euclaise/mathqa_programs huggingface dataset:
Problem: average expenditure of a person for the first 3 days of a week is rs . 340 and for the next 4 days is rs . 420 . average expenditure of the man for the whole week is :
Options: a ) 350 , b ) 370 , c ) 380 , d ) 430 , e ) none
Rationale: "explanation : assumed mean = rs . 340 total excess than assumed mean = 4 × ( rs . 420 - rs . 350 ) = rs . 280 therefore , increase in average expenditure = rs . 280 / 7 = rs . 40 therefore , average expenditure for 7 days = rs . 340 + rs . 40 = rs . 380 correct option : c"
Answer: c
Python program:
a = 420 - 340
b = 4 * a
c = 3 + 4 
d = b / c
e = 340 + d
Problem: if rs . 400 amount to rs . 540 in 4 years , what will it amount to in 6 years at the same rate % per annum ?
Options: a ) s . 575 , b ) s . 595 , c ) s . 590 , d ) s . 610 , e ) s . 585
Rationale: "80 = ( 400 * 4 * r ) / 100 r = 8.75 % i = ( 400 * 6 * 8.75 ) / 100 = 210 400 + 210 = 610 answer : d"
Answer: d
Python program:
a = 540 - 400
b = a * 6
c = 540 - 400
d = b - c
Problem: whats the reminder when 879,548 , 521,456 , 258,759 , 653,258 , 778,455 , 658,985 is divided by 4
Options: a ) 1 , b ) 7 . , c ) 2 . , d ) 3 , e ) 9
Rationale: "a number ending in a 0 is divisible by 2 . a number ending in 2 zeroes is divisible by 4 . given the obscene number , you should immediately be convinced that you will need to focus on a very small part of it . 879,548 , 521,456 , 258,759 , 653,258 , 778,455 , 658,985 = 879,548 , 521,456 , 258,759 , 653,258 , 778,455 , 658,900 + 85 the first number is divisible by 16 . you just have to find the remainder when you divide 5287 by 16 . that will be the remainder when you divide the original number by 4 . 85 / 4 gives remainder 1 . answer ( a )"
Answer: a
Python program:
a = 4 * 2
b = 10 - 1
c = b * 100
d = 3 + 2 
e = d * 100
f = e * 10
g = c + f 
h = 3 + 2 
i = 12 + h 
j = 3 + 2 
k = i * j
l = g + k 
m = a + reminder
Problem: 400 metres long yard , 26 trees are palnted at equal distances , one tree being at each end of the yard . what is the distance between 2 consecutive trees
Options: a ) 10 , b ) 12 , c ) 14 , d ) 16 , e ) 18
Rationale: "26 trees have 25 gaps between them , required distance ( 400 / 25 ) = 16 d"
Answer: d
Python program:
a = 26 - 2
b = a + 1 
c = 400 / b
Problem: a car averages 30 miles per hour for the first 6 hours of a trip and averages 46 miles per hour for each additional hour of travel time . if the average speed for the entire trip is 34 miles per hour , how many hours long is the trip ?
Options: a ) 8 , b ) 10 , c ) 12 , d ) 14 , e ) 16
Rationale: "let t be the total time of the trip . 30 * 6 + 46 ( t - 6 ) = 34 t 12 t = 276 - 180 t = 8 the answer is a ."
Answer: a
Python program:
a = 34 * 6
b = 30 * 6
c = a - b
d = 46 - 34
e = c / d
f = e + 6
Problem: 5 / 8 of the population of the country of venezia lives in montague province , while the rest lives in capulet province . in the upcoming election , 80 % of montague residents support romeo , while 70 % of capulet residents support juliet ; each resident of venezia supports exactly one of these two candidates . rounded if necessary to the nearest percent , the probability that a juliet supporter chosen at random resides in capulet is
Options: a ) 28 % , b ) 41 % , c ) 45 % , d ) 72 % , e ) 68 %
Rationale: "total population = 80 ( assume ) . 5 / 8 * 80 = 50 people from montague . 3 / 8 * 80 = 30 people from capulet . 0.2 * 50 = 10 people from montague support juliet . 0.7 * 30 = 21 people from capulet support juliet . the probability that a juliet supporter chosen at random resides in capulet is 21 / ( 10 + 21 ) = ~ 68 . answer : e"
Answer: e
Python program:
a = 70 / 100
b = 8 - 5
c = b / 8
d = a * c
e = 100 - 80
f = e / 100
g = 5 / 8
h = f * g
i = 70 / 100
j = 8 - 5
k = j / 8
l = i * k
m = h + l 
n = d / m
o = n * 100
Problem: a “ sophie germain ” prime is any positive prime number p for which 2 p + 1 is also prime . the product of all the possible units digits of sophie germain primes greater than 5 is
Options: a ) 3 , b ) 7 , c ) 21 , d ) 27 , e ) 189
Rationale: "a prime number greater than 5 can have only the following four units digits : 1 , 3 , 7 , or 9 . if the units digit of p is 1 then the units digit of 2 p + 1 would be 3 , which is a possible units digit for a prime . for example consider p = 11 = prime - - > 2 p + 1 = 23 = prime ; if the units digit of p is 3 then the units digit of 2 p + 1 would be 7 , which is a possible units digit for a prime . for example consider p = 23 = prime - - > 2 p + 1 = 47 = prime ; if the units digit of p is 7 then the units digit of 2 p + 1 would be 5 , which is not a possible units digit for a prime ; if the units digit of p is 9 then the units digit of 2 p + 1 would be 9 , which is a possible units digit for a prime . for example consider p = 29 = prime - - > 2 p + 1 = 59 = prime . the product of all the possible units digits of sophie germain primes greater than 5 is 1 * 3 * 9 = 27 . answer : d ."
Answer: d
Python program:
a = 5 - 1
b = 2 + 1 
c = a + b 
d = 2 + 1 
e = c + d 
f = e - 10
g = 5 - 1
h = 2 + 1 
i = g + h 
j = 2 * i
k = j + 1 
l = k - 10
m = f * l
n = 2 + 1 
o = m * n
p = 5 - 1
q = 2 + 1 
r = p + q 
s = 2 + 1 
t = r + s 
u = 2 + 1 
v = t + u 
w = 2 * v
x = w + 1 
y = 2 * 10
z = x - y
A = o * z
Problem: 32 % of 5 / 8 =
Options: a ) 0.2 , b ) 0.5 , c ) 0.6 , d ) 0.75 , e ) 1.0
Rationale: "should be simple . 0.32 * 5 / 8 = 1.6 / 8 = 0.2 correct option : a"
Answer: a
Python program:
a = 8 * 5
b = a / 100
c = b * 32
d = c / 100
Problem: in a mayoral election , candidate x received 1 / 2 more votes than candidate y , and candidate y received 2 / 5 fewer votes than z . if z received 25,000 votes how many votes did candidate x received ?
Options: a ) 18000 , b ) 22500 , c ) 24000 , d ) 26000 , e ) 32000
Rationale: z = 25 - - > y received 2 / 5 fewer votes than z - - > y = z - 2 / 5 * z = 15 ; x received 1 / 2 more votes than y - - > x = y + 1 / 2 * y = 22,5 . answer : b .
Answer: b
Python program:
a = 2 / 5
b = 1 - a
c = const_0_25 * 100
d = c * 100
e = d * 10
f = b * e
g = 1 / 2
h = g + 1 
i = f * h
Problem: a train 150 meters long completely crosses a 240 meters long bridge in 42 seconds . what is the speed of the train is ?
Options: a ) 32 , b ) 33 , c ) 88 , d ) 66 , e ) 09
Rationale: "s = ( 150 + 240 ) / 42 = 390 / 42 * 18 / 5 = 33 answer : b"
Answer: b
Python program:
a = 150 + 240 
b = a / 1000
c = 42 / 3600
d = b / c
Problem: on july 1 of last year , total employees at company e was decreased by 10 percent . without any change in the salaries of the remaining employees , the average ( arithmetic mean ) employee salary was 10 percent more after the decrease in the number of employees than before the decrease . the total of the combined salaries of all the employees at company e after july 1 last year was what percent t of thatbeforejuly 1 last year ?
Options: a ) 90 % , b ) 99 % , c ) 100 % , d ) 101 % , e ) 110 %
Rationale: "the total number of employees = n the average salary = x total salary to all emplyoees = xn after the total number of employees = n - 0.1 n = 0.9 n the average salary = x + 10 % of x = 1.1 x total salary to all emplyoees = 0.9 n ( 1.1 x ) total salary after as a % of total salary before t = [ 0.9 n ( 1.1 x ) ] / xn = 0.99 or 99 % . b"
Answer: b
Python program:
a = 10 * 10
Problem: if 2 men or 3 women can reap a field in 8 days how long will 3 men and 4 women take to reap it ?
Options: a ) 2 / 16 , b ) 1 / 16 , c ) 3 / 24 , d ) 5 / 16 , e ) 6 / 26
Rationale: "explanation : 2 men reap 1 / 8 field in 1 day 1 man reap 1 / ( 2 x 8 ) 3 women reap 1 / 8 field in 1 day 1 woman reap 1 / ( 3 x 8 ) 3 men and 4 women reap ( 3 / ( 2 x 8 ) + 4 / ( 3 x 8 ) ) = 5 / 16 in 1 day 3 men and 4 women will reap the field in 5 / 16 days answer : option d"
Answer: d
Python program:
a = 8 / 2
b = 3 * a
c = 8 / 3
d = 4 * c
e = b + d 
f = 8 / e
Problem: if 15 men , working 9 hours a day , can reap a field in 16 days , in how many days will 18 men reap the field , working 8 hours a day ?
Options: a ) 10 , b ) 15 , c ) 20 , d ) 25 , e ) none of them
Rationale: let the required number of days be x . more men , less days ( indirect proportion ) less hours per day , more days ( indirect proportion ) men 18 : 15 hours per day 8 : 9 } : : 16 : x ( 18 x 8 x x ) = ( 15 x 9 x 16 ) = x = ( 44 x 15 ) 144 = 15 hence , required number of days = 15 . answer is b .
Answer: b
Python program:
a = 15 * 9
b = a * 16
c = 18 * 8
d = b / c
Problem: find the sum the difference between the compound and s . i . on a certain sum of money for 5 years at 50 % per annum is rs . 200 of money ?
Options: a ) 1256 , b ) 2000 , c ) 3600 , d ) 8400 , e ) 4566
Rationale: "p = 200 ( 100 / 50 ) 5 = > p = 2000 answer : b"
Answer: b
Python program:
a = 50 * 5
b = 200 / a
c = b * 100
d = 50 * 5
e = c * d
Problem: a small beaker is 1 / 2 filled with salt water . another beaker , which has 5 times the capacity of the small beaker , is 1 / 5 filled with fresh water . after dumping all of the salt water from the small beaker into the large beaker , to what fraction of its capacity will the large beaker be filled ?
Options: a ) 2 / 3 , b ) 2 / 5 , c ) 3 / 5 , d ) 3 / 10 , e ) 7 / 20
Rationale: 1 / 2 of the small beaker is 1 / 10 of the large beaker . 1 / 10 + 1 / 5 = 3 / 10 the answer is d .
Answer: d
Python program:
a = 1 + 2 
b = 2 * 5
c = a / b
Problem: a football field is 9600 square yards . if 800 pounds of fertilizer are spread evenly across the entire field , how many pounds of fertilizer were spread over an area of the field totaling 3600 square yards ?
Options: a ) 450 , b ) 600 , c ) 750 , d ) 2400 , e ) 300
Rationale: "answer e ) 9600 yards need 1200 lbs 1 yard will need 800 / 9600 = 1 / 12 lbs 3600 yards will need 1 / 12 * 3600 yards = 300 lbs"
Answer: e
Python program:
a = 800 / 9600
b = 3600 * a
Problem: 4.036 divided by 0.04 gives
Options: a ) 1.009 , b ) 100.09 , c ) 10.9 , d ) none of these , e ) can not be determined
Rationale: "solution 4.036 / 0.04 = 403.6 / 4 = 100.9 answer a"
Answer: a
Python program:
a = 4 / 36
Problem: sum of the squares of 3 numbers is 222 and the sum of their products taken two at a time is 131 . find the sum ?
Options: a ) 22 , b ) 25 , c ) 26 , d ) 28 , e ) 29
Rationale: ( a + b + c ) 2 = a 2 + b 2 + c 2 + 2 ( ab + bc + ca ) = 222 + 2 * 131 a + b + c = √ 484 = 22 a
Answer: a
Python program:
a = 131 * 2
b = a + 222 
c = math.sqrt(b)
Problem: a train 410 m long is running at a speed of 45 km / hr . in what time will it pass a bridge 140 m long ?
Options: a ) 40 sec , b ) 50 sec , c ) 44 sec , d ) 49 sec , e ) 60 sec
Rationale: "speed = 45 * 5 / 18 = 25 / 2 m / sec total distance covered = 410 + 140 = 550 m required time = 550 * 2 / 25 = 44 sec answer : c"
Answer: c
Python program:
a = 45 - 140
b = a * const_0_2778
c = 410 / b
Problem: the total price of a basic computer and printer are $ 2,500 . if the same printer had been purchased with an enhanced computer whose price was $ 500 more than the price of the basic computer , then the price of the printer would have been 1 / 4 of that total . what was the price of the basic computer ?
Options: a ) 1500 , b ) 1600 , c ) 1750 , d ) 1900 , e ) 2000
Rationale: "let the price of basic computer be c and the price of the printer be p : c + p = $ 2,500 . the price of the enhanced computer will be c + 500 and total price for that computer and the printer will be 2,500 + 500 = $ 3,000 . now , we are told that the price of the printer is 1 / 4 of that new total price : p = 1 / 4 * $ 3,000 = $ 750 . plug this value in the first equation : c + 750 = $ 2,500 - - > c = $ 1,750 answer : c ."
Answer: c
Python program:
a = const_0_25 * 1000
b = a * 10
c = const_0_25 * 1000
d = c * 10
e = 500 + d 
f = e / 4
g = b - f
Problem: 3 / [ ( 1 / 0.03 ) + ( 1 / 0.37 ) ] = ?
Options: a ) 0.004 , b ) 0.08333 , c ) 2.775 , d ) 3.6036 , e ) 36.036
Rationale: "approximate . 1 / . 03 = 100 / 3 = 33 1 / . 37 = 100 / 37 = 3 denominator becomes 33 + 3 = 36 3 / 36 = . 08 something answer ( b )"
Answer: b
Python program:
a = 3 / 0
b = 3 / 0
c = a + b 
d = 1/(c)
Problem: n ^ ( n / 2 ) = 6 is true when n = 6 in the same way what is the value of n if n ^ ( n / 2 ) = 9 ?
Options: a ) 16 , b ) 14 , c ) 18 , d ) 6 , e ) 9
Rationale: n ^ ( n / 2 ) = 9 apply log n / 2 logn = log 9 nlogn = 2 log 9 = log 9 ^ 2 = log 81 logn = log 81 now apply antilog n = 81 / n now n = 9 . answer : e
Answer: e
Python program:
a = 9 ** 2
b = a / 9
Problem: y and z are in a relay race . y runs the first leg of the course in 58 seconds . z runs the second leg of the course in 26 seconds . what was the average time they took to run a leg of the course ?
Options: a ) 39 , b ) 40 , c ) 41 , d ) 42 , e ) 43
Rationale: ( 58 seconds + 26 seconds ) / 2 = 42 seconds correct option is : d
Answer: d
Python program:
a = 58 + 26 
b = a / 2
Problem: a , b , and c are integers and a < b < c . s is the set of all integers from a to b , inclusive . q is the set of all integers from b to c , inclusive . the median of set s is ( 3 / 4 ) * b . the median of set q is ( 5 / 8 ) * c . if r is the set of all integers from a to c , inclusive , what fraction of c is the median of set r ?
Options: a ) 3 / 8 , b ) 1 / 2 , c ) 9 / 16 , d ) 5 / 7 , e ) 3 / 4
Rationale: the answer isc : 11 / 16 . the key to this problem is remembering that the median for a consecutive set of numbers is equivalent to its mean . for example , the mean and median of a set consisting of x , x + 1 , x + 2 , . . . , y will always be ( x + y ) / 2 . for set s , consisting of numbers ( a , a + 1 , . . . , b ) , the median is given to be 3 / 4 * b : ( a + b ) / 2 = ( 3 / 4 ) * b a = b / 2 for set q , consisting of numbers ( b , b + 1 , . . . , c ) , the median is given to be 5 / 8 * c : ( b + c ) / 2 = ( 5 / 8 ) * c b = ( 1 / 4 ) * c for set r , consisting of numbers ( a , a + 1 , . . . c ) , the median needs to be found : a = b / 2 = ( 1 / 4 * c ) / 2 = ( 1 / 8 ) * c median = ( a + c ) / 2 = ( 1 / 8 * c + c ) / 2 = ( 9 / 8 ) * c / 2 = ( 9 / 16 ) * c ( answer c )
Answer: c
Python program:
a = 5 / 8
b = a * 2
c = b - 1
d = 3 / 4
e = d * 2
f = e - 1
g = 1 / f
h = c / g
i = 1 + h 
j = i / 2
Problem: the mean of 30 values was 180 . it was detected on rechecking that one value 155 was wrongly copied as 135 for the computation of the mean . find the correct mean .
Options: a ) 151 , b ) 149 , c ) 152 , d ) 148 , e ) 180.67
Rationale: "corrected mean = 180 × 30 − 135 + 155 / 30 = 5400 − 135 + 155 / 30 = 5420 / 30 = 180.67 answer e"
Answer: e
Python program:
a = 30 * 180
b = 155 - 135
c = a + b 
d = c / 30
Problem: three interviewers , x , y , and z are interviewing 40 applicants . only with three interviewers ' admission can an applicant be admitted . if interviewer x admitted 15 applicants , y admitted 17 applicants , and z admitted 20 applicants , at least how many applicants get the admission ?
Options: a ) 0
b ) 2
c ) 6
d ) 8
e ) 12
Rationale: if x admitted 15 are overlapping with y admission of 17 but z does not overlap with anybody . then no student will get nod from all the 3 . hence 0 student will get admission . answer : a
Answer: a
Python program:
a = min(15)
b = min(a)
Problem: a man took a loan at rate of 12 % per annum simple interest . after 3 years he had to pay 6480 interest . the principal amount borrowed by him was .
Options: a ) rs 14000 , b ) rs 15000 , c ) rs 16000 , d ) rs 18000 , e ) none of these
Rationale: "explanation : s . i . = p â ˆ — r â ˆ — t / 100 = > p = s . i . â ˆ — 100 / r â ˆ — t = > p = 6480 â ˆ — 100 / 12 â ˆ — 3 = rs 18000 option d"
Answer: d
Python program:
a = 6480 * 100
b = 12 * 3
c = a / b
Problem: how long will take a leak at the bottom of a tank to empty it if it will take 3 hours to fill it without the leak , but due to the leak it will take one additional hour to be filled ?
Options: a ) 12 hours , b ) 111 hours , c ) 15 hours , d ) 14 hours , e ) 11 hours
Rationale: part filled without leak in 1 hour = 1 / 3 part filled with leak in 1 hour = 1 / 4 work done by leak in 1 hour = 1 / 3 â ˆ ’ 1 / 4 = 12 hours answer : a
Answer: a
Python program:
a = 1/(3)
b = 3 + 1 
c = 1/(b)
d = a - c
e = 1/(d)
Problem: the security gate at a storage facility requires a 5 - digit lock code . if the lock code must consist only of digits from 1 through 7 , inclusive , with no repeated digits , and the first and last digits of the code must be even , how many lock codes are possible ?
Options: a ) 120 , b ) 240 , c ) 360 , d ) 720 , e ) 1440
Rationale: x - x - x - x - x - - > there are 3 even digits from 1 to 7 , inclusive thus options for the first and the last x ' s are : 3 - x - x - x - 2 . other x ' s can take following values : 3 - 5 - 4 - 3 - 2 - - > 3 * 5 * 4 * 3 * 2 = 360 . answer : c .
Answer: c
Python program:
a = math.factorial(3)
b = math.factorial(5)
c = b / 2
d = a * c
Problem: if 5400 mn = k ^ 4 , where m , n , and k are positive integers , what is the least possible value of 5 m + n ?
Options: a ) 65 , b ) 18 , c ) 20 , d ) 25 , e ) 33
Rationale: "k ^ 4 = 5400 ∗ mn k ^ 4 = 3 ^ 3.2 ^ 3.5 ^ 2 . mn in order to make rhs a perfect power of 4 , we require it to be multiplied by 3 , 2 & 5 ^ 2 mn = 3 . 2.5 ^ 2 mn = 150 = 10 * 15 ( least possible ) answer = 5 * 10 + 15 = 65 answer : a"
Answer: a
Python program:
a = 3 ** 5
b = 4 * 0
Problem: the h . c . f . of two numbers is 59 and the other two factors of their l . c . m . are 13 and 16 . the larger of the two numbers is :
Options: a ) 678 , b ) 944 , c ) 456 , d ) 323 , e ) 899
Rationale: : explanation : clearly , the numbers are ( 59 x 13 ) and ( 59 x 16 ) . { \ color { blue } \ therefore } larger number = ( 59 x 16 ) = 944 . answer : b ) 944
Answer: b
Python program:
a = 59 * 16
Problem: 0.012 x 0.5 = ?
Options: a ) 0.0006 , b ) 0.06 , c ) 0.6 , d ) 0.006 , e ) 6.0
Rationale: "12 x 5 = 60 . sum of decimal places = 4 0.012 x 0.5 = 0.006 answer : option d"
Answer: d
Python program:
a = 0 / 12
b = a * 100
Problem: the rate of interest on a sum of money is 5 % p . a . for the first 3 years , 4 % p . a . for the next 4 years , and 5 % for the period beyond 7 years . if the s . i , occured on the sum for the total period of 8 years is rs . 540 / - , the sum is
Options: a ) 1,500 , b ) 2,000 , c ) 2,100 , d ) 2,250 , e ) 2,540
Rationale: "explanation : i 1 = ( p x 3 x 5 ) / 100 = 3 p / 20 i 2 = ( p x 4 x 4 ) / 100 = 4 p / 25 i 3 = ( p x 1 x 5 ) / 100 = p / 20 3 p / 20 + 4 p / 25 + p / 20 = 540 9 p / 25 = 540 p = 1500 answer : option a"
Answer: a
Python program:
a = 540 / 540
Problem: a certain manufacturer produces items for which the production costs consist of annual fixed costs totaling $ 130,000 and variables costs averaging $ 10 per item . if the manufacturer ’ s selling price per item is $ 15 , how many items the manufacturer produce and sell to earn an annual profit of $ 150,000 ?
Options: a ) 2,858 , b ) 18,667 , c ) 21,429 , d ) 35,000 , e ) 56,000
Rationale: let the items manufactured or sold bex 130000 + 10 x = 15 x - 150000 5 x = 280000 x = 56000 ans : e
Answer: e
Python program:
a = 3 + 10 
b = a + 15 
c = 100 ** 2
d = b * c
e = 15 - 10
f = d / e
g = 4 * 2
h = f / g
i = h * 3
j = i / 1000
Problem: the difference between simple and compound interest on rs . 1700 for one year at 10 % per annum reckoned half - yearly is ?
Options: a ) 8.25 , b ) 4.25 , c ) 9.25 , d ) 3.25 , e ) 2.25
Rationale: "s . i . = ( 1700 * 10 * 1 ) / 100 = rs . 170 c . i . = [ 1700 * ( 1 + 5 / 100 ) 2 - 1700 ] = rs . 174.25 difference = ( 174.25 - 174 ) = rs . 4.25 . answer : b"
Answer: b
Python program:
a = 10 / 2
b = a / 100
c = b + 1 
d = c ** 2
e = 10 / 100
f = e + 1 
g = d - f
h = g * 1700
Problem: two whole numbers whose sum is 24 is the ratio
Options: a ) 1 : 3 , b ) 2 : 8 , c ) 1 : 6 , d ) 2 : 3 , e ) 2 : 5
Rationale: a ) 1 : 3
Answer: a
Python program:
a = 100 / 0
b = a - 10
c = b / 2
d = 24 / 2
e = d + 10 
f = c / e
Problem: vijay sells a cupboard at 16 % below cost price . had he got rs . 1800 more , he would have made a profit of 16 % . what is the cost price of the cupboard ?
Options: a ) 7450 , b ) 14900 , c ) 5625 , d ) 7500 , e ) none of these
Rationale: explanation : cost price = 1800 / ( 0.16 + 0.16 ) = 1800 / 0.32 = rs . 5625 answer c
Answer: c
Python program:
a = 100 + 16 
b = 100 - 16
c = a - b
d = c / 100
e = 1800 / d
Problem: if a : b = 4 : 7 and b : c = 5 : 9 , then a : c = ?
Options: a ) 28 : 37 , b ) 18 : 37 , c ) 16 : 53 , d ) 20 : 63 , e ) 15 : 48
Rationale: a / b = 4 / 7 and b / c = 5 / 9 a / b * b / c = 4 / 7 * 5 / 9 = 20 / 63 so a / c = 20 / 63 20 : 63 answer d
Answer: d
Python program:
a = 4 * 5
b = 7 * 9
c = a / b
Problem: there are 7 red balls and 5 blue balls in a jar . if 3 balls are selected from the jar , what is the probability that 3 balls selected are red balls ?
Options: a ) 19 / 44 , b ) 5 / 44 , c ) 3 / 41 , d ) 13 / 44 , e ) 7 / 44
Rationale: "probability = favorable outcomes / total outcomes probability = 7 c 3 / 12 c 3 or ( 7 / 12 ) * ( 6 / 11 ) * ( 5 / 10 ) = 7 / 55 answer option e"
Answer: e
Python program:
a = math.comb(5, 3)
b = 7 + 5 
c = math.comb(b, 3)
d = a / c
Problem: on the first of the year , james invested x dollars at proudstar bank in an account that yields 3 % in interest every quarter year . at the end of the year , during which he made no additional deposits or withdrawals , he had y dollars in the account . if james had invested the same amount in an account which pays interest on a yearly basis , what must the interest rate be for james to have y dollars at the end of the year ?
Options: a ) 22.04 % , b ) 16.12 % , c ) 12.5 % , d ) 18.25 % , e ) 10 %
Rationale: per quarter , interest = 3 % so for a year , interest = 12 % due to quarter cumulation , effective yield ( ytm ) would be slight higher than 12 % answer = 12.5 % = answer : c
Answer: c
Python program:
a = 3 * 4
Problem: the length of a room is 5.5 m and width is 3.75 m . what is the cost of paying the floor by slabs at the rate of rs . 800 per sq . meter .
Options: a ) rs . 12000 , b ) rs . 19500 , c ) rs . 18000 , d ) rs . 16500 , e ) rs . 17500
Rationale: "explanation : area = 5.5 × 3.75 sq . metre . cost for 11 sq . metre . = rs . 800 hence , total cost = 5.5 × 3.75 × 800 = 5.5 × 3000 = rs . 16500 answer : option d"
Answer: d
Python program:
a = 5 * 5
b = 800 * a
Problem: a group of n students can be divided into equal groups of 4 with 1 student left over or equal groups of 7 with 2 students left over . what is the sum of the two smallest possible values of n ?
Options: a ) 42 . , b ) 46 . , c ) 50 . , d ) 54 . , e ) 58 .
Rationale: "n = 4 k + 1 = 7 j + 2 let ' s start at 1 = 4 ( 0 ) + 1 and keep adding 4 until we find a number in the form 7 j + 2 . 1 , 5 , 9 = 7 ( 1 ) + 2 the next such number is 9 + 4 * 7 = 37 . 9 + 37 = 46 the answer is b ."
Answer: b
Python program:
a = 7 * 2
b = a + 2 
c = 2 * 2
d = 7 * c
e = d + 2 
f = b + e
Problem: the breath of a rectangular landscape is 8 times its length . there is a playground in it whose area is 3200 square mtr & which is 1 / 9 rd of the total landscape . what is the breath of the landscape ?
Options: a ) 420
b ) 430
c ) 280
d ) 360
e ) 480
Rationale: sol . 8 x * x = 9 * 3200 x = 60 length = 8 * 60 = 480 e
Answer: e
Python program:
a = 3200 * 9
b = a / 8
c = math.sqrt(b)
d = c * 8
Problem: machine c takes 2 more hours than machine b to make 20 widgets . if working together , the machines can make 25 widgets in 3 hours , how long will it take machine c to make 40 widgets ?
Options: a ) 5 , b ) 6 , c ) 8 , d ) 10 , e ) 12
Rationale: i approached this one by plugging in numbers . . . started with c . if 40 are made in 8 hours , then 20 are made in 4 hours . so time of c is 4 , and time of b is 2 . rate together : 20 / 4 + 20 / 2 = 5 + 10 = 15 . so in 1 hour , together make 15 widgets . in 3 hours = 45 . way too much . we can eliminate right away c , b , and a - because b and c reduces the time - the total # of widgets made will be even higher . now between d and e - > try only one . . if it does n ' t work , then the other one is the answer . i picked e : 12 h to make 40 widgets , and 6 hours to make 20 . this is the time of c . time of b = 4 hours . 20 / 6 + 20 / 4 = 10 / 3 + 20 / 4 find lcm of 3 and 4 = 12 . multiply first by 4 , and second by 3 : 40 + 60 / 12 = 100 / 12 divide by 4 : 25 / 3 so this is the rate given . e is the correct answer
Answer: e
Python program:
a = 4 + 2 
b = a * 40
c = b / 20