euclaise/mathqa_programs huggingface dataset:
Problem: john and jacob set out together on bicycle traveling at 15 and 12 miles per hour , respectively . after 40 minutes , john stops to fix a flat tire . if it takes john two hour to fix the flat tire and jacob continues to ride during this time , how many hours will it take john to catch up to jacob assuming he resumes his ride at 15 miles per hour ? ( consider john ' s deceleration / acceleration before / after the flat to be negligible )
Options: a ) 7 , b ) 7 1 / 3 , c ) 7 1 / 2 , d ) 4 , e ) 7 1 / 2
Rationale: "john ' s speed - 15 miles / hr jacob ' s speed - 12 miles / hr after 40 min ( i . e 2 / 3 hr ) , distance covered by john = 15 x 2 / 3 = 10 miles . jacob continues to ride for a total of 2 hour and 40 min ( until john ' s bike is repaired ) . distance covered in 2 hour 40 min ( i . e 8 / 3 hr ) = 12 x 8 / 3 = 32 miles . now , when john starts riding back , the distance between them is 22 miles . jacob and john are moving in the same direction . for john to catch jacob , the effective relative speed will be 15 - 12 = 3 miles / hr . thus , to cover 22 miles at 3 miles / hr , john will take 22 / 3 = 7 1 / 3 hours answer b"
Answer: b
Python program:
a = 15 - 12
b = 40 / const_60
c = b * 15
d = 40 / const_60
e = d * 12
f = c - e
g = 12 - f
h = a + g 
i = 40 / const_60
j = i * 15
k = 40 / const_60
l = k * 12
m = j - l
n = h / m
Problem: a 1200 m long train crosses a tree in 120 sec , how much time will i take to pass a platform 600 m long ?
Options: a ) 266 sec , b ) 180 sec , c ) 776 sec , d ) 166 sec , e ) 997 sec
Rationale: "l = s * t s = 1200 / 120 s = 10 m / sec . total length ( d ) = 1800 m t = d / s t = 1800 / 10 t = 180 sec answer : b"
Answer: b
Python program:
a = 1200 + 600 
b = 1200 / 120
c = a / b
Problem: two mba admissions committees are to be formed randomly from 6 second year mbas with 3 members each . what is the probability v that jane will be on the same committee as albert ?
Options: a ) 12 % , b ) 20 % , c ) 33 % , d ) 40 % , e ) 50 %
Rationale: "total number of ways to choose 3 member committee - 6 c 3 = ( 6 ! / 3 ! 3 ! ) = 20 no . of ways albert n jane are in same committee : - ( 4 c 1 * 2 ) = 8 probability v = ( 8 / 20 ) * 100 = 40 % . + 1 for me . . : d"
Answer: d
Python program:
a = math.comb(4, 1)
b = a * 2
c = math.comb(6, 3)
d = b / c
e = 5 * 5
f = e * 4
g = d * f
Problem: if a car had traveled 40 kmh faster than it actually did , the trip would have lasted 30 minutes less . if the car went exactly 120 km , at what speed did it travel ?
Options: a ) 50 kmh , b ) 60 kmh , c ) 70 kmh , d ) 80 kmh , e ) 90 kmh
Rationale: "time = distance / speed difference in time = 1 / 2 hrs 120 / x - 120 / ( x + 40 ) = 1 / 2 substitute the value of x from the options . - - > x = 80 - - > 120 / 80 - 120 / 120 = 3 / 2 - 1 = 1 / 2 answer : d"
Answer: d
Python program:
a = 120 * 40
b = 2 * a
c = b * 4
d = 40 ** 2
e = c + d 
f = math.sqrt(e)
g = f - 40
h = g / 2
Problem: a grocer has a sale of rs . 3435 , rs . 3927 , rs . 3855 , rs . 4230 and rs . 3562 for 5 consecutive months . how much sale must he have in the sixth month so that he gets an average sale of rs . 3500 ?
Options: a ) s . 1991 , b ) s . 2991 , c ) s . 3991 , d ) s . 4991 , e ) s . 5991
Rationale: "explanation : total sale for 5 months = rs . ( 3435 + 3927 + 3855 + 4230 + 3562 ) = rs . 19009 . required sale = rs . [ ( 3500 x 6 ) â € “ 19009 ] = rs . ( 21000 â € “ 19009 ) = rs . 1991 . answer a"
Answer: a
Python program:
a = 5 + 1 
b = a * 3500
c = 3435 + 3927 
d = c + 3855 
e = d + 4230 
f = e + 3562 
g = b - f
Problem: what is the probability of getting a number less than 4 when a die is rolled ?
Options: a ) 5 / 5 , b ) 1 / 2 , c ) 5 / 1 , d ) 5 / 7 , e ) 5 / 2
Rationale: "total number of outcomes possible when a die is rolled = 6 ( ∵ any one face out of the 6 faces ) i . e . , n ( s ) = 6 e = getting a number less than 4 = { 1 , 2 , 3 } hence , n ( e ) = 3 the probability = 3 / 6 = 1 / 2 . answer : b"
Answer: b
Python program:
a = 3 + 3 
b = math.comb(a, 3)
c = 2 / b
Problem: a 270 m long train running at the speed of 120 kmph crosses another train running in opposite direction at the speed of 80 kmph in 9 second . what is the length of the other train ?
Options: a ) 150 m , b ) 230 m , c ) 290 m , d ) 310 m , e ) 420 m
Rationale: relative speed = 120 + 80 = 200 * 5 / 18 = 500 / 9 m / s let the length of the other train be x meters x + 270 / 9 = 500 / 9 x = 230 m answer is b
Answer: b
Python program:
a = 120 + 80 
b = a / const_3_6
c = b * 9
d = c - 270
Problem: two trains of equal length , running with the speeds of 60 and 40 kmph , take 40 seconds to cross each other while they are running in the same direction . what time will they take to cross each other if they are running in opposite directions ?
Options: a ) 10 sec , b ) 16 sec , c ) 13 sec , d ) 67 sec , e ) 8 sec
Rationale: "rs = 60 - 40 = 20 * 5 / 18 = 100 / 18 t = 40 d = 40 * 100 / 18 = 2000 / 9 rs = 60 + 40 = 100 * 5 / 18 t = 2000 / 9 * 18 / 500 = 8 sec answer : e"
Answer: e
Python program:
a = 60 - 40
b = const_0_2778 * a
c = b * 40
d = 60 + 40 
e = const_0_2778 * d
f = 1/(e)
g = c * f
Problem: a dog takes 2 leaps for every 3 leaps of a hare . if one leap of the dog is equal to 3 leaps of the hare , the ratio of the speed of the dog to that of the hare is :
Options: a ) 1 : 5 , b ) 2 : 5 , c ) 3 : 5 , d ) 4 : 5 , e ) 6 : 5
Rationale: "explanation : dog : hare = ( 2 * 3 ) leaps of hare : 3 leaps of hare = 6 : 5 . answer : e ) 6 : 5"
Answer: e
Python program:
a = 2 * 3
b = a / 3
Problem: in a group of pigs and hens , the number of legs are 22 more than twice the number of heads . the number of pigs is
Options: a ) 5 , b ) 7 , c ) 10 , d ) 12 , e ) 11
Rationale: explanation : let the number of pigs be x and the number of hens be y . then , 4 x + 2 y = 2 ( x + y ) + 22 4 x + 2 y = 2 x + 2 y + 22 2 x = 22 x = 11 answer : e
Answer: e
Python program:
a = 22 / 2
Problem: x + y = 19 , and x + 3 y = 1 . find the value of x + 2 y
Options: a ) 20 , b ) 18 , c ) 11 , d ) 10 , e ) 5
Rationale: add these two equations 2 x + 4 y = 20 divide by 2 ( to get x + 2 y ) answer will be d . 10
Answer: d
Python program:
a = 2 + 4 
b = a * 2
c = b - 2
Problem: in the fifth grade at parkway elementary school there are 470 students . 300 students are boys and 250 students are playing soccer . 86 % of the students that play soccer are boys . how many girl student are in parkway that is not playing soccer ?
Options: a ) 69 . , b ) 135 . , c ) 81 . , d ) 91 . , e ) 108 .
Rationale: "total students = 470 boys = 300 , girls = 170 total playing soccer = 250 86 % of 250 = 215 are boys who play soccer . girls who play soccer = 35 . total girls who do not play soccer = 170 - 35 = 135 . correct option : b"
Answer: b
Python program:
a = 470 - 300
b = 250 * 86
c = b / 100
d = 250 - c
e = a - d
Problem: how long does a train 110 m long traveling at 60 kmph takes to cross a bridge of 390 m in length ?
Options: a ) 18.9 sec , b ) 88.9 sec , c ) 22.9 sec , d ) 30.00 sec , e ) 72.0 sec
Rationale: "d = 110 + 390 = 500 m s = 60 * 5 / 18 = 50 / 3 t = 500 * 3 / 50 = 30 sec answer : d"
Answer: d
Python program:
a = 110 + 390 
b = 60 * const_0_2778
c = a / b
Problem: a can finish a work in 24 days , b in 9 days and c in 12 days . b and c start the work but are forced to leave after 3 days . when a done the work ?
Options: a ) 10 days , b ) 12 days , c ) 13 days , d ) 9 days , e ) 14 days
Rationale: "b + c = = > 1 / 9 + 1 / 12 = 7 / 36 b , c = in 3 days = 7 / 36 * 3 = 7 / 12 remaining work = 1 - 7 / 12 = 5 / 12 1 / 24 work is done by a in 1 day 5 / 12 work is done a 24 * 5 / 12 = 10 days answer a"
Answer: a
Python program:
a = 1 / 9
b = 1 / 12
c = a + b 
d = 1 / c
e = d * 3
Problem: in a recent election , james received 1.5 percent of the 2,000 votes cast . to win the election , a candidate needed to receive more than 50 percent of the vote . how many additional votes would james have needed to win the election ?
Options: a ) 901 , b ) 989 , c ) 990 , d ) 971 , e ) 1,001
Rationale: "james = ( 1.5 / 100 ) * 2000 = 30 votes to win = ( 50 / 100 ) * total votes + 1 = ( 50 / 100 ) * 2000 + 1 = 1001 remaining voted needed to win election = 1001 - 30 = 971 answer : option d"
Answer: d
Python program:
a = 1000 + 1000 
b = 1000 + 1000 
c = b * 0
d = a - c
Problem: jolene entered an 18 - month investment contract that guarantees to pay 2 percent interest at the end of 6 months , another 3 percent interest at the end of 10 months , and 4 percent interest at the end of the 18 month contract . if each interest payment is reinvested in the contract , and jolene invested $ 10,000 initially , what will be the total amount of interest paid during the 18 - month contract ?
Options: a ) $ 506.00 , b ) $ 726.24 , c ) $ 900.00 , d ) $ 920.24 , e ) $ 926.24
Rationale: if interest were not compounded in every six months ( so if interest were not earned on interest ) then we would have ( 2 + 3 + 4 ) = 9 % simple interest earned on $ 10,000 , which is $ 900 . so , you can rule out a , b and c right away . interest earned after the first time interval : $ 10,000 * 2 % = $ 200 ; interest earned after the second time interval : ( $ 10,000 + $ 200 ) * 3 % = $ 300 + $ 6 = $ 306 ; interest earned after the third time interval : ( $ 10,000 + $ 200 + $ 306 ) * 4 % = $ 400 + $ 8 + ( ~ $ 12 ) = ~ $ 420 ; total : 200 + 306 + ( ~ 420 ) = ~ $ 726.24 . answer : b .
Answer: b
Python program:
a = 3 / 100
b = 2 / 100
c = 100 ** 2
d = b * c
e = 100 ** 2
f = d + e 
g = a * f
h = 2 / 100
i = 100 ** 2
j = h * i
k = 100 ** 2
l = j + k 
m = g + l 
n = 4 / 100
o = m * n
p = 3 / 100
q = 2 / 100
r = 100 ** 2
s = q * r
t = 100 ** 2
u = s + t 
v = p * u
w = o + v
Problem: walking 4 / 3 of his usual rate , a boy reaches his school 4 min early . find his usual time to reach the school ?
Options: a ) 22 , b ) 16 , c ) 27 , d ) 28 , e ) 20
Rationale: "speed ratio = 1 : 4 / 3 = 3 : 4 time ratio = 4 : 3 1 - - - - - - - - 4 4 - - - - - - - - - ? 16 m . answer : b"
Answer: b
Python program:
a = 4 * 4
Problem: which is the least number that must be subtracted from 1256 so that the remainder when divided by 7 , 12 , 16 is 4 ?
Options: a ) 242 , b ) 232 , c ) 236 , d ) 240 , e ) 244
Rationale: "first we need to figure out what numbers are exactly divisible by 7 , 12,16 . this will be the set { lcm , lcmx 2 , lcmx 3 , . . . } lcm ( 7 , 12,16 ) = 48 * 7 = 336 the numbers which will leave remainder 4 will be { 336 + 4 , 336 x 2 + 4 , 336 x 3 + 4 , . . . } the largest such number less than or equal to 1256 is 336 x 3 + 4 or 1012 to obtain this you need to subtract 244 . e"
Answer: e
Python program:
a = math.lcm(7, 12)
b = math.lcm(a, 16)
c = math.gcd(1256, b)
d = math.lcm(7, 12)
e = math.lcm(d, 16)
f = c * e
g = 4 + f 
h = 1256 - g
Problem: if n is the smallest integer such that 108 times n is the square of an integer , what is the value of n ?
Options: a ) 2 , b ) 3 , c ) 6 , d ) 12 , e ) 24
Rationale: "108 can written as = 2 * 2 * 3 * 3 * 3 - - > 2 ^ 2 * 3 ^ 3 - - - ( 1 ) so for 108 * n to be a square of an integer , the integer should have even powers to the prime numbers it composed of . here 2 already has even power - > so n has to be 2 to make the power of 2 in ( 1 ) even option a is correct"
Answer: a
Python program:
a = 108 / 2
b = a / 2
c = b / 2
d = c / 2
e = d / 3
f = e / 3
Problem: of the 500 employees in a certain company , 25 percent will be relocated to city x and the remaining 75 percent will be relocated to city y . however , 40 percent of the employees prefer city y and 60 percent prefer city x . what is the highest possible number of employees who will be relocated to the city they prefer ?
Options: a ) 65 , b ) 100 , c ) 115 , d ) 130 , e ) 325
Rationale: "300 prefer x ( group 1 ) ; 200 prefer y ( group 2 ) . city y needs 375 people : letall 200 who prefer y ( entire group 2 ) be relocated there , the rest 175 will be those who prefer x from group 1 ; city x needs 125 people : 300 - 175 = 125 from group 1 will be relocated to x , which they prefer . so , the highest possible number of employees who will be relocated to the city they prefer is 200 + 125 = 325 . answer : e ."
Answer: e
Python program:
a = 40 * 2
b = a + 60
Problem: the average of 1 st 3 of 4 numbers is 6 and of the last 3 are 5 . if the sum of the first and the last number is 11 . what is the last numbers ?
Options: a ) 4 , b ) 5 , c ) 6 , d ) 7 , e ) 8
Rationale: "a + b + c = 18 b + c + d = 15 a + d = 11 a – d = 3 a + d = 11 2 d = 8 d = 4 answer : a"
Answer: a
Python program:
a = 3 * 6
b = 11 - 6
c = b + 3 
d = a - c
e = d - 6
Problem: if the cost price of 50 articles is equal to the selling price of 35 articles , then the gain or loss percent is ?
Options: a ) 16 , b ) 127 , c ) 12 , d ) 18 , e ) 43
Rationale: "percentage of profit = 15 / 35 * 100 = 43 % answer : e"
Answer: e
Python program:
a = 100 * 35
b = a / 50
c = 100 - b
d = 100 * 35
e = d / 50
f = c / e
g = 100 * f
Problem: a batch of cookies was divided amomg 3 tins : 3 / 4 of all the cookies were placed in either the blue or the green tin , and the rest were placed in the red tin . if 1 / 4 of all the cookies were placed in the blue tin , what fraction of the cookies that were placed in the other tins were placed in the green tin
Options: a ) 15 / 2 , b ) 9 / 4 , c ) 5 / 9 , d ) 3 / 5 , e ) 9 / 7
Rationale: "this will help reduce the number of variables you have to deal with : g + b = 3 / 4 r = 1 / 3 b = 1 / 4 we can solve for g which is 1 / 2 what fraction ( let it equal x ) of the cookies that were placed in the other tins were placed in the green tin ? so . . x * ( g + r ) = g x * ( 1 / 2 + 1 / 3 ) = 1 / 2 x = 3 / 5 answer : d"
Answer: d
Python program:
a = 3 / 4
b = 1 - a
c = 3 / 4
d = 1 / 4
e = c - d
f = b + e
Problem: 10 different biology books and 8 different chemistry books lie on a shelf . in how many ways can a student pick 2 books of each type ?
Options: a ) 80 , b ) 160 , c ) 720 , d ) 1100 , e ) 1260
Rationale: "no . of ways of picking 2 biology books ( from 10 books ) = 10 c 2 = ( 10 * 9 ) / 2 = 45 no . of ways of picking 2 chemistry books ( from 8 books ) = 8 c 2 = ( 8 * 7 ) / 2 = 28 total ways of picking 2 books of each type = 45 * 28 = 1260 ( option e )"
Answer: e
Python program:
a = math.factorial(10)
b = 10 - 2
c = math.factorial(b)
d = a / c
e = d / 2
f = math.factorial(8)
g = 8 - 2
h = math.factorial(g)
i = f / h
j = i / 2
k = e * j
Problem: a grocer has a sale of rs . 6400 , rs . 7000 , rs . 6800 , rs . 7200 and rs . 6500 for 5 consecutive months . how much sale must he have in the sixth month so that he gets an average sale of rs . 6500 ?
Options: a ) rs . 4500 , b ) rs . 4700 , c ) rs . 4800 , d ) rs . 5000 , e ) rs . 5100
Rationale: "total sale for 5 months = rs . ( 6400 + 7000 + 6800 + 7200 + 6500 ) = rs . 33900 required sale = rs . [ ( 6500 x 6 ) - 34009 ] = rs . ( 39000 - 33900 ) = rs . 5100 answer : e"
Answer: e
Python program:
a = 5 + 1 
b = a * 6500
c = 6400 + 7000 
d = c + 6800 
e = d + 7200 
f = e + 6500 
g = b - f
Problem: given that a is the average ( arithmetic mean ) of the first 5 positive multiples of 6 and b is the median of the first 12 positive multiples of 6 , what is the ratio of a to b ?
Options: a ) 3 : 4 , b ) 6 : 13 , c ) 5 : 6 , d ) 13 : 10 , e ) 4 : 3
Rationale: the first nine positive multiples of six are { 6 , 12 , 18 , 24,30 } the first twelve positive multiples of six are { 6 , 12 , 18 , 24 , 30 , 36,42 , 48 , 54 , 60 , 66 , 72 } both sets are evenly spaced , thus their median = mean : a = 18 and b = ( 36 + 42 ) / 2 = 39 - - > a / b = 18 / 39 = 6 / 13 . answer : b .
Answer: b
Python program:
a = 5 + 1 
b = a / 2
c = b * 6
d = 12 + 1 
e = d / 2
f = e * 6
g = c / f
Problem: find the compound interest on rs . 7500 at 4 % per annum for 2 years , compounded annually .
Options: a ) rs . 610 , b ) rs . 612 , c ) rs . 614 , d ) rs . 616 , e ) none of these
Rationale: "explanation : amount = [ 7500 × ( 1 + 4100 ) 2 ] = ( 7500 × 2625 × 2625 ) = 8112 so compound interest = ( 8112 - 7500 ) = 612 answer : b"
Answer: b
Python program:
a = 4 / 4
b = a / 100
c = 1 + b 
d = c ** 3
e = 4 * 4
f = e * 100
g = math.sqrt(100)
h = f * g
i = d * h
j = 4 * 4
k = j * 100
l = math.sqrt(100)
m = k * l
n = i - m
Problem: in the xy - plane , a triangle has vertices ( 0,0 ) , ( 4,0 ) and ( 4,9 ) . if a point ( a , b ) is selected at random from the triangular region , what is the probability that a - b > 0 ?
Options: a ) 1 / 5 , b ) 1 / 3 , c ) 1 / 2 , d ) 2 / 9 , e ) 4 / 5
Rationale: "the area of the right triangle is ( 1 / 2 ) * 4 * 9 = 18 . only the points ( a , b ) below the line y = x satisfy a - b > 0 . the part of the triangle which is below the line y = x has an area of ( 1 / 2 ) ( 4 ) ( 4 ) = 8 . p ( a - b > 0 ) = 8 / 18 = 2 / 9 the answer is d ."
Answer: d
Python program:
a = 0 + 0 
b = 4 / a
Problem: if a sum of money doubles itself in 5 years at simple interest , the ratepercent per annum is
Options: a ) 12 , b ) 12.5 , c ) 20 , d ) 13.5 , e ) 14
Rationale: "explanation : let sum = x then simple interest = x rate = ( 100 * x ) / ( x * 5 ) = 20 option c"
Answer: c
Python program:
a = 5 / 100
b = 2 / a
c = b / 2
Problem: elvin ' s monthly telephone bill is the sum of the charge for the calls he made during the month and a fixed monthly charge for internet service . elvin ' s total telephone bill for january was $ 52 and elvin ' s total telephone bill for february was 76 $ . if elvin ' s charge for the calls he made in february was twice the charge for the calls he made in january , what is elvin ' s fixed monthly charge for internet service ?
Options: a ) $ 5 , b ) $ 10 , c ) $ 14 , d ) $ 28 , e ) $ 29
Rationale: "bill = fixed charge + charge of calls made in jan , bill = fixed charge ( let , y ) + charge of calls made in jan ( let , x ) = $ 52 in feb , bill = fixed charge ( let , y ) + charge of calls made in feb ( then , 2 x ) = $ 76 i . e . x + y = 52 and 2 x + y = 76 take the difference if two equations i . e . ( 2 x + y ) - ( x + y ) = 76 - 52 i . e . x = 24 i . e . fixed monthly charge , y = 28 answer : option d"
Answer: d
Python program:
a = 52 * 2
b = a - 76
Problem: a started a business with an investment of rs . 70000 and after 9 months b joined him investing rs . 120000 . if the profit at the end of a year is rs . 76000 , then the share of b is ?
Options: a ) 33008 , b ) 24000 , c ) 28000 , d ) 48000 , e ) 81122
Rationale: "ratio of investments of a and b is ( 70000 * 12 ) : ( 120000 * 3 ) = 7 : 12 total profit = rs . 76000 share of b = 12 / 19 ( 76000 ) = rs . 48000 answer : d"
Answer: d
Python program:
a = const_60 * 100
b = 76000 - a
Problem: how many 7 in between 1 to 110 ?
Options: a ) 18 , b ) 21 , c ) 22 , d ) 23 , e ) 24
Rationale: "7 , 17,27 , 37,47 , 57,67 , 70,71 , 72,73 , 74,75 , 76,77 ( two 7 ' s ) , 78 , 79,87 , 97,107 21 7 ' s between 1 to 110 answer : b"
Answer: b
Python program:
a = 7 * 3
b = 110 / a
Problem: a alone can finish a work in 10 days which b alone can finish in 15 days . if they work together and finish it , then out of a total wages of rs . 3000 , a will get :
Options: a ) rs . 1200 , b ) rs . 1500 , c ) rs . 1800 , d ) rs . 2000 , e ) none of these
Rationale: "explanation : ratio of working days of a : b = 10 : 15 therefore , their wages ratio = reverse ratio = 15 : 10 therefore , a will get 15 units of ratio total ratio = 25 1 unit of ratio = 3000 / 25 = 120 so , a ’ s amount = 120 × 15 = rs . 1800 . answer : option c"
Answer: c
Python program:
a = 15 * 2
b = a / 10
c = 15 * 2
d = c / 10
e = 15 * 2
f = e / 15
g = d + f 
h = b / g
i = h * 3000
Problem: a started a business with an investment of rs . 70000 and after 6 months b joined him investing rs . 120000 . if the profit at the end of a year is rs . 78000 , then the share of b is ?
Options: a ) a ) 34500 , b ) b ) 36099 , c ) c ) 36000 , d ) d ) 38007 , e ) e ) 42000
Rationale: "ratio of investments of a and b is ( 70000 * 12 ) : ( 120000 * 6 ) = 7 : 6 total profit = rs . 78000 share of b = 6 / 13 ( 78000 ) = rs . 36000 answer : c"
Answer: c
Python program:
a = const_60 * 100
b = 78000 - a
Problem: if an object travels 90 feet in 3 seconds , what is the object ’ s approximate speed in miles per hour ? ( note : 1 mile = 5280 feet )
Options: a ) 17.36 , b ) 20.45 , c ) 23.87 , d ) 26.92 , e ) 29.56
Rationale: "90 feet / 3 seconds = 30 feet / second ( 30 feet / second ) * ( 3600 seconds / hour ) * ( 1 mile / 5280 feet ) = 20.45 miles / hour ( approximately ) the answer is b ."
Answer: b
Python program:
a = 90 / 5280
b = 1 / 3600
c = 3 * b
d = a / c
Problem: if 2 x + y = 7 and x + 2 y = 5 , then xy / 3 =
Options: a ) 1 , b ) 4 / 3 , c ) 17 / 5 , d ) 18 / 5 , e ) 4
Rationale: "2 * ( x + 2 y = 5 ) equals 2 x + 4 y = 10 2 x + 4 y = 10 - 2 x + y = 7 = 3 y = 3 therefore y = 1 plug and solve . . . 2 x + 1 = 7 2 x = 6 x = 3 xy / 3 = 3 * 1 / 3 = 1 a"
Answer: a
Python program:
a = 7 * 2
b = a - 5
c = 2 * 2
d = c - 1
e = b / d
f = 7 * 2
g = f - 5
h = 2 * 2
i = h - 1
j = g / i
k = 2 * j
l = 7 - k
m = e + l 
n = m / 3
Problem: there are 21 students in a class . in how many different ways can a committee of 3 students be formed ?
Options: a ) 1180 , b ) 1330 , c ) 1540 , d ) 1760 , e ) 1920
Rationale: "21 c 3 = 21 * 20 * 19 / 6 = 1330 the answer is b ."
Answer: b
Python program:
a = 3 / 21
b = 1 - a
c = b * 21
Problem: the average age of boys in a class is 16 years and that of the girls is 15 years . the average age for the whole class is
Options: a ) 15 years , b ) 15.5 years , c ) 16 years , d ) 17 years , e ) can not be computed
Rationale: "clearly , to find the average , we ought to know the numbers of boys , girls or students in the class , neither of which has been given . so the data provided is inadequate . answer : e"
Answer: e
Python program:
a = 16 - 15
Problem: of 800 surveyed students , 20 % of those who read book a also read book b and 25 % of those who read book b also read book a . if each student read at least one of the books , what is the difference between the number of students who read only book a and the number of students who read only book b ?
Options: a ) 20 , b ) 25 , c ) 30 , d ) 55 , e ) 100
Rationale: "say the number of students who read book a is a and the number of students who read book b is b . given that 20 % of those who read book a also read book b and 25 % of those who read book b also read book a , so the number of students who read both books is 0.2 a = 0.25 b - - > a = 1.25 b . since each student read at least one of the books then { total } = { a } + { b } - { both } - - > 800 = 1.25 b + b - 0.25 b - - > b = 400 , a = 1.25 b = 500 and { both } = 0.25 b = 100 . the number of students who read only book a is { a } - { both } = 500 - 100 = 400 ; the number of students who read only book b is { b } - { both } = 400 - 100 = 300 ; the difference is 400 - 300 = 100 . answer : e ."
Answer: e
Python program:
a = 25 / 100
b = 20 / 100
c = a / b
d = c + 1 
e = 25 / 100
f = d - e
g = 800 / f
h = 25 / 100
i = 20 / 100
j = h / i
k = g * j
l = 20 / 100
m = 1 - l
n = k * m
o = 25 / 100
p = 20 / 100
q = o / p
r = q + 1 
s = 25 / 100
t = r - s
u = 800 / t
v = 25 / 100
w = 1 - v
x = u * w
y = n - x
Problem: what annual payment will discharge a debt of rs . 1090 due in 2 years at the rate of 5 % compound interest ?
Options: a ) 993.2 , b ) 586.21 , c ) 534.33 , d ) 543.33 , e ) 646.33
Rationale: explanation : let each installment be rs . x . then , x / ( 1 + 5 / 100 ) + x / ( 1 + 5 / 100 ) 2 = 1090 820 x + 1090 * 441 x = 586.21 so , value of each installment = rs . 586.21 answer : option b
Answer: b
Python program:
a = 5 / 100
b = a + 1 
c = b ** 2
d = c * 1090
e = d / 2
Problem: a man sells a car to his friend at 15 % loss . if the friend sells it for rs . 54000 and gains 20 % , the original c . p . of the car was :
Options: a ) rs . 22941.18 , b ) rs . 32941.18 , c ) rs . 52941.18 , d ) rs . 62941.18 , e ) none of these
Rationale: "explanation : s . p = rs . 54,000 . gain earned = 20 % c . p = rs . [ 100 / 120 ã — 54000 ] = rs . 45000 this is the price the first person sold to the second at at loss of 15 % . now s . p = rs . 45000 and loss = 15 % c . p . rs . [ 100 / 85 ã — 45000 ] = rs . 52941.18 correct option : c"
Answer: c
Python program:
a = 54000 * 100
b = 100 + 20 
c = a / b
d = c * 100
e = 100 - 15
f = d / e