euclaise/mathqa_programs huggingface dataset:
Problem: donovan and michael are racing around a circular 600 - meter track . if donovan runs each lap in 45 seconds and michael runs each lap in 40 seconds , how many laps will michael have to complete in order to pass donovan , assuming they start at the same time ?
Options: a ) 8 , b ) 7 , c ) 9 , d ) 6 , e ) 5
Rationale: one way of approaching this question is by relative speed method 1 . speed / rate of donovan = distance / time = > 600 / 45 = > 40 / 3 2 . speed / rate of michael = distance / time = > 600 / 40 = > 15 relative speed between them = 15 - 40 / 3 = > 5 / 3 ( we subtract the rates if moving in the same direction and add the rates if moving in the opposite direction ) in order to pass donovan - distance to be covered = 600 , relative rate = 5 / 3 total time taken by micheal to surpass donovan = distance / rate = > 600 * 3 / 5 = > 360 no . of laps taken by michael = total time / michael ' s rate = > 360 / 40 = > 9 hence correct answer is 9 laps . c
Answer: c
Python program:
a = 600 / 40
b = 600 / 45
c = a - b
d = 600 / c
e = d / 40
Problem: if the function q is defined by the formula q = 5 w / ( 4 m ( z ^ 2 ) ) , by what factor will q be multiplied if w is quadrupled , m is doubled , and z is tripled ?
Options: a ) 1 / 9 , b ) 2 / 9 , c ) 4 / 9 , d ) 3 / 9 , e ) 2 / 27
Rationale: we just need to find the factor thats all , w - > quadrupled - > 4 w m - > doubled - > 2 m z - > tripled - > 3 z hence , z ^ 2 = 9 z ^ 2 w is in numerator , and m * z in denominator . hence , additional factor being introduced = 4 / 2 * 9 = 4 / 18 = 2 / 9 = b
Answer: b
Python program:
a = 3 ** 2
b = 2 * a
c = 4 / b
Problem: carol spends 1 / 4 of her savings on a stereo and 2 / 3 less than she spent on the stereo for a television . what fraction of her savings did she spend on the stereo and television ?
Options: a ) 1 / 4 , b ) 2 / 7 , c ) 5 / 12 , d ) 1 / 2 , e ) 7 / 12
Rationale: total savings = s amount spent on stereo = ( 1 / 4 ) s amount spent on television = ( 1 - 2 / 3 ) ( 1 / 4 ) s = ( 1 / 3 ) * ( 1 / 4 ) * s = ( 1 / 12 ) s ( stereo + tv ) / total savings = s ( 1 / 4 + 1 / 12 ) / s = 1 / 4 answer : a
Answer: a
Python program:
a = 1 / 4
Problem: one week , a certain truck rental lot had a total of 18 trucks , all of which were on the lot monday morning . if 50 % of the trucks that were rented out during the week were returned to the lot on or before saturday morning of that week , and if there were at least 12 trucks on the lot that saturday morning , what is the greatest number of different trucks that could have been rented out during the week ?
Options: a ) 18 , b ) 16 , c ) 12 , d ) 8 , e ) 4
Rationale: "n - not rented trucks ; r - rented trucks n + r = 18 n + r / 2 = 12 r = 12 c"
Answer: c
Python program:
a = 50 / 100
b = 18 * a
c = 12 + b
Problem: a grocer has 400 pounds of coffee in stock , 25 percent of which is decaffeinated . if the grocer buys another 100 pounds of coffee of which 60 percent is decaffeinated , what percent , by weight , of the grocer ’ s stock of coffee is decaffeinated ?
Options: a ) 28 % , b ) 30 % , c ) 32 % , d ) 34 % , e ) 40 %
Rationale: 1 . 25 % of 400 = 100 pounds of decaffeinated coffee 2 . 60 % of 100 = 60 pounds of decaffeinated coffee 3 . wt have 160 pounds of decaffeinated out of 500 pounds , that means 160 / 500 * 100 % = 32 % . the correct answer is c .
Answer: c
Python program:
a = 25 / 100
b = a * 400
c = 60 / 100
d = 100 * c
e = b + d 
f = 400 + 100 
g = e / f
h = g * 100
Problem: calculate how much time could be saved if the train would run at its usual speed , given that it ran at 6 / 8 of its own speed and got to its destination in 11 hours ?
Options: a ) 2.5 hrs , b ) 2.9 hrs , c ) 4.5 hrs , d ) 3.5 hrs , e ) 1.5 hrs
Rationale: new speed = 6 / 8 of usual speed new time = 6 / 8 of usual time 6 / 8 of usual time = 10 hrs usual time = 10 * 6 / 8 = 7.5 hrs time saved = 10 - 7.5 = 2.5 hrs answer is a
Answer: a
Python program:
a = 11 * const_60
b = 6 / 8
c = 11 * b
d = c * const_60
e = a - d
f = reminder / (
g = f + 100
Problem: a person spent rs . 7,540 from his salary on food and 5,690 on house rent . after that he was left with 60 % of his monthly salary . what is his monthly salary ?
Options: a ) 73,075 , b ) 34,075 , c ) 23,075 , d ) 33,075 , e ) 32,075
Rationale: "total money spent on food and house rent = 7,540 + 5,690 = 13,230 which is 100 - 60 = 40 % of his monthly salary ∴ his salary = 13230 x 100 / 40 = 33075 answer : d"
Answer: d
Python program:
a = 4 + 1 
b = a * 100
c = b + 60 
d = math.sqrt(100)
e = c / d
Problem: a survey was sent to 80 customers , 9 of whom responded . then the survey was redesigned and sent to another 63 customers , 12 of whom responded . by approximately what percent did the response rate increase from the original survey to the redesigned survey ?
Options: a ) 2 % , b ) 5 % , c ) 14 % , d ) 28 % , e ) 69 %
Rationale: "rate of first survey = 9 / 80 rate of second survey = 12 / 63 % response rate increase ( 12 / 63 - 9 / 80 ) / ( 9 / 80 ) = 69 % answer is e = 69 %"
Answer: e
Python program:
a = 12 / 63
b = 9 / 80
c = a - b
d = c * 100
e = math.floor(d)
Problem: the speed of a boat in still water is 15 km / hr and the rate of current is 3 km / hr . the distance travelled downstream in 12 minutes is
Options: a ) 1.2 km , b ) 1.8 km , c ) 2.4 km , d ) 3.6 km , e ) 1.6 km
Rationale: "b = 15 km / hr , s = 3 km / hr , downstream b + s = 15 + 3 = 18 km / hr down stream time t = 12 min , we have to change it to hours so t = 12 / 60 = 1 / 5 hrs . distance = speed * time = 18 * 1 / 5 = 3.6 km . answer : d"
Answer: d
Python program:
a = 12 / const_60
b = 15 + 3 
c = a * b
Problem: a sum of rs . 395 was divided among a , b , and c in such a way that b gets 25 % more than a and 20 % more than c . what is the share of a ?
Options: a ) rs . 195 , b ) rs . 180 , c ) rs . 98 , d ) rs . 120 , e ) rs . 130
Rationale: let each one ’ s share is a , b and c respectively , then b = 125 a / 100 = 120 c / 100 a = 100 b / 125 = 4 / 5 b , c = 100 b / 120 = 5 / 6 b 4 / 5 b + b + 5 / 6 b = 395 , 79 b / 30 = 395 , b = 395 * 30 / 79 = 150 a = 4 * 150 / 5 = 120 answer : d
Answer: d
Python program:
a = 100 - 25
b = a / 100
c = 100 - 25
d = c / 100
e = 100 - 20
f = e / 100
g = d + f 
h = g + 1 
i = 395 / h
j = b * i
Problem: the ratio 5 : 4 expressed as a percent equals
Options: a ) 12.5 % , b ) 40 % , c ) 80 % , d ) 125 % , e ) none
Rationale: "solution 5 : 4 = 5 / 4 = ( 5 / 4 x 100 ) % . = 125 % . answer d"
Answer: d
Python program:
a = 5 / 4
b = a * 100
Problem: the current birth rate per certain number of people is 52 , whereas corresponding death rate is 16 per same number of people . if the net growth rate in terms of population increase is 1.2 percent , find number of persons . ( initally )
Options: a ) 4000 , b ) 2000 , c ) 3000 , d ) 5000 , e ) 1000
Rationale: "sol . net growth on x = ( 52 - 16 ) = 36 . net growth on 100 = ( 36 / x ã — 100 ) % = 1.2 % . then x = 3000 answer : c"
Answer: c
Python program:
a = 52 - 16
b = a / 1
c = 100 * b
Problem: 14 , 28 , 20 , 40 , 32 , 64 , . . . ?
Options: a ) 10 , b ) 25 , c ) 56 , d ) 21 , e ) 36
Rationale: "first , multiply by 2 and then subtract 8 . 14 14 * 2 = 28 28 - 8 = 20 20 * 2 = 40 40 - 8 = 32 32 * 2 = 64 64 - 8 = 56 answer : c"
Answer: c
Python program:
a = negate - (
Problem: the average of runs of a cricket player of 20 innings was 32 . how many runs must he make in his next innings so as to increase his average of runs by 6 ?
Options: a ) 96 , b ) 106 , c ) 158 , d ) 116 , e ) 122
Rationale: "average = total runs / no . of innings = 32 so , total = average x no . of innings = 32 * 20 = 640 now increase in avg = 4 runs . so , new avg = 32 + 6 = 38 runs total runs = new avg x new no . of innings = 38 * 21 = 798 runs made in the 11 th inning = 798 - 640 = 158 answer : c"
Answer: c
Python program:
a = 20 + 1 
b = 6 + 32 
c = a * b
d = 20 * 32
e = c - d
Problem: a is half good a work man as b and together they finish a job in 26 days . in how many days working alone b finish the job ?
Options: a ) 98 days , b ) 21 days , c ) 17 days , d ) 39 days , e ) 19 days
Rationale: "wc = 1 : 2 2 x + x = 1 / 26 = > x = 1 / 78 2 x = 1 / 78 = > 39 days answer : d"
Answer: d
Python program:
a = 3 / 2
b = 26 * a
Problem: jane and ashley take 20 days and 10 days respectively to complete a project when they work on it alone . they thought if they worked on the project together , they would take fewer days to complete it . during the period that they were working together , jane took an eight day leave from work . this led to jane ' s working for four extra days on her own to complete the project . how long did it take to finish the project ?
Options: a ) 12 days , b ) 15 days , c ) 16 days , d ) 18 days , e ) 20 days
Rationale: "let us assume that the work is laying 40 bricks . jane = 2 bricks per day ashley = 4 brick per day together = 6 bricks per day let ' s say first 8 days ashley works alone , no of bricks = 32 last 4 days jane works alone , no . of bricks = 8 remaining bricks = 40 - 40 = 0 so together , they would take 0 / 6 = 0 total no . of days = 8 + 4 + 0 = 12 answer is a"
Answer: a
Python program:
a = 1 / 20
b = 4 * a
c = 1 - b
d = 4 + 4 
e = 1 / 10
f = d * e
g = c - f
h = 1 / 20
i = 1 / 10
j = h + i 
k = g / j
l = 4 + 4 
m = k + l 
n = m + 4
Problem: if john runs in the speed of 9 km / hr from his house , in what time will he reach the park which is 300 m long from his house ?
Options: a ) 2 , b ) 4 , c ) 5 , d ) 3 , e ) 6
Rationale: speed = 9 * 5 / 18 = 2.5 m / sec time taken = 300 / 2.5 = 120 sec ie . 2 mins . answer : a
Answer: a
Python program:
a = 9 * 1000
b = 300 / a
c = b * const_60
Problem: a dishonest person wants to make a profit on the selling of milk . he would like to mix water ( costing nothing ) with milk costing 33 $ per litre so as to make a profit of 40 % on cost when he sells the resulting milk and water mixture for 36 $ . in what ratio should he mix the water and milk ?
Options: a ) 1 : 20 , b ) 1 : 10 , c ) 17 : 8 , d ) 17 : 4 , e ) 17 : 60
Rationale: first of all , let ' s consider 1 liter of the stuff he is going to sell - - - naive customers think it ' s pure milk , but we know it ' s some milk - water mixture . he is going to sell this liter of milk - water for $ 36 . this $ 36 should be a 40 % increase over cost . here , we need to think about percentage increases as multipliers . using multipliers ( cost ) * 1.40 = $ 36 cost = 36 / 1.4 = 360 / 12 = $ 25.71 if he wants a 40 % increase over cost on the sale of one liter of his milk - water , the cost has to be $ 25.71 . well , a liter of milk costs $ 33 , so if he is going to use just $ 30 of milk in his mixture , that ' s 25.71 / 33 = 60 / 77 of a liter . if milk is 60 / 77 of the liter , then water is 17 / 77 of the liter , and the ratio of water to milk is 17 : 60 . answer choice ( e )
Answer: e
Python program:
a = 100 + 40 
b = a / 100
c = 36 / b
d = 33 - c
e = 100 + 40 
f = e / 100
g = 36 / f
h = d / g
Problem: if the sides of a triangle are 26 cm , 18 cm and 10 cm , what is its area ?
Options: a ) 90
b ) 110
c ) 130
d ) 140
e ) 150
Rationale: the triangle with sides 26 cm , 18 cm and 10 cm is right angled , where the hypotenuse is 26 cm . area of the triangle = 1 / 2 * 18 * 10 = 90 cm 2 answer : option a
Answer: a
Python program:
a = 18 * 10
b = a / 2
Problem: if x is the sum of first 100 positive even integers and y is the sum of first 100 positive odd integers , what is the value of x - y ? please try to explain your answers
Options: a ) 0 , b ) 25 , c ) 50 , d ) 75 , e ) 100
Rationale: first even minus first odd = 2 - 1 = 1 ; the sum of first 2 even integers minus the sum of first 2 odd integers = ( 2 + 4 ) - ( 1 + 3 ) = 2 ; the sum of first 3 even integers minus the sum of first 3 odd integers = ( 2 + 4 + 6 ) - ( 1 + 3 + 5 ) = 3 ; we can see the patterns here , so the sum of first 100 positive even integers minus the sum of first 100 positive odd integers will be 100 . answer : e .
Answer: e
Python program:
a = 100 * 1
Problem: the ratio of the amount of the oil bill for the month of february to the amount of the oil bill for the month of january was 3 : 2 . if the oil bill for february had been $ 30 more , the corresponding ratio would have been 5 : 3 . how much was the oil bill for january ?
Options: a ) $ 120 , b ) $ 150 , c ) $ 180 , d ) $ 210 , e ) $ 240
Rationale: "3 : 2 = 9 : 6 and 5 : 3 = 10 : 6 . an increase in $ 30 increases the ratio by 1 : 6 . therefore , january ' s bill was 6 ( $ 30 ) = $ 180 . the answer is c ."
Answer: c
Python program:
a = 5 / 3
b = 3 / 2
c = a - b
d = 30 / c
Problem: if x - y - z = 03 x + 4 y + 3 z = 45 x + 2 y + 7 z = 22 , what is the value of z ?
Options: a ) 3 , b ) 4 , c ) 5 , d ) 2 , e ) 1
Rationale: explanation : 4 x + 2 y - 5 z = - 21 â € “ - - - - - - - i 2 x - 2 y + z = 7 â € “ - - - - - - ii 4 x + 3 y - z = - 1 - - - - - - - - iii solve the first equation for x . x - y - z = 0 x = y + z substitute the solution for x into the second and third equations . ii - - - > 3 * ( y + z ) + 4 y + 3 z = 4 3 y + 3 z + 4 y + 3 z = 4 7 y + 6 z = 4 iii - - - - > 5 * ( y + z ) + 2 y + 7 z = 22 5 y + 5 z + 2 y + 7 z = 22 7 y + 12 z = 22 subtract the new second equation from the new third equation and solve for z . 7 y + 12 z = 22 - ( 7 y + 6 z = 4 ) 6 z = 18 z = 3 answer is a
Answer: a
Python program:
a = 1 + 4 
b = 4 * 22
c = 22 + b 
d = a * c
e = 2 * 22
f = 22 + e 
g = d + f 
h = 45 + 2 
i = 1 + 4 
j = i * 7
k = h + j 
l = g / k
m = l * 7
n = m / 22
o = 1 + 4 
p = n / o
Problem: a call center has two teams . each member of team a was able to process 1 / 5 calls as compared to each member of team b . if team a has 5 / 8 as many number of call center agents as team b , what fraction of the total calls was processed by team b ?
Options: a ) 3 / 2 , b ) 3 / 4 , c ) 8 / 9 , d ) 1 / 2 , e ) 1 / 5
Rationale: "let team b has 8 agents , so team a has 5 agents let each agent of team b picked up 5 calls , so total calls by team b = 40 so , each agent in team a picked up 1 calls , so total calls for team a = 5 fraction for team b = 40 / ( 40 + 5 ) = 8 / 9 = answer = c"
Answer: c
Python program:
a = 8 * 5
b = 8 * 5
c = 5 * 1
d = b + c 
e = a / d
Problem: how much space , in cubic units , is left vacant when maximum number of 3 x 3 x 3 cubes are fitted in a rectangular box measuring 6 x 9 x 11 ?
Options: a ) 112 , b ) 111 , c ) 110 , d ) 109 , e ) 108
Rationale: "no of cubes that can be accommodated in box = ( 6 * 9 * 11 ) / ( 3 * 3 * 3 ) 6 * 9 in numerator can be perfectly divided by 3 * 3 in denominator . side with length 11 ca n ' t be perfectly divided by 3 and hence is the limiting factor . closet multiple of 3 less that 11 is 9 . so vacant area in cube = = 6 * 9 * ( 11 - 9 ) = 6 * 9 * 2 = 108 ans - e"
Answer: e
Python program:
a = 3 * 2
b = 6 - a
c = 9 * 11
d = b * c
Problem: the jogging track in a sports complex is 1000 meters in circumference . deepak and his wife start from the same point and walk in opposite directions at 20 km / hr and 17 km / hr respectively . they will meet for the first time in ?
Options: a ) 50 min , b ) 40 min , c ) 35 min , d ) 37 min , e ) 20 min
Rationale: "clearly , the two will meet when they are 1000 m apart to be 20 + 17 = 37 km apart , they take 1 hour to be 1000 m apart , they take 37 * 1000 / 1000 = 37 min . answer is d"
Answer: d
Python program:
a = 20 + 17
Problem: if the sum of two numbers is 18 and the sum of their squares is 180 , then the product of the numbers is
Options: a ) 72 , b ) 44 , c ) 80 , d ) 88 , e ) 48
Rationale: "according to the given conditions x + y = 18 and x ^ 2 + y ^ 2 = 180 now ( x + y ) ^ 2 = x ^ 2 + y ^ 2 + 2 xy so 18 ^ 2 = 180 + 2 xy so xy = 144 / 2 = 72 answer : a"
Answer: a
Python program:
a = 18 ** 2
b = a - 180
c = b / 2
Problem: sam invested rs . 15000 @ 10 % per annum for one year . if the interest is compounded half - yearly , then the amount received by sam at the end of the year will be ?
Options: a ) rs . 16,500 , b ) rs . 16 , 525.50 , c ) rs . 16 , 537.50 , d ) rs . 18,150 , e ) rs . 19,150
Rationale: "p = rs . 15000 ; r = 10 % p . a . = 5 % per half - year ; t = 1 year = 2 half - year amount = [ 15000 * ( 1 + 5 / 100 ) 2 ] = ( 15000 * 21 / 20 * 21 / 20 ) = rs . 16537.50 answer : c"
Answer: c
Python program:
a = 10 / 2
b = a / 100
c = b + 1 
d = c ** 2
e = d * 15000
Problem: if the area of a square with sides of length 3 centimeters is equal to the area of a rectangle with a width of 3 centimeters , what is the length of the rectangle , in centimeters ?
Options: a ) 3 , b ) 8 , c ) 12 , d ) 16 , e ) 18
Rationale: "let length of rectangle = l 3 ^ 2 = l * 3 = > l = 9 / 3 = 3 answer a"
Answer: a
Python program:
a = 3 ** 2
b = a / 3
Problem: a is 1.5 times as fast as b . a alone can do the work in 30 days . if a and b work on alternative days , beginning with a , in how many days will the work be completed ?
Options: a ) 23 , b ) 22 , c ) 21 , d ) 36 , e ) 25
Rationale: "a can finish 1 work in 30 days b can finish 1 / 1.5 work in 30 days - since a is 1.5 faster than b this means b can finish 1 work in 30 * 1.5 days = 45 days now using the awesome gmat formula when two machines work together they can finish the job in = ab / ( a + b ) = 45 * 30 / ( 45 + 30 ) = 20 * 30 / 50 = 18 days since they alternate on days , it will take them double this time so total time = 18 * 2 = 36 days so answer is d"
Answer: d
Python program:
a = 1 / 30
b = 1 / 30
c = b / 1
d = a + c 
e = 1 / d
Problem: 5355 x 51 = ?
Options: a ) 273105 , b ) 273243 , c ) 273247 , d ) 273250 , e ) 273258
Rationale: "5355 x 51 = 5355 x ( 50 + 1 ) = 5355 x 50 + 5355 x 1 = 267750 + 5355 = 273105 a"
Answer: a
Python program:
a = 5355 / 51
b = a * 100
Problem: he ratio between the sale price and the cost price of an article is 3 : 1 . what is the ratio between the profit and the cost price of that article ?
Options: a ) 2 : 1 , b ) 2 : 9 , c ) 2 : 4 , d ) 2 : 1 , e ) 2 : 5
Rationale: "let c . p . = rs . x and s . p . = rs . 3 x . then , gain = rs . 2 x required ratio = 2 x : x = 2 : 1 . answer : a"
Answer: a
Python program:
a = 1 / 3
b = 1 - a
c = 1/(b)
Problem: p and q started a business investing rs . 85,000 and rs . 45,000 respectively . in what ratio the profit earned after 2 years be divided between p and q respectively ?
Options: a ) 17 : 6 , b ) 17 : 0 , c ) 17 : 4 , d ) 17 : 9 , e ) 17 : 3
Rationale: "p : q = 85000 : 45000 = 17 : 9 . answer : d"
Answer: d
Python program:
a = 2 + 3 
b = a + 3 
c = 2 + 3 
d = c * 2
e = b * d
f = 2 + 3 
g = e + f 
h = 2 + 3 
i = h * 2
j = 3 * i
k = 2 + 3 
l = j + k 
m = g / l
Problem: there are a total of 100 jars on the shelf . small jars hold 3 liters and large jars hold 5 liters . the jars can hold a total of 376 liters . how many small jars are on the shelf ?
Options: a ) 49 , b ) 53 , c ) 56 , d ) 59 , e ) 62
Rationale: let s be the number of small jars and let l be the number of large jars . s + l = 100 . l = 100 - s . 3 s + 5 l = 376 . 3 s + 5 ( 100 - s ) = 376 . - 2 s + 500 = 376 . 2 s = 124 . s = 62 . the answer is e .
Answer: e
Python program:
a = 3 * 100
b = 376 - a
c = b / 2
d = 100 - c
Problem: trapezoid jklm in the x - y plane has coordinates j = ( – 2 , – 5 ) , k = ( – 2 , 1 ) , l = ( 6 , 7 ) , and m = ( 6 , – 5 ) . what is its perimeter ?
Options: a ) 34 , b ) 35 , c ) 38 , d ) 40 , e ) ( f ) 42
Rationale: "jk = 6 lm = 11 kl = using distance formula 10 jm = using distance formula 8 sum of all is 35 b"
Answer: b
Python program:
a = 1 + 5 
b = 10 + a 
c = 2 + 6 
d = b + c 
e = 7 + 5 
f = d + e
Problem: find large no . from below question the difference of two numbers is 1365 . on dividing the larger number by the smaller , we get 6 as quotient and the 10 as remainder
Options: a ) 1235 , b ) 1456 , c ) 1567 , d ) 1636 , e ) 1635
Rationale: "let the smaller number be x . then larger number = ( x + 1365 ) . x + 1365 = 6 x + 10 5 x = 1355 x = 271 large number = 271 + 1365 = 1636 d"
Answer: d
Python program:
a = 1365 - 10
b = 6 - 1
c = a / b
d = c * 6
e = d + 10
Problem: 1 , 0.2 , 0.08 , 0.48 , 0.0384 , ____
Options: a ) 0.0584 , b ) 0.0484 , c ) 0.0434 , d ) 0.0384 , e ) none
Rationale: "1 , 0.2 , 0.08 , 0.48 , 0.0384 , . . . . . 1 * 0.2 = 0.2 0.2 * 0.4 = 0.08 0.08 * 0.6 = 0.048 0.048 * 0.8 = 0.0384 so 0.0384 * 1 = 0.0384 answer : d"
Answer: d
Python program:
a = negate - (
Problem: a person is saving money to purchase a car . he earns â £ 4000 per month and saves â £ 500 to buy the car . if he needs â £ 45000 to buy his dream car . how much money he will earn , before he saves enough money to buy the car ?
Options: a ) a - 352000 , b ) b - 356000 , c ) c - 360000 , d ) d - 348000 , e ) e - 340000
Rationale: he is saving â £ 500 per month . he needs â £ 45000 and it takes â £ 45000 / â £ 500 = 90 months to save the money . in 90 months , he earns 90 * â £ 4000 = â £ 36000 . answer : c
Answer: c
Python program:
a = 45000 / 500
b = a * 4000
Problem: by investing rs . 1800 in 9 % stock , syam earns rs . 120 . the stock is then quoted at
Options: a ) rs . 135 , b ) rs . 96 , c ) rs . 85 , d ) rs . 122 , e ) rs . 142
Rationale: "explanation : assume that face value = rs . 100 . dividend per share = rs . 9 ( as it is a 9 % stock ) by investing rs . 1800 , he earns rs . 120 investment needed to earn rs . 9 = 1800 × 9 / 120 = rs . 135 ie , stock is then quoted ( then market value ) = rs . 135 answer : option a"
Answer: a
Python program:
a = 1800 / 120
b = 9 / 100
c = a * b
d = c * 100
Problem: the rowing athletes in a rowing conference voted for coach of the year . each rower who voted chose exactly 3 coaches to vote for among the 36 coaches in the conference . if each of the 36 coaches received exactly 5 votes ( a 36 way tie ) , how many rowers voted for coach of the year ?
Options: a ) 60 , b ) 70 , c ) 75 , d ) 84 , e ) 90
Rationale: there were 36 * 5 = 180 total votes made . if each voter picked 3 coaches , there were 180 / 3 = 60 voters . a
Answer: a
Python program:
a = 36 * 5
b = a / 3
Problem: i . x + 2 y + 3 z = 2 ii . x + y - z = 0 iii . 2 x + 2 y - z = 1 what is the value of y in the system above ?
Options: a ) - 2 , b ) - 1 , c ) 0 , d ) 1 , e ) 2
Rationale: 1 . from the given system of equations i can make equation ii . to be x + y = z 2 . now put that in iii . : 2 x + 2 y - ( x + y ) = 1 = 2 x + 2 y - x - y = 1 = x + y = 1 that gives usz = 1 ! 3 . put z = 1 in i . and solve : x + 2 y + 3 = 2 ; calculate minus 3 = x + 2 y = - 1 ; calculate minus x = 2 y = - 1 - x ; 4 . now put 2 y = - 1 - x in iii . and solve : 2 x + ( - 1 - x ) - 1 = 1 = x - 2 = 1 ; calculate plus 2 that gives usx = 3 5 . now solve for y with x = 3 and z = 1 : x + y = 1 = 3 + y = 1 ; calculate minus 3 that gives y = - 2 , and hence answer ( a ) - 2
Answer: a
Python program:
a = 3 + 1 
b = 2 - a
Problem: if grapes are 90 % water and raisins are 15 % water , then how many kilograms did a quantity of raisins , which currently weighs 12 kilograms , weigh when all the raisins were grapes ? ( assume that the only difference between their raisin - weight and their grape - weight is water that evaporated during their transformation . )
Options: a ) 96 , b ) 98 , c ) 100 , d ) 102 , e ) 104
Rationale: "let x be the original weight of the grapes . the weight of the grape pulp was 0.1 x . since the grape pulp is 85 % of the raisins , 0.1 x = 0.85 ( 12 kg ) . then x = 8.5 * 12 = 102 kg . the answer is d ."
Answer: d
Python program:
a = 100 - 15
b = a / 100
c = b * 12
d = 100 - 90
e = d / 100
f = c / e
Problem: salesperson a ' s compensation for any week is $ 210 plus 6 percent of the portion of a ' s total sales above $ 1,000 for that week . salesperson b ' s compensation for any week is 8 percent of b ' s total sales for that week . for what amount of total weekly sales would both salespeople earn the same compensation ?
Options: a ) $ 3500 , b ) $ 5500 , c ) $ 7500 , d ) $ 9500 , e ) $ 11,500
Rationale: "210 + 0.06 ( x - 1000 ) = 0.08 x 0.02 x = 150 x = $ 7,500 the answer is c ."
Answer: c
Python program:
a = 6 / 100
b = a * 1
c = 210 - b
d = 8 / 100
e = 6 / 100
f = d - e
g = c / f
h = 6 / 100
i = h * 1
j = 210 - i
k = 8 / 100
l = 6 / 100
m = k - l
n = j / m
o = g + n 
p = o / 1