euclaise/mathqa_programs huggingface dataset:
Problem: a wooden box of dimensions 8 m x 7 m x 6 m is to carry rectangularboxes of dimensions 2 cm x 7 cm x 3 cm . the maximum number ofboxes that can be carried in the wooden box , is
Options: a ) 8000000 , b ) 1000000 , c ) 7500000 , d ) 1200000 , e ) none of these
Rationale: explanation : number = ( 800 * 700 * 600 ) / 2 * 7 * 3 = 8000000 answer : a
Answer: a
Python program:
a = 6 * 100
b = 7 * 100
c = a * b
d = 8 * 100
e = c * d
f = 8 * 7
g = f * 7
h = e / g
Problem: x can finish a work in 18 days . y can finish the same work in 15 days . yworked for 5 days and left the job . how many days does x alone need to finish the remaining work ?
Options: a ) 12 , b ) 5 , c ) 6 , d ) 8 , e ) 9
Rationale: work done by x in 1 day = 1 / 18 work done by y in 1 day = 1 / 15 work done by y in 5 days = 5 / 15 = 1 / 3 remaining work = 1 – 1 / 3 = 2 / 3 number of days in which x can finish the remaining work = ( 2 / 3 ) / ( 1 / 18 ) = 12 a
Answer: a
Python program:
a = 1 / 15
b = 5 * a
c = 1 - b
d = 1 / 18
e = c / d
Problem: the diameter of the wheel of a car is 120 m . how many revolution / min mustthe wheel makeing order to keep a speed of 60 km / hour approximately ?
Options: a ) 140 , b ) 160 , c ) 220 , d ) 250 , e ) 265
Rationale: "distance to be covered in 1 min . = ( 60 x 1000 ) / ( 60 ) m = 1000 m . circumference of the wheel = ( 2 x ( 22 / 7 ) x 0.60 ) m = 3.77 m . number of revolutions per min . = ( 1000 / 3.77 ) = 265 e"
Answer: e
Python program:
a = 60 * 1000
b = a / 60
c = 2 * 10
d = c + 2 
e = 4 + 3 
f = d / e
g = 120 / 100
h = f * g
i = b / h
Problem: a and b together can do a work in 5 days . if a alone can do it in 15 days . in how many days can b alone do it ?
Options: a ) 10 , b ) 99 , c ) 7.5 , d ) 55 , e ) 21
Rationale: "1 / 5 – 1 / 15 = 2 / 15 = > 7.5 answer : c"
Answer: c
Python program:
a = 1 / 5
b = 1 / 15
c = a - b
d = 1/(c)
e = 2 + 3 
f = 2 / e
g = d + f
Problem: if a coin has an equal probability of landing heads up or tails up each time it is flipped , what is the probability that the coin will land heads up exectly twice in 3 consecutive flips ?
Options: a ) 0.125 , b ) 0.25 , c ) 0.375 , d ) 0.5 , e ) 0.666
Rationale: "p = ncm * p ^ m * q ^ ( n - m ) n - the total number of trials . m - the number of trials with heads . n - m - the number of trials with tails . p - probability of heads . q - probability of tails . p = 3 c 2 * ( 1 / 2 ) ^ 2 * ( 1 / 2 ) ^ 1 = 3 / 8 = 0.375 answer : c"
Answer: c
Python program:
a = 1 / 2
b = a ** 3
c = b * 3
Problem: one hour after yolanda started walking from x to y , a distance of 40 miles , bob started walking along the same road from y to x . if yolanda â s walking rate was 2 miles per hour and bob â s was 4 miles per hour , how many miles had bob walked when they met ?
Options: a ) 24 , b ) 23.5 , c ) 22 , d ) 21.2 , e ) 25.32
Rationale: "let t be the number of hours that bob had walked when he met yolanda . then , when they met , bob had walked 4 t miles and yolanda had walked 2 ( t + 1 ) miles . these distances must sum to 40 miles , so 4 t + 2 ( t + 1 ) = 40 , which may be solved for t as follows 4 t + 2 ( t + 1 ) = 40 4 t + 2 t + 2 = 40 6 t = 38 t = 6.33 ( hours ) therefore , bob had walked 4 t = 4 ( 7.6 ) = 25.32 miles when they met . the best answer is e ."
Answer: e
Python program:
a = 40 - 2
b = 2 + 4 
c = a / b
d = c * 4
Problem: 23 , 29 , 31 , 37 , 41 , 43 , 47 , 53 , ( . . . )
Options: a ) 53 , b ) 47 , c ) 48 , d ) 59 , e ) 45
Rationale: "explanation : all are prime numbers in their order , starting from 23 hence , next number is 59 answer : d"
Answer: d
Python program:
a = negate - (
Problem: what is the rate percent when the simple interest on rs . 800 amount to rs . 160 in 4 years ?
Options: a ) 5 % , b ) 7 % , c ) 9 % , d ) 2 % , e ) 4 %
Rationale: "160 = ( 180 * 4 * r ) / 100 r = 5 % answer : a"
Answer: a
Python program:
a = 100 * 160
b = 800 * 4
c = a / b
Problem: a and b can do a piece of work in 4 2 / 3 days and 5 days respectively . they work together for 1 days and then a leaves . in how many days after that b will complete the work alone .
Options: a ) 3.92 days , b ) 1.92 days , c ) 2.12 days , d ) 2.02 days , e ) 2.92 days
Rationale: 3 / 14 * 1 + ( 1 + x ) / 5 = 1 x = 2.92 days answer : e
Answer: e
Python program:
a = 1/(5)
b = 2 / 3
c = 4 + b 
d = 1/(c)
e = a + d 
f = 1 - e
g = 5 * f
Problem: a semicircle is drawn with ab as its diameter . from c , a point on ab , a line perpendicular to ab is drawn , meeting the circumference of the semicircle at d . given that ac = 2 cm and cd = 6 cm , the area of the semicircle in square cm will be ?
Options: a ) 30 pi
b ) 40 pi
c ) 50 pi
d ) 60 pi
e ) 70 pi
Rationale: let o be center of circle and radius be x . c can be anywhere on ab . let us suppose that c is somewhere between a and o . ac = 2 cm . . . . so co = ( x - 2 ) do = x , cd = 6 cm cdo form a right angled triangle with right angle at c . using pythagoras theorem , x ^ 2 = 6 ^ 2 + ( x - 2 ) ^ 2 4 x = 40 x = 10 cm area = [ pi ( x ) ^ 2 ] / 2 area = 50 pi answer : c
Answer: c
Python program:
a = 2 ** 2
b = 6 ** 2
c = a + b 
d = math.sqrt(c)
e = d ** 2
f = e - 4
g = 2 ** 2
h = 6 ** 2
i = g + h 
j = math.sqrt(i)
k = j ** 2
l = f + k 
m = 2 ** 2
n = l - m
o = 2 ** 2
p = n / o
q = p + 2 
r = q / 2
s = r ** 2
t = s * math.pi
u = t / 2
Problem: two trains , one from howrah to patna and the other from patna to howrah , start simultaneously . after they meet , the trains reach their destinations after 24 hours and 8 hours respectively . the ratio of their speeds is
Options: a ) 4 : 9 , b ) 4 : 3 , c ) 1 : 3 , d ) 4 : 8 , e ) 4 : 5
Rationale: let us name the trains as a and b . then , ( a ' s speed ) : ( b ' s speed ) = b : a = 8 : 24 = 1 : 3 . answer : c
Answer: c
Python program:
a = math.sqrt(8)
b = math.sqrt(24)
c = a / b
Problem: length of a rectangular plot is 20 mtr more than its breadth . if the cost of fencin gthe plot at 26.50 per meter is rs . 5300 , what is the length of the plot in mtr ?
Options: a ) 50 m , b ) 60 m , c ) 65 m , d ) 75 m , e ) 80 m
Rationale: "let breadth = x metres . then , length = ( x + 20 ) metres . perimeter = 5300 m = 200 m . 26.50 2 [ ( x + 20 ) + x ] = 200 2 x + 20 = 100 2 x = 80 x = 40 . hence , length = x + 20 = 60 m b"
Answer: b
Python program:
a = 5300 / 26
b = 2 * 20
c = a + b 
d = c / 4
Problem: a train is running at a speed of 40 km / hr and it crosses a post in 17.1 seconds . what is the length of the train ?
Options: a ) 190 metres , b ) 160 metres , c ) 200 metres , d ) 120 metres , e ) 250 metres
Rationale: "speed of the train , v = 40 km / hr = 40000 / 3600 m / s = 400 / 36 m / s time taken to cross , t = 17.1 s distance covered , d = vt = ( 400 / 36 ) ã — 17.1 = 190 m distance covered is equal to the length of the train = 190 m correct answer is 190 metres a"
Answer: a
Python program:
a = 40 * const_0_2778
b = 17 * 1
Problem: of the 160 people at a party , 70 were women , and 50 women tried the appetizer . if 50 people did not try the appetizer , what is the total number of men who tried the appetizer ?
Options: a ) 40 , b ) 50 , c ) 60 , d ) 70 , e ) 80
Rationale: "total people at party = 160 women = 70 so men 160 - 70 = 90 no . of pple who tried appetizer = 160 - 50 ( given info ) = 110 no of women who tried appetizer = 50 so remaining ppl ( men ) who tried the appetizer = 110 - 50 = 60 correct option c"
Answer: c
Python program:
a = 160 - 50
b = a - 50
Problem: a 300 m long train crosses a platform in 39 sec while it crosses a signal pole in 20 sec . what is the length of the platform ?
Options: a ) 389 m , b ) 350 m , c ) 285 m , d ) 299 m , e ) 219 m
Rationale: "speed = 300 / 20 = 15 m / sec . let the length of the platform be x meters . then , ( x + 300 ) / 39 = 15 = > x = 285 m . answer : c"
Answer: c
Python program:
a = speed * (
b = a - 39
Problem: a box measuring 49 inches long by 42 inches wide by 14 inches deep is to be filled entirely with identical cubes . no space is to be left unfilled . what is the smallest number of cubes that can accomplish this objective ?
Options: a ) 78 , b ) 82 , c ) 84 , d ) 86 , e ) 88
Rationale: "least number of cubes will be required when the cubes that could fit in are biggest . 7 is the biggest number that could divide all three , 49 , 42 and 14 . thus side of cube must be 7 , and total number of cubes = 49 / 7 * 42 / 7 * 14 / 7 = 84 ans c ."
Answer: c
Python program:
a = 49 * 42
b = a * 14
c = 14 / 2
d = b / volume_cube
Problem: if 20 liters of chemical x are added to 80 liters of a mixture that is 20 % chemical x and 80 % chemical y , then what percentage of the resulting mixture is chemical x ?
Options: a ) 30 % , b ) 33 % , c ) 36 % , d ) 39 % , e ) 42 %
Rationale: "the amount of chemical x in the solution is 20 + 0.2 ( 80 ) = 36 liters . 36 liters / 100 liters = 36 % the answer is c ."
Answer: c
Python program:
a = 20 / 100
b = a * 80
c = 20 + b
Problem: working together , jose and jane can complete an assigned task in 20 days . however , if jose worked alone and completed half the work and then jane takes over and completes the second half , the task will be completed in 45 days . how long will jose take to complete the task if he worked alone ? assume that jane is more efficient than jose .
Options: a ) 25 days , b ) 30 days , c ) 60 days , d ) 65 days , e ) 36 days
Rationale: "explanatory answer step 1 : assign variables and frame equations let jose take ' x ' days to complete the task if he worked alone . let jane take ' y ' days to complete the task if she worked alone . statement 1 of the question : they will complete the task in 20 days , if they worked together . in 1 day , jose will complete 1 / x of the task . in 1 day , jane will complete 1 / yof the task . together , in 1 day they will complete 1 / 20 of the task . therefore , 1 / x + 1 / y = 1 / 20 . . . . ( 1 ) statement 2 of the question : if jose worked alone and completed half the work and then jane takes over and completes the second half , the task will be completed in 45 days . jose will complete half the task in x / 2 days . jane will complete half the task in y / 2 days . ∴ x / 2 + y / 2 = 45 or , x + y = 90 or x = 90 - y . . . . ( 2 ) step 2 : solve the two equations and find x and y substitute the value of x as ( 90 - y ) in the first equation 1 / 90 − y + 1 / y = 1 / 20 or y 2 - 90 + 1800 = 0 . the quadratic equation factorizes as ( y - 60 ) ( y - 30 ) = 0 so , y = 60 or y = 30 . if y = 60 , then x = 90 - y = 90 - 60 = 30 and if y = 30 , then x = 90 - y = 90 - 30 = 60 . the question clearly states that jane is more efficient than jose . therefore , jane will take lesser time than jose . hence , jose will take 60 days to complete the task if he worked alone and jane will take 30 days to complete the same task . choice c"
Answer: c
Python program:
a = 3 * 20
Problem: a certain university will select 1 of 7 candidates eligible to fill a position in the mathematics department and 3 of 10 candidates eligible to fill 3 identical positions in the computer science department . if none of the candidates is eligible for a position in both departments , how many different sets of 4 candidates are there to fill the 4 positions ?
Options: a ) 420 , b ) 770 , c ) 840 , d ) 165 , e ) 315
Rationale: "1 of 7 will be chosen for the math 3 of 10 will be chosen for the computer none of the 4 chosen people can be in more than one departments . we can choose any of the 7 candidates for the math dep . , which gives as 7 selections . we can choose 3 of the 10 candidates for the computer dep . , which gives us 3 selections and 7 rejections . so , the way to find how many different selections of 2 candidates we can have for the computer dep . , we do : 10 ! / 3 ! * 7 ! = 120 we are multiplying our individual selections : 7 * 120 = 840 in the bolded part , we do n ' t have to multiply all of the numbers , as those in 8 ! are included in 10 ! , so we simplify instead . ans c"
Answer: c
Python program:
a = 10 * 4
b = a * 7
Problem: a boeing 757 flies a direct route from dallas , tx , to phoenix , az and then returns to dallas , tx . the flight is 900 miles one way . it took 2 hrs and 15 minutes for the flight to phoenix and 2 hrs for the flight back to dallas . what was the speed of the wind in mph ?
Options: a ) 20 mph , b ) 25 mph , c ) 30 mph , d ) 35 mph , e ) 40 mph
Rationale: explanation : change the times in the problem to minutes first . speed of airplane from dallas to phoenix : ( 900 / 135 ) x 60 = 400 mph speed of airplane from phoenix to dallas : ( 900 / 120 ) x 60 = 450 mph wind speed : 1 / 2 ( 450 - 400 ) = 50 / 2 = 25 mph answer : option b
Answer: b
Python program:
a = 900 / 2
b = 15 / const_60
c = 2 + b 
d = 900 / c
e = a - d
f = e / 2
Problem: tanks a and b are each in the shape of a right circular cylinder . the interior of tank a has a height of 5 meters and a circumference of 4 meters , and the interior of tank b has a height of 8 meters and a circumference of 10 meters . the capacity of tank a is what percent of the capacity of tank b ?
Options: a ) 10 %
b ) 80 %
c ) 100 %
d ) 120 %
e ) 125 %
Rationale: for a , r = 4 / 2 pi . its capacity = ( 2 pi ) ^ 2 * 5 = 20 pi for b , r = 10 / pi . its capacity = ( 5 pi ) ^ 2 * 8 = 200 pi a / b = 20 pi / 200 pi = 0.1 a
Answer: a
Python program:
a = 4 / 10
b = a ** 2
c = 5 / 8
d = b * c
e = d * 100
Problem: he total marks obtained by a student in physics , chemistry and mathematics is 180 more than the marks obtained by him in physics . what is the average mark obtained by him in chemistry and mathematics ?
Options: a ) 55 , b ) 65 , c ) 75 , d ) 85 , e ) 90
Rationale: let the marks obtained by the student in physics , chemistry and mathematics be p , c and m respectively . p + c + m = 180 + p c + m = 180 average mark obtained by the student in chemistry and mathematics = ( c + m ) / 2 = 180 / 2 = 90 . answer : e
Answer: e
Python program:
a = 180 / 2
Problem: rahim bought 27 books for rs . 581 from one shop and 20 books for rs . 594 from another . what is the average price he paid per book ?
Options: a ) 28 , b ) 18 , c ) 27 , d ) 25 , e ) 21
Rationale: "average price per book = ( 581 + 594 ) / ( 27 + 20 ) = 1175 / 47 = rs . 25 answer : d"
Answer: d
Python program:
a = 581 + 594 
b = 27 + 20 
c = a / b
Problem: a , b and c enter into partnership . a invests some money at the beginning , b invests double the amount after 6 months , and c invests thrice the amount after 8 months . if the annual gain be rs . 24000 . a ' s share is ?
Options: a ) 2999 , b ) 8000 , c ) 6000 , d ) 2889 , e ) 6612
Rationale: "x * 12 : 2 x * 6 : 3 x * 4 1 : 1 : 1 1 / 3 * 24000 = 8000 answer : b"
Answer: b
Python program:
a = 1 * 12
b = 1 * 12
c = 12 - 6
d = c * 2
e = b + d 
f = 12 - 8
g = f * 3
h = e + g 
i = 24000 / h
j = a * i
Problem: the ratio of flour to water to sugar in a recipe is 10 : 6 : 3 . the ratio in a new recipe calls for a doubling of the ratio of flour to water from the original recipe and a halving of the ratio of flour to sugar . if the new recipe calls for 2 cups of water , how much sugar is required ?
Options: a ) 3 , b ) 4 , c ) 5 , d ) 6 , e ) 7
Rationale: "the ratio of flour to water is 10 : 3 . the ratio of flour to sugar is 5 : 3 = 10 : 6 . the new ratio of flour to water to sugar is 10 : 3 : 6 if we need 2 cups of water , then we need 4 cups of sugar . the answer is b ."
Answer: b
Python program:
a = 2 / 6
b = 4 * 3
c = a * b
Problem: an artist wishes to paint a circular region on a square poster that is 4 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 ( 8 / pi ) , c ) 1 , d ) 2 / sqrt ( pi ) , e ) pi / 2
Rationale: "area of the poster is 4 x 4 = 16 1 / 2 the area = 8 pi * r ^ 2 = 8 r ^ 2 = 8 / pi r = sqrt ( 8 / pi ) answer : c"
Answer: c
Python program:
a = square_area / (
b = a / 2
c = math.sqrt(b)
Problem: the smallest number which when diminished by 4 , is divisible by 12 , 16 , 18 , 21 and 28 is
Options: a ) 1008 , b ) 1012 , c ) 1022 , d ) 1032 , e ) 1043
Rationale: "required number = ( l . c . m of 12 , 16 , 18 , 21,28 ) + 4 = 1008 + 4 = 1012 answer : b"
Answer: b
Python program:
a = 3 ** 2
b = 2 ** 0
c = a * b
d = 3 + 4 
e = c * d
f = e + 4
Problem: two numbers are in the ratio 3 : 5 . if 9 is subtracted from each , the new numbers are in the ratio 12 : 23 . the smaller number is :
Options: a ) 15 , b ) 33 , c ) 58 , d ) 56 , e ) 91
Rationale: "let the numbers be 3 x and 5 x . then , ( 3 x - 9 ) / ( 5 x - 9 ) = 12 / 23 9 x = 99 = > x = 11 the smallest number = 3 * 11 = 33 . answerb"
Answer: b
Python program:
a = 3 * 5
b = 9 / a
c = 3 * b
d = 3 * 5
e = 9 / d
f = 5 * e
g = c + f
Problem: two cars , car 1 and car 2 move towards each other from q and y respectively with respective speeds of 20 m / s and 15 m / s . after meeting each other car 1 reaches y in 10 seconds . in how many seconds does car 2 reach q starting from y ?
Options: a ) 15.5 sec , b ) 8.4 sec , c ) 33.6 sec , d ) 31.11 sec , e ) 16.8 sec
Rationale: q - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - | - - - - - - - - - - - - - - - - - - - - - - - - - - - - y car a ( 20 mps ) - - - - - - - - - - - - - - - - - - - - - - - - - > p < - - - - - - - - - - - - - - - car b ( 15 mps ) let 2 cars meet each other at point p in t seconds . car 1 covers distance = 20 t . car 2 covers distance = 15 t . so , total distance qy = 35 t . from p , car 1 reaches onto y in 10 secs . so it covers 15 t further . so , 15 t / 20 = 10 so t = 40 / 3 sec and total distance = ( 35 * 40 ) / 3 hence car 2 will cover total distance in ( 35 * 40 ) / ( 3 * 15 ) = 31.11 sec approx . answer d
Answer: d
Python program:
a = 15 / 20
b = 10 / a
c = 20 + 15 
d = b * c
e = d / 15
Problem: in a division sum , the remainder is 8 and the divisor is 3 times the quotient and is obtained by adding 3 to the thrice of the remainder . the dividend is :
Options: a ) 200 , b ) 251 , c ) 250 , d ) 262 , e ) 254
Rationale: "diver = ( 8 * 3 ) + 3 = 27 3 * quotient = 27 quotient = 9 dividend = ( divisor * quotient ) + remainder dividend = ( 27 * 9 ) + 8 = 251 b"
Answer: b
Python program:
a = 8 * 3
b = a + 3 
c = 8 * 3
d = c + 3 
e = d / 3
f = b * e
g = f + 8
Problem: the area of a sector of a circle of radius 5 cm formed by an arc of length 4.5 cm is ?
Options: a ) 8.78 , b ) 11.25 , c ) 8.75 , d ) 8.98 , e ) 8.28
Rationale: "( 5 * 4.5 ) / 2 = 11.25 answer : b"
Answer: b
Python program:
a = 1 / 2
b = 5 * 4
c = a * b
Problem: if x = - 5 and y = 8 , what is the value of 2 ( x - y ) ^ 2 - xy ?
Options: a ) 358 , b ) 348 , c ) 368 , d ) 388 , e ) 378
Rationale: x = - 5 and y = 8 x - y = - 5 - 8 = - 13 x * y = - 5 * 8 = - 40 now we apply it in the equation 2 ( x - y ) ^ 2 - xy = 2 ( - 13 ) ^ 2 - ( - 40 ) = = > 2 * 169 + 40 = 338 + 40 = 378 answer : e
Answer: e
Python program:
a = negate - (
b = a ** 8
c = b * 2
d = c - 2
Problem: kim has 7 pairs of shoes ; each pair is a different color . if kim randomly selects 2 shoes without replacement from the 14 shoes , what is the probability that she will select 2 shoes of the same color ?
Options: a ) 1 / 13 , b ) 1 / 15 , c ) 11 / 9 , d ) 1 / 10 , e ) 1 / 25
Rationale: "can be tackled in this way as well : probability of selecting any 1 out of 14 shoes = 14 / 14 = 1 probability of selecting the next shoe ( out of 14 available ) having the same color = 1 / 14 ( as after selecting the 1 st one , there is only 1 another shoe left with the same color ) . thus the total probability = 1 * 1 / 13 = 1 / 13 . a is the correct answer ."
Answer: a
Python program:
a = math.comb(14, 2)
b = 7 / a
Problem: find the distance covered by a man walking for 36 min at a speed of 10 km / hr ?
Options: a ) 1 km , b ) 3 km , c ) 6 km , d ) 5 km , e ) 6 km
Rationale: distance = 10 * 36 / 60 = 6 km answer is c
Answer: c
Python program:
a = 10 * 1000
b = a / const_60
c = 36 * b
d = c / 1000
Problem: a can finish a piece of work in 5 days . b can do it in 10 days . they work together for 1 day and then a goes away . in how many days will b finish the work ?
Options: a ) 8 days , b ) 5 days , c ) 6 days , d ) 7 days , e ) 9 days
Rationale: "1 / 5 + ( 1 + x ) / 10 = 1 = > x = 7 days answer : d"
Answer: d
Python program:
a = 1 / 5
b = a * 2
c = 1 / 10
d = c * 2
e = b + d 
f = 1 - e
g = 1 / 10
h = f / g
Problem: in an xy - coordinate plane , a line is defined by y = kx + 1 . if ( 4 , b ) , ( a , 5 ) , and ( a , b + 1 ) are 3 points on the line , where a and b are unknown , then k = ?
Options: a ) 1 / 2 , b ) 1 , c ) 3 / 4 , d ) 2 , e ) 5 / 2
Rationale: b = 4 k + 1 . . . ( 1 ) b + 1 = ak + 1 . . . ( 2 ) 5 = ak + 1 . . . ( 3 ) taking ( 2 ) and ( 3 ) 5 = b + 1 b = 4 taking ( 1 ) 4 = 4 k + 1 k = 3 / 4 answer : c
Answer: c
Python program:
a = 5 - 4
b = a * 3
c = b / 4
Problem: david has $ 1,500 at the beginning of his trip , after spending money , he still has exactly $ 500 less than he spent on the trip . how much money does john still have ?
Options: a ) $ 200 , b ) $ 400 , c ) $ 500 , d ) $ 800 , e ) $ 1,200
Rationale: "suppose total money spent = x not spend ( money he still has ) = x - 500 x + x - 500 = 1500 x = 1000 money not spend = 1000 - 500 = 500 answer : c"
Answer: c
Python program:
a = 100 * 10
b = a + 500 
c = b + 500 
d = c / 2
e = d - 500
Problem: a student was asked to find 4 / 5 of a number . but the student divided the number by 4 / 5 , thus the student got 18 more than the correct answer . find the number .
Options: a ) 30 , b ) 35 , c ) 40 , d ) 45 , e ) 50
Rationale: "let the number be x . ( 5 / 4 ) * x = ( 4 / 5 ) * x + 18 25 x = 16 x + 360 9 x = 360 x = 40 the answer is c ."
Answer: c
Python program:
a = 4 / 5
b = 18 * a
c = 4 / 5
d = b * c
e = 4 / 5
f = 4 / 5
g = e * f
h = 1 - g
i = d / h
j = 4 / 5
k = i / j
Problem: jo ' s collection contains us , indian and british stamps . if the ratio of us to indian stamps is 5 to 3 and the ratio of indian to british stamps is 5 to 1 , what is the ratio of us to british stamps ?
Options: a ) 5 : 1 , b ) 10 : 5 , c ) 15 : 2 , d ) 20 : 2 , e ) 25 : 2
Rationale: "u / i = 5 / 3 i / b = 5 / 1 since i is multiple of both 2 ( as per first ratio ) and 5 ( as per second ratio ) so let ' s assume that i = 10 i . e . multiplying teh first ratio by 5 and second ration by 2 in each numerator and denominator then , u : i : b = 25 : 15 : 2 i . e . u : b = 25 : 2 answer : option e"
Answer: e
Python program:
a = 5 * 5
b = 1 * 3
c = a / b
Problem: in 2008 , the profits of company n were 10 percent of revenues . in 2009 , the revenues of company n fell by 5 percent , but profits were 10 percent of revenues . the profits in 2009 were what percent of the profits in 2008 ?
Options: a ) 80 % , b ) 105 % , c ) 120 % , d ) 124.2 % , e ) 95 %
Rationale: "the profit 0 f 2009 interms of 2008 = 0.95 * 10 / 10 * 100 = 95 % e"
Answer: e
Python program:
a = 5 / 100
b = 1 - a
c = 10 * b
d = c / 10
e = d * 100
Problem: a house wife saved $ 3.50 in buying an item on sale . if she spent $ 32.50 for the item , approximately how much percent she saved in the transaction ?
Options: a ) 8 % , b ) 9 % , c ) 10 % , d ) 11 % , e ) 12 %
Rationale: "actual price = 32.50 + 3.50 = $ 36 saving = 3.50 / 36 * 100 = 10 % approximately answer is c"
Answer: c
Python program:
a = 32 + 50 
b = 3 / 50
c = b * 100
Problem: a garrison of 1000 men has provisions for 60 days . at the end of 15 days , a reinforcement arrives , and it is now found that the provisions will last only for 20 days more . what is the reinforcement ?
Options: a ) 1000 , b ) 2250 , c ) 60 , d ) 45 , e ) 1250
Rationale: "1000 - - - - 60 1000 - - - - 45 x - - - - - 20 x * 20 = 1000 * 45 x = 2250 1000 - - - - - - - 1250 answer : e"
Answer: e
Python program:
a = 1000 * 60
b = 1000 * 15
c = a - b
d = c / 20
e = d - 1000
Problem: on an order of 99 dozen boxes of a consumer product , a retailer receives an extra dozen free . this is equivalent to allowing him a discount of :
Options: a ) 0.1 % , b ) 0.5 % , c ) 1 % , d ) 5 % , e ) 10 %
Rationale: "clearly , the retailer gets 1 dozen out of 100 dozens free . equivalent discount = 1 / 100 * 100 = 1 % . answer c ) 1 %"
Answer: c
Python program:
a = 99 / 4
b = a * 100
c = 100 - b