euclaise/mathqa_programs huggingface dataset:
Problem: a and b start walking towards each other at 6 pm at speed of 6 kmph and 4 kmph . they were initially 50 km apart . at what time do they meet ?
Options: a ) 8 pm , b ) 6 pm , c ) 11 pm , d ) 10 pm , e ) 5 pm
Rationale: "time of meeting = distance / relative speed = 50 / 4 + 6 = 50 / 10 = 5 hrs after 6 pm = 11 pm answer is c"
Answer: c
Python program:
a = 6 + 4 
b = 50 / a
c = 6 + b
Problem: what is the units digit of 33 ^ 2 * 17 ^ 3 * 49 ^ 3 ?
Options: a ) 1 , b ) 3 , c ) 5 , d ) 7 , e ) 9
Rationale: "the units digit of 33 ^ 2 is the units digit of 3 * 3 = 9 which is 9 . the units digit of 17 ^ 3 is the units digit of 7 * 7 * 7 = 343 which is 3 . the units digit of 49 ^ 3 is the units digit of 9 * 9 * 9 = 729 which is 9 . the units digit of 9 * 3 * 9 = 243 is 3 . the answer is b ."
Answer: b
Python program:
a = math.factorial(33)
b = math.factorial(2)
c = a * b
d = math.factorial(33)
e = math.factorial(3)
f = d * e
g = c + f 
h = g / 33
Problem: solution y is 30 percent liquid x and 70 percent water . if 2 kilograms of water evaporate from 10 kilograms of solution y and 2 kilograms of solution y are added to the remaining 6 kilograms of liquid , what percent of this new solution is liquid x ?
Options: a ) 34 , b ) 35 , c ) 36 , d ) 37 1 / 25 , e ) 40
Rationale: "in 8 kilograms of solution y there are 0.3 * 10 = 3 kilograms of solution x ; after 2 kilograms of water are replaced by 2 kilograms of solution y , to the existing 2.4 kilograms of solution x , 0.3 * 2 = 0.6 kilograms of solution x are added , so in the new solution of 8 kilograms there are 3 + 0.6 = 3.6 kilograms of solution x , which is 3.6 / 10 * 100 = 36 % of this new solution . answer : c ."
Answer: c
Python program:
a = 30 / 100
b = 10 * a
c = 30 / 100
d = 2 * c
e = b + d 
f = 30 / 100
g = 10 * f
h = 30 / 100
i = 2 * h
j = g + i 
k = 70 / 100
l = 10 * k
m = l - 2
n = 70 / 100
o = 2 * n
p = m + o 
q = j + p 
r = e / q
s = 100 * r
Problem: water is poured into a tank so that the tank is being filled at the rate of 4 cubic feet per hour . if the empty rectangular tank is 6 feet long , 4 feet wide , and 3 feet deep , approximately how many hours does it take to fill the tank ?
Options: a ) 16 , b ) 18 , c ) 20 , d ) 22 , e ) 24
Rationale: "the volume the tank is : length * width * depth = 6 * 4 * 3 = 72 cubic feet . 72 cubic feet / 4 cubic feet per hour = 18 hours . it will take 18 hours to fill the tank . the answer is b ."
Answer: b
Python program:
a = volume_rectangular_prism / (
Problem: two pipes a and b can separately fill a cistern in 60 min and 75 min respectively . there is a third pipe in the bottom of the cistern to empty it . if all the 3 pipes are simultaneously opened , then the cistern is full in 50 min . in how much time , the third pipe alone can empty the cistern ?
Options: a ) 197 min , b ) 100 min , c ) 177 min , d ) 176 min , e ) 186 min
Rationale: work done by the third pipe in 1 min = 1 / 50 - ( 1 / 60 + 1 / 75 ) = - 1 / 100 . [ - ve sign means emptying ] the third pipe alone can empty the cistern in 100 min . answer : b
Answer: b
Python program:
a = 1 / 60
b = 1 / 75
c = a + b 
d = 1 / 50
e = c - d
f = 1/(e)
Problem: a and b undertake to do a piece of work for rs . 1200 . a alone can do it in 6 days while b alone can do it in 8 days . with the help of c , they finish it in 3 days . find the share of b .
Options: a ) 250 , b ) 450 , c ) 750 , d ) 800 , e ) none of them
Rationale: "c ' s 1 day ' s work = 1 / 3 - ( 1 / 6 + 1 / 8 ) = 24 a : b : c = ratio of their 1 day ' s work = 1 / 6 : 1 / 8 : 1 / 24 = 4 : 3 : 1 . a ’ s share = rs . ( 1200 * 4 / 8 ) = rs . 600 , b ' s share = rs . ( 1200 * 3 / 8 ) = rs . 450 c ' s share = rs . [ 1200 - ( 300 + 225 » ) = rs . 150 . answer is b"
Answer: b
Python program:
a = 4 + 3 
b = a + 1 
c = 1 / b
d = c * 1200
Problem: a trader sells 92 meters of cloth for rs . 9890 at the profit of rs . 24 per metre of cloth . what is the cost price of one metre of cloth ?
Options: a ) 22 , b ) 89.5 , c ) 76.9 , d ) 83.5 , e ) 11
Rationale: "sp of 1 m of cloth = 9890 / 92 = rs . 107.5 cp of 1 m of cloth = sp of 1 m of cloth - profit on 1 m of cloth = rs . 107.5 - rs . 24 = rs . 83.5 answer : d"
Answer: d
Python program:
a = 9890 / 92
b = a - 24
Problem: what is the least value of x . so that 21 x 57 is divisible by 3 .
Options: a ) 2 , b ) 0 , c ) 1 , d ) 3 , e ) 4
Rationale: "explanation : the sum of the digits of the number is divisible by 3 , then the number is divisible by 3 . 2 + 1 + x + 5 + 7 = 15 + x least value of x may be 0 therefore 15 + 0 = 15 is divisible by 3 . answer : option b"
Answer: b
Python program:
a = math.lcm(21, 57)
b = a / 57
c = b / 4
d = c / 4
Problem: the ratio of numbers is 3 : 4 and their h . c . f is 3 . their l . c . m is :
Options: a ) 12 , b ) 16 , c ) 36 , d ) 48 , e ) 98
Rationale: "let the numbers be 3 x and 4 x . then their h . c . f = x . so , x = 3 . so , the numbers are 9 and 12 . l . c . m of 9 and 12 = 36 . answer : c"
Answer: c
Python program:
a = 3 * 3
b = 4 * 3
c = math.lcm(a, b)
Problem: the average weight of a class of 20 boys was calculated to be 58.4 kgs and it was later found that one weight was misread as 56 kg instead of 65 kg . what is the correct weight ?
Options: a ) 67.4 kg , b ) 57.75 kg , c ) 58.85 kg , d ) 49.4 kg , e ) none of these
Rationale: "actual total weight is ( 20 ã — 58.4 - 56 + 65 ) = 1177 kgs actual average weight is 1177 / 20 = 58.85 kgs answer is c"
Answer: c
Python program:
a = 58 * 4
b = 65 - 56
c = a + b 
d = c / 20
Problem: the sale price sarees listed for rs . 400 after successive discount is 30 % and 20 % is ?
Options: a ) 297 , b ) 879 , c ) 342 , d ) 762 , e ) 224
Rationale: "400 * ( 70 / 100 ) * ( 80 / 100 ) = 224 answer : e"
Answer: e
Python program:
a = 400 * 30
b = a / 100
c = 400 - b
d = 400 * 30
e = d / 100
f = 400 - e
g = f * 20
h = g / 100
i = c - h
Problem: a runs 1 ¾ times as fast as b . if a gives b a start of 84 m , bow far must winning post be so that a and b might reach it at the same time ?
Options: a ) 196 m , b ) 194 m , c ) 186 m , d ) 296 m , e ) 106 m
Rationale: . ratio of the rates of a and b = 7 / 4 : 1 = 7 : 4 . so , in a race of 7 m , a gains 3 m over b . : . 3 m are gained by a in a race of 7 m . : . 84 m are gained by a in a race of ( 7 / 3 x 84 ) m = 196 m . : . winning post must be 196 m away from the starting point . answer is a .
Answer: a
Python program:
a = 4 + 3 
b = a / 3
c = b * 84
Problem: a box contains 13 apples , 12 of which are red . an apple is drawn from the box and its color is noted before it is eaten . this is done a total of n times , and the probability that a red apple is drawn each time is less than 0.5 . what is the smallest possible value of n ?
Options: a ) 3 , b ) 4 , c ) 5 , d ) 6 , e ) 7
Rationale: "p ( choosing a red apple 7 times in a row ) = 12 / 13 * 11 / 12 * 10 / 11 * 9 / 10 * 8 / 9 * 7 / 8 * 6 / 7 = 6 / 13 < 0.5 the answer is e ."
Answer: e
Python program:
a = 0 * 5
b = a + 1
Problem: a soccer store typically sells replica jerseys at a discount of 30 percent to 50 percent off list price . during the annual summer sale , everything in the store is an additional 40 percent off the original list price . if a replica jersey ' s list price is $ 80 , approximately what percent of the list price is the lowest possible sale price ?
Options: a ) 20 , b ) 25 , c ) 30 , d ) 40 , e ) 50
Rationale: "let the list price be 2 x for min sale price , the first discount given should be 50 % , 2 x becomes x here now , during summer sale additional 20 % off is given ie sale price becomes 0.8 x it is given lise price is $ 80 = > 2 x = 80 = > x = 20 and 0.8 x = 32 so lowest sale price is 32 , which is 40 % of 80 hence , a is the answer"
Answer: a
Python program:
a = 80 / 2
Problem: a = { 2 , 3 , 5 , 7 , 11 } b = { 2 , 4 , 6 , 19 } two integers will be randomly selected from sets a and b , one integer from set a and one from set b , and then multiplied together . how many different products can be obtained ?
Options: a ) 15 , b ) 16 , c ) 19 , d ) 24 , e ) 36
Rationale: step 1 : find out the number of products you get . 5 distinct numbers in set a and 4 distinct in set b so number of products = 5 * 4 = 20 step 2 : remove the products that appear more than once . notice that 5 , 7 , 11 and 13 are primes and none of their multiples are in either set . so ignore them . we just need to focus on 2 and 3 of set a and 2 , 4 and 6 of set b . 2 , 3 2 , 4 , 6 the only product repeated when you take a number from each set is 12 . ( 3 * 4 and 2 * 6 ) rest all are distinct . answer = 20 - 1 = 24 note here that the second step will involve manual calculation since it will depend on the specific numbers you have in the two sets . d
Answer: d
Python program:
a = 6 * 4
Problem: if one - seventh of a number exceeds its eleventh part by 100 then the number is …
Options: a ) 770 , b ) 870 , c ) 1825 , d ) 1925 , e ) 925
Rationale: let no be : x 1 / 7 x - 1 / 11 x = 100 4 x / 77 = 100 x = 7700 / 4 = 1925 answer : d
Answer: d
Python program:
a = 10 + 1 
b = 100 * a
c = 3 + 4 
d = b * c
e = 10 + 1 
f = 3 + 4 
g = e - f
h = d / g
Problem: a regular 10 sided area is inscribed in a circle . if a and b are adjacent vertices of the pentagon and o is the center of the circle , what is the value of ∠ oab ?
Options: a ) 48 degrees
b ) 54 degrees
c ) 72 degrees
d ) 84 degrees
e ) 72 degrees
Rationale: its a regular 10 sided so divide the globe by 10 . = 360 / 10 = 36 36 would be the angle at o . angles at a and b are equivalent , so 36 + 2 x = 180 2 x = 144 x = 72 angles oab and oba will be 72 degrees each . e
Answer: e
Python program:
a = 360 / 10
b = const_180 - a
c = b / 2
Problem: a rower whose speed is 6 km / hr in still water rows to a certain point upstream and back to the starting point in a river which flows at 3 km / hr . what is the rower ' s average speed ( in km / hr ) for the total journey ?
Options: a ) 3.9 , b ) 4.2 , c ) 4.5 , d ) 4.8 , e ) 5.1
Rationale: "time upstream = d / 3 time downstream = d / 9 total time = d / 3 + d / 9 = 4 d / 9 average speed = 2 d / ( 4 d / 9 ) = 4.5 km / hr the answer is c ."
Answer: c
Python program:
a = 6 - 3
b = 6 + 3 
c = a + b 
d = c / 2
Problem: list i : 3 , 4 , 8 , 19 list ii : x , 3 , 4 , 8 , 19
Options: a ) 6 , b ) 7 , c ) 8 , d ) 9 , e ) 10
Rationale: we start by calculating the median of the numbers of list i : 3 , 4 , 8 , 19 . we see that the numbers in the list are in order already and , since we have an even number of numbers , the median is the average of the two middle numbers . median = ( 4 + 8 ) / 2 median = 12 / 2 median = 6 the median of list i is 6 . looking at list ii : x , 3 , 4 , 8 , 19 , we see that we have an odd number of terms . thus , when the list is ordered from least to greatest the median must be the middle term . since the medians of the two lists must be equal , we know that the median of list ii must be 6 and therefore x is 6 . the answer is a .
Answer: a
Python program:
a = 3 - 1
b = a * 3
Problem: there are 4 more women than there are men on a local co - ed softball team . if there are a total of 20 players on the team , what is the ratio of men to women ?
Options: a ) 8 / 12 , b ) 6 / 16 , c ) 4 / 16 , d ) 6 / 10 , e ) 4 / 10
Rationale: "w = m + 4 w + m = 20 m + 4 + m = 20 2 m = 16 m = 8 w = 12 ratio : 8 : 12 ans : a"
Answer: a
Python program:
a = 20 - 4
b = 1 + 1 
c = a / b
d = 20 - 4
e = 1 + 1 
f = d / e
g = f + 4 
h = c / g
Problem: it is currently 9 : 53 pm . what time was it in the morning exactly 149,061 minutes ago ?
Options: a ) 9 : 12 , b ) 9 : 18 , c ) 9 : 26 , d ) 9 : 32 , e ) 9 : 38
Rationale: divide by 60 to convert 149,061 minutes to hours : 149,061 / 60 = 2,484 r 21 . that is 2,484 hours and 21 minutes . all of the answers are in the 9 am hour before : 53 , thus we can assume 2,484 previous must be 9 : 53 am . 21 minutes before that is 9 : 32 am . d
Answer: d
Python program:
a = 53 - 3
b = 9 / a
Problem: a man can row his boat with the stream at 20 km / h and against the stream in 4 km / h . the man ' s rate is ?
Options: a ) 1 kmph , b ) 7 kmph , c ) 98 kmph , d ) 6 kmph , e ) 8 kmph
Rationale: "ds = 20 us = 4 s = ? s = ( 20 - 4 ) / 2 = 8 kmph answer : e"
Answer: e
Python program:
a = 20 - 4
b = a / 2
Problem: 6 chess players take part in a tournament . every player plays twice with each of his opponents . how many games are to be played ?
Options: a ) 19 , b ) 20 , c ) 30 , d ) 33 , e ) 34
Rationale: "though 2 * ( 6 c 2 ) is the correct approcah to do this , but for people like me who find perm , comb n prob a nightmare , an easy approach can be used . the first guy has to play 2 matches with the rest of 5 , so he ' ll play 10 matches . similarly , second guy has to play with the rest of 4 as his 2 games with the first guy are already played . so he plays 8 matches . this continues like this and the total matches are 10 + 8 + 6 . . . + 2 10 + 8 + . . . + 2 = 2 ( 5 + 4 + . . . + 1 ) = 2 ( ( 5 * 6 ) / 2 ) = 5 * 6 = 30 . answer : c"
Answer: c
Python program:
a = 6 - 1
b = 6 * a
Problem: the time taken by a man to row his boat upstream is twice the time taken by him to row the same distance downstream . if the speed of the boat in still water is 51 kmph , find the speed of the stream ?
Options: a ) 12 kmph , b ) 13 kmph , c ) 14 kmph , d ) 15 kmph , e ) 17 kmph
Rationale: "the ratio of the times taken is 2 : 1 . the ratio of the speed of the boat in still water to the speed of the stream = ( 2 + 1 ) / ( 2 - 1 ) = 3 / 1 = 3 : 1 speed of the stream = 51 / 3 = 17 kmph answer : e"
Answer: e
Python program:
a = 51 * 2
b = a / 3
c = 51 - b
Problem: the average ( arithmetic man ) of 3 integers a , b , and c is exactly 4 times the median . if a < b < c and a = 0 , what is the value of c / b ?
Options: a ) 2 , b ) 3 , c ) 4 , d ) 11 , e ) can not be determined from the information given .
Rationale: the average of three integers a , b , and c is exactly twice the median - - > ( a + b + c ) / 3 = 4 b - - > since a = 0 , then ( 0 + b + c ) / 3 = 4 b - - > c = 11 b - - > c / b = 11 . answer : d .
Answer: d
Python program:
a = 4 * 3
b = a - 1
Problem: in 1950 , richard was 4 times as old as robert . in 1955 , richard was 3 times as old as robert . in which year was richard 1.75 times as old as robert ?
Options: a ) 1960 , b ) 1965 , c ) 1970 , d ) 1975 , e ) 1980
Rationale: "in 1950 : ri = 4 ro - - - - - - - - - - - - - - eq 1 in 1955 : ri + 5 = 3 ( ro + 5 ) - - - - - - - - - eq 2 thus in 1950 , solving eq 1 and eq 2 ro = 10 , ri = 40 now for each year we can calculate : 1960 : ri = 50 , ro = 20 1965 : ri = 55 , ro = 25 1980 : ri = 40 , ro = 70 thus 8 ans : e"
Answer: e
Python program:
a = 4 + 3 
b = 1 + 75 
c = 1950 + b
Problem: raman ' s salary was decreased by 50 % and subsequently increased by 50 % . how much percent does he loss
Options: a ) 75 , b ) 65 , c ) 45 , d ) 25 , e ) 35
Rationale: "explanation : let the origianl salary = rs . 100 it will be 150 % of ( 50 % of 100 ) = ( 150 / 100 ) * ( 50 / 100 ) * 100 = 75 so new salary is 75 , it means his loss is 25 % answer : option d"
Answer: d
Python program:
a = 100 * 100
b = 100 - 50
c = 100 + 50 
d = b * c
e = a - d
f = e / 100
Problem: a dishonest shopkeeper professes to sell pulses at the cost price , but he uses a false weight of 930 gm . for a kg . his gain is … % .
Options: a ) 5.26 % , b ) 5.36 % , c ) 4.26 % , d ) 6.26 % , e ) 7.53 %
Rationale: "his percentage gain is 100 * 7 / 930 as he is gaining 70 units for his purchase of 930 units . so 7.53 % . answer : e"
Answer: e
Python program:
a = 4 + 1 
b = a * 2
c = b * 100
d = 930 / c
e = 1/(d)
f = e - 1
g = f * 100
Problem: the majority owner of a business received 25 % of the profit , with each of 4 partners receiving 25 % of the remaining profit . if the majority owner and two of the owners combined to receive $ 62,500 , how much profit did the business make ?
Options: a ) $ 100,000 , b ) $ 125,000 , c ) $ 150,000 , d ) $ 200,000 , e ) $ 250,000
Rationale: "majority owner + two partners = 0.25 * p + 2 * ( 0.25 ) * ( 0.75 ) * p = 0.25 * p + ( 0.5 ) * ( 0.75 ) * p = 0.25 * p + ( 0.375 ) * p = ( 0.625 ) * p this equals $ 62,500 . ( 0.625 ) * p = 62,500 - - - - - divide both sides by 625 ( 0.001 ) * p = 100 - - - - - - multiply by 1000 p = 100,000 answer = a"
Answer: a
Python program:
a = 1 + 4 
b = 100 * a
c = 100 * b
d = 25 / 100
e = 25 / 100
f = 25 / 100
g = 1 - f
h = e * g
i = h * 2
j = d + i 
k = c / j
Problem: when a random experiment is conducted , the probability that event a occurs is 1 / 5 . if the random experiment is conducted 4 independent times , what is the probability that event a occurs exactly twice ?
Options: a ) 16 / 625 , b ) 56 / 625 , c ) 96 / 625 , d ) 126 / 625 , e ) 156 / 625
Rationale: "one case is : 1 / 5 * 1 / 5 * 4 / 5 * 4 / 5 = 16 / 625 the total number of possible cases is 4 c 2 = 6 p ( event a occurs exactly twice ) = 6 * ( 16 / 625 ) = 96 / 625 the answer is c ."
Answer: c
Python program:
a = 2 / 5
b = 1 - a
Problem: two trains are moving in opposite directions at 60 km / hr and 90 km / hr . their lengths are 1.10 km and 0.9 km respectively . the time taken by the slower train to cross the faster train in seconds is :
Options: a ) 28 sec , b ) 36 sec , c ) 48 sec , d ) 52 sec , e ) 56 sec
Rationale: "relative speed = ( 60 + 90 ) km / hr = 150 x 5 / 18 = 120 / 3 m / sec distance covered = ( 1.10 + 0.9 ) km = 2 km = 2000 m . required time = 2000 x 3 / 125 = 48 sec . answer : c ."
Answer: c
Python program:
a = 1 * 10
b = 60 * 1000
c = b / 3600
d = a / c
e = 0 * 9
f = 90 * 1000
g = f / 3600
h = e / g
i = d - h
Problem: a 6 - liter solution is 30 % alcohol . how many liters of pure alcohol must be added to produce a solution that is 50 % alcohol ?
Options: a ) 1.8 , b ) 2.1 , c ) 2.4 , d ) 2.7 , e ) 3.0
Rationale: "let x be the amount of pure alcohol required . 0.3 ( 6 ) + x = 0.5 ( x + 6 ) 0.5 x = 3 - 1.8 x = 2.4 liters the answer is c ."
Answer: c
Python program:
a = 6 * 30
b = a / 100
c = b * 2
d = 6 - c
Problem: find the average of all the numbers between 17 and 32 which are divisible by 3 .
Options: a ) 15 , b ) 18 , c ) 20 , d ) 26 , e ) none
Rationale: "sol . average = ( 21 + 24 + 27 + 30 / 4 ) = 102 / 4 = 25.5 answer d"
Answer: d
Python program:
a = 17 + 4 
b = 32 - 4
c = a + b 
d = c / 2
Problem: a boat can travel with a speed of 13 km / hr in still water . if the speed of the stream is 4 km / hr . find the time taken by the boat to go 72 km downstream ?
Options: a ) 2 hours , b ) 4 hours 12 minutes , c ) 4 hours , d ) 5 hours , e ) none
Rationale: "solution speed downstream = ( 13 + 4 ) km / hr = 17 km / hr . time taken to travel 72 km downstream = ( 72 / 17 ) hrs = 4 hrs 12 minutes . answer b"
Answer: b
Python program:
a = 13 + 4 
b = 72 / a
Problem: if you add all the numbers on your mobile phone , what is the answer ?
Options: a ) 45 , b ) 50 , c ) 55 , d ) 100 , e ) 60
Rationale: 0 , 1 , 2 , 3 , 4 , 5 , 6 , 7 , 8 , 9 are in your mobile phone . therefore 0 + 1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 + 9 = 45 answer is a
Answer: a
Python program:
a = 10 - 1
b = 1 + a 
c = b / 2
d = 10 - 1
e = c * d
Problem: what is the sum of the integers from - 190 to 192 inclusive ?
Options: a ) 0 , b ) 5 , c ) 383 , d ) 875 , e ) 965
Rationale: "sum / n = average . sum = ( average ) ( n ) average = a + b / 2 = 190 + 192 / 2 = 1 number of items ( n ) = b - a + 1 = 192 - ( - 190 ) + 1 = 192 + 191 = 383 . sum = average * n = 1 * 383 = 383 . answer is c"
Answer: c
Python program:
a = 190 * 192
b = a / 4
Problem: in a certain candy store , 22 % of the customers are caught sampling the candy and are charged a small fine , but 15 % of the customers who sample the candy are not caught . what is the total percent of all customers who sample candy ?
Options: a ) 22 % , b ) 23 % , c ) 24 % , d ) 26 % , e ) 34 %
Rationale: since 15 % of the customers who sample the candyare notcaught , then 88 % of the customers who sample the candyarecaught : { % of customers who sample candy } * 0.85 = 0.22 ; { % of customers who sample candy } = 0.259 answer : d .
Answer: d
Python program:
a = 100 - 15
b = a / 100
c = 22 / b
Problem: the jogging track in a sports complex is 561 m in circumference . deepak and his wife start from the same point and walk in opposite directions at 4.5 km / hr and 3.75 km / hr respectively . they will meet for the first time in ?
Options: a ) 5.29 min , b ) 5.28 min , c ) 4.08 min , d ) 9.28 min , e ) 5.988 min
Rationale: clearly , the two will meet when they are 561 m apart . to be ( 4.5 + 3.75 ) = 8.25 km apart , they take 1 hour . to be 561 m apart , they take ( 100 / 825 * 561 / 1000 ) hrs = ( 561 / 8250 * 60 ) min = 4.08 min . answer : c
Answer: c
Python program:
a = 561 / 1000
b = 4 + 5 
c = a / b
d = c * const_60
Problem: at a small company , 76 percent of the employees are women , and 60 percent of the employees are married . if 2 / 3 of the men are single , what fraction of the women are married ?
Options: a ) 13 / 19 , b ) 1 / 3 , c ) 9 / 20 , d ) 7 / 10 , e ) 5 / 7
Rationale: "lets take total employees are 100 . given that , total women = 76 and total married = 60 . total men = 100 - 76 = 24 and single men = 2 / 3 * 24 = 16 . married men = total men - single men = 24 - 16 = 8 . married women = total married - married men = 60 - 8 = 52 . fraction of women are married = married women / total women = 52 / 76 = 13 / 19 . ans a"
Answer: a
Python program:
a = 60 / 100
b = 76 / 100
c = 1 - b
d = 2 / 3
e = 1 - d
f = c * e
g = a - f
h = 76 / 100
i = g / h
Problem: a shopkeeper sells 20 % of his stock at 25 % profit ans sells the remaining at a loss of 5 % . he incurred an overall profit of rs . 400 . find the total worth of the stock ?
Options: a ) 25500 , b ) 25000 , c ) 40500 , d ) 20000 , e ) 40000
Rationale: "let the total worth of the stock be rs . x . the sp of 20 % of the stock = 1 / 5 * x * 5 / 4 = 5 x / 20 the sp of 80 % of the stock = 4 / 5 * x * 0.95 = 152 x / 200 total sp = 50 x / 200 + 152 x / 200 = 202 x / 200 overall profit = 152 x / 200 - x = 2 x / 200 x / 50 = 400 = > x = 40000 answer : e"
Answer: e
Python program:
a = 5 / 100
b = 100 - 20
c = b / 100
d = a * c
e = 25 / 100
f = 20 / 100
g = e * f
h = d - g
i = 400 / h
Problem: a store reported total sales of $ 385 million for february of this year . if the total sales for the same month last year was $ 340 million , approximately what was the percent increase in sales ?
Options: a ) 2 % , b ) 17 % , c ) 20 % , d ) 65 % , e ) 13 %
Rationale: "new value – old value ) / old value x 100 we are given : february sales this year = 385 million february sales last year = 340 million we need to determine the percent increase between sales from last year to sales this year . thus , the new value = 385 million and the old value = 340 million . let ’ s plug them into our percent change formula . ( new value – old value ) / old value x 100 [ ( 385 – 340 ) / 340 ] x 100 65 / 340 x 100 ≈ 13 % . the answer is e ."
Answer: e
Python program:
a = 385 - 340
b = a / 340
c = b * 100
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 , 36 have long fur , 27 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 ) 6
Rationale: "no of dogs = 45 long fur = 36 brown = 27 neither long fur nor brown = 8 therefore , either long fur or brown = 45 - 8 = 37 37 = 36 + 27 - both both = 26 answer a"
Answer: a
Python program:
a = 36 + 27 
b = 45 - 8
c = a - b