 = 1.55 $ amount remaining = 2.2 - 1.75 = 0.45 $ this amount is too less to buy any 8 - pack . greatest number of hot dogs one can buy with 250 $ = 250 * 10 + 20 * 6 + 8 * 1 = 2628 answer d"
Answer: d
Python program:
a = 250 / 22
b = a * 250
Problem: a bag contains an equal number of one rupee , 50 paise and 25 paise coins respectively . if the total value is 70 , how many coins of each type are there ?
Options: a ) 20 coins , b ) 30 coins , c ) 40 coins , d ) 25 coins , e ) none of these
Rationale: "let number of each type of coin = x . then , 1 × x + . 50 × x + . 25 x = 70 ⇒ 1.75 x = 70 ⇒ x = 40 coins answer c"
Answer: c
Python program:
a = 1/(4)
b = 1/(2)
c = a + b 
d = c + 1 
e = 70 / d
Problem: how many positive integers less than 26 are prime numbers , odd multiples of 5 , or the sum of a positive multiple of 2 and a positive multiple of 4 ?
Options: a ) 27 , b ) 21 , c ) 24 , d ) 22 , e ) 20
Rationale: 9 prime numbers less than 28 : { 2 , 3 , 5 , 7 , 11 , 13 , 17 , 19 , 23 } 3 odd multiples of 5 : { 5 , 15 , 25 } 10 numbers which are the sum of a positive multiple of 2 and a positive multiple of 4 : { 6 , 8 , 10 , 12 , 14 , 16 , 18 , 20 , 22 , 24 } notice , that 5 is in two sets , thus total # of integers satisfying the given conditions is 9 + 3 + 10 - 1 = 21 . answer : b .
Answer: b
Python program:
a = 26 - 2
b = a - 1
c = b - 1
Problem: how many liters of water must be evaporated from 50 liters of a 4 percent sugar solution to get a 5 percent sugar solution ?
Options: a ) 4 , b ) 6 , c ) 8 , d ) 10 , e ) 12
Rationale: "let x be the amount that needs to be evaporated . 0.04 ( 50 ) = 0.05 ( 50 - x ) 0.05 x = 2.5 - 2 x = 0.5 / 0.05 = 10 liters the answer is d ."
Answer: d
Python program:
a = 50 / 100
b = a * 5
c = 50 - b
Problem: a person lent a certain sum of money at 6 % per annum at simple interest and in 8 years the interest amounted to $ 520 less than the sum lent . what was the sum lent ?
Options: a ) 800 , b ) 1000 , c ) 1200 , d ) 1400 , e ) 1600
Rationale: "p - 520 = ( p * 6 * 8 ) / 100 p = 1000 the answer is b ."
Answer: b
Python program:
a = 6 * 8
b = a / 100
c = 1 - b
d = 520 / c
Problem: there are 30 players in a chess group , and each player plays each of the others once . given that each game is played by two players , how many total games will be played ?
Options: a ) 10 , b ) 30 , c ) 435 , d ) 60 , e ) 90
Rationale: "30 players are there . two players play one game with one another . so 30 c 2 = 30 * 29 / 2 = 435 so option c is correct"
Answer: c
Python program:
a = 30 - 1
b = 30 * a
c = b / 2
Problem: a wholesaler wishes to sell 100 pounds of mixed nuts at $ 1.50 a pound . she mixes peanuts worth $ 1.50 a pound with cashews worth $ 4.00 a pound . how many pounds of cashews must she use ?
Options: a ) 40 , b ) 45 , c ) 50 , d ) 55 , e ) 60
Rationale: "from the question stem we know that we need a mixture of 100 pounds of peanuts and cashews . if we represent peanuts as x and cashews as y , we get x + y = 100 . since the wholesaler wants to sell the mixture of 100 pounds @ $ 2.50 , we can write this as : $ 1.5 * ( x + y ) = $ 1.5 x + $ 4 y from the equation x + y = 100 , we can rewrite y as y = 100 - x and substitute this into our equation to get : $ 2.5 * ( x + 100 - x ) = $ 1.5 x + $ 4 ( 100 - x ) if you solve for x , you will get x = 60 , and therefore y = 40 . so the wholesaler must use 40 pounds of cashews . you can substitute into the original equation to see that : $ 250 = $ 1.5 ( 60 ) + $ 4 ( 40 ) answer is a ."
Answer: a
Python program:
a = 4 - 0
b = a * 100
c = b / 1
Problem: a certain number of horses and an equal number of men are going somewhere . half of the owners are on their horses ' back while the remaining ones are walking along leading their horses . if the number of legs walking on the ground is 90 , how many horses are there ?
Options: a ) 10 , b ) 12 , c ) 14 , d ) 16 , e ) 18
Rationale: "legs 18 * 4 = 72 now half on their horses so remaining on the walk so 9 men 9 men has 18 legs so , 18 + 72 = 90 legs walking answer : e"
Answer: e
Python program:
a = 2 / 2
b = 4 + a 
c = 90 / b
Problem: 240 is increased by 20 % . find the final number .
Options: a ) 200 , b ) 210 , c ) 180 , d ) 288 , e ) 220
Rationale: explanation final number = initial number + 20 % ( original number ) = 240 + 20 % ( 240 ) = 240 + 48 = 288 . answer d
Answer: d
Python program:
a = 20 / 100
b = 240 * a
c = 240 + b
Problem: convert 20 miles into yards ?
Options: a ) 25630 yards , b ) 35200 yards , c ) 39520 yards , d ) 42560 yards , e ) 41520 yards
Rationale: "1 mile = 1760 yards 20 miles = 20 * 1760 = 35200 yards answer is b"
Answer: b
Python program:
a = 3 + 2 
b = a * 2
c = 3 + 2 
d = c * 2
e = b * d
f = e * 20
g = 3 + 2 
h = g * 2
i = 3 + 2 
j = i * 2
k = h * j
l = f / k