euclaise/mathqa_programs huggingface dataset:
Problem: if a speaks the truth 80 % of the times , b speaks the truth 60 % of the times . what is the probability that at least one will tell the truth
Options: a ) 0.8 , b ) 0.92 , c ) 1.02 , d ) 1.2 , e ) 1.3
Rationale: "probability of a speaks truth p ( a ) = 8 / 10 ; false = 2 / 10 probability of b speaks truth p ( b ) = 6 / 10 ; false = 4 / 10 . for given qtn ans = 1 - ( neither of them tell truth ) . because a & b are independent events = 1 - [ ( 2 / 10 ) * ( 4 / 10 ) ] = 1 - 8 / 10 = 1 - 0.08 = 0.92 answer : b"
Answer: b
Python program:
a = 4 * 5
b = a * 5
c = 80 / b
d = 4 * 5
e = d * 5
f = 60 / e
g = c * f
Problem: joe invested a certain sum of money in a simple interest bond whose value grew to $ 460 at the end of 3 years and to $ 560 at the end of another 5 years . what was the rate of interest in which he invested his sum ?
Options: a ) 3 % , b ) 4 % , c ) 5 % , d ) 6 % , e ) 7 %
Rationale: "in 5 years , the value grew $ 100 , so the simple interest was $ 20 per year . in 3 years , the total interest was 3 * $ 20 = $ 60 the principal is $ 460 - $ 60 = 400 . the interest rate is $ 20 / $ 400 = 5 % the answer is c ."
Answer: c
Python program:
a = 560 - 460
b = a / 5
c = 560 - 460
d = c / 5
e = d * 3
f = 460 - e
g = b / f
h = g * 100
Problem: jane makes toy bears . when she works with an assistant , she makes 80 percent more bears per week and works 10 percent fewer hours each week . having an assistant increases jane ’ s output of toy bears per hour by what percent t ?
Options: a ) 20 % , b ) 80 % , c ) 100 % , d ) 180 % , e ) 200 %
Rationale: "c . let ' s assume just jane 40 bears per 40 / hrs a week , so that is 1 bear / hr . with an assistant she makes 72 bears per 36 hours a week or 2 bears / hr ( [ 40 bears * 1.8 ] / [ 40 hrs * . 90 ] ) . t = [ ( 2 - 1 ) / 1 ] * 100 % = 100 % . c"
Answer: c
Python program:
a = 100 - 80
b = a - 10
c = 10 / b
d = c * 100
Problem: 36 people { a 1 , a 2 , . . . , a 36 } meet and shake hands in a circular fashion . in other words , there are totally 36 handshakes involving the pairs , { a 1 , a 2 } , { a 2 , a 3 } , . . . , { a 35 , a 36 } , { a 36 , a 1 } . then size of the smallest set of people such that the rest have shaken hands with at least one person in the set is
Options: a ) 11
b ) 12
c ) 13
d ) 15
e ) 18
Rationale: if we take person a 1 in the set then it will cover a 36 and a 2 for shaking hand . similarly if we take person a 4 in the set then it will cover a 5 and a 3 for shaking hand and so on , so minimum 12 persons are required . answer : b
Answer: b
Python program:
a = 1 + 2 
b = 36 / a
Problem: a palindrome is a number that reads the same forward and backward , such as 787 . how many even , 8 - digit numbers are palindromes ?
Options: a ) 4055 , b ) 4500 , c ) 5000 , d ) 9000 , e ) 4000
Rationale: "first recognize you only need to consider the first four digits ( because the second four are just the first four flipped ) there are 9000 possibilities for the first four digits of a 8 digit number , 1000 - 9999 inclusive . everything starting with a 2,4 , 6,8 will be odd , which is 4 / 9 ths of the combinations . 4 / 9 * 9000 = 4000 answer : e"
Answer: e
Python program:
a = 8 / 2
b = 10 ** a
c = b / 2
Problem: the maitre ' d at an expensive manhattan restaurant has noticed that 60 % of the couples order dessert and coffee . however , 20 % of the couples who order dessert do n ' t order coffee . what is the probability y that the next couple the maitre ' d seats will not order dessert ?
Options: a ) 20 % , b ) 25 % , c ) 40 % , d ) 60 % , e ) 75 %
Rationale: "could you use a venn diagram and just go with the number 100 . 60 people order dessert and coffee . . . which is the union of d and c . y = 2 / 10 of d are n ' t in d u c = so 8 / 10 of d are in duc which means = 60 = 8 / 10 d . so d in total = 75 , and 15 d ' s are n ' t in d union c . which means 25 people are in c only + neither . b 25 %"
Answer: b
Python program:
a = 2 * 5
b = 2 * 5
c = a * b
d = 60 / c
e = 2 * 5
f = 2 * 5
g = e * f
h = 20 / g
i = 1 - h
j = d / i
k = 1 - j
l = 2 * 5
m = 2 * 5
n = l * m
o = k * n
Problem: if a boat is rowed downstream for 200 km in 10 hours and upstream for 96 km in 12 hours , what is the speed of the boat and the river ?
Options: a ) 14 , 18 , b ) 14 , 6 , c ) 14 , 14 , d ) 6 , 6 , e ) 14 , 10
Rationale: "explanation : if x : speed of boats man in still water y : speed of the river downstream speed ( ds ) = x + y upstream speed ( us ) = x â € “ y x = ( ds + us ) / 2 y = ( ds â € “ us ) / 2 in the above problem ds = 20 ; us = 8 x = ( 20 + 8 ) / 2 = 28 / 2 = 14 km / hr y = ( 20 - 8 ) / 2 = 12 / 2 = 6 km / hr answer : b"
Answer: b
Python program:
a = 96 / 12
b = 200 / 10
c = a + b 
d = c / 2
Problem: in what time will a car 10 m long moving at the rate of 36 kmph pass a telegraph post on its way ?
Options: a ) 8 sec , b ) 1 sec , c ) 9 sec , d ) 6 sec , e ) 2 sec
Rationale: t = 10 / 36 * 18 / 5 = 1 sec answer : b
Answer: b
Python program:
a = 36 * const_0_2778
b = 10 / a
Problem: at an upscale fast - food restaurant , shin can buy 3 burgers , 7 shakes , and one cola for $ 130 . at the same place it would cost $ 164.50 for 4 burgers , 10 shakes , and one cola . how much would it cost for a meal of one burger , one shake , and one cola ?
Options: a ) $ 21 , b ) $ 27 , c ) $ 31 , d ) $ 61 , e ) it can not be determined
Rationale: "let ' s suppose that the price of a burger is bb , of a shake - ss and that of a cola is cc . we can then construct these equations : 3 b + 7 s + c = 130 4 b + 10 s + c = 164.5 subtracting the first equation from the second gives us b + 3 s = 34.5 now if we subtract the new equation two times from first or 3 times from second we will get b + s + c = 61 . in any case , there is no necessity to know each item ' s price , just the sum . answer : d"
Answer: d
Python program:
a = 164 - 50
b = 130 + a 
c = 164 - 50
d = c * 3
e = b - d
Problem: if the sum of a number and its square is 306 , what is the number ?
Options: a ) 16 , b ) 77 , c ) 25 , d ) 17 , e ) 171
Rationale: "explanation : let the integer be x . then , x + x 2 = 306 x 2 + x - 306 = 0 ( x + 18 ) ( x – 17 ) = 0 x = 17 answer : d"
Answer: d
Python program:
a = math.sqrt(306)
b = math.floor(a)
Problem: the price of a t . v . set worth rs . 15000 is to be paid in 20 installments of rs . 2000 each . if the rate of interest be 6 % per annum , and the first installment be paid at the time of purchase , then the value of the last installment covering the interest as well will be ?
Options: a ) 29997 , b ) 28088 , c ) 27098 , d ) 13000 , e ) 2799
Rationale: "money paid in cash = rs . 2000 balance payment = ( 15000 - 2000 ) = rs . 13000 . answer : d"
Answer: d
Python program:
a = 15000 - 2000
Problem: a train 180 m long running at 70 kmph crosses a platform in 20 sec . what is the length of the platform ?
Options: a ) 208 , b ) 277 , c ) 350 , d ) 881 , e ) 271
Rationale: "d = 70 * 5 / 18 = 20 = 388 – 180 = 208 answer : a"
Answer: a
Python program:
a = 70 * const_0_2778
b = 20 * a
c = b - 180
Problem: a person spends 40 % of his salary on food , 25 % on house rent , 15 % on entertainment and 5 % on conveyance . if his savings at the end of the month is rs . 2700 , then his salary per month in rupees is :
Options: a ) 4000 , b ) 6000 , c ) 18000 , d ) 10000 , e ) none of these
Rationale: "total expenditure = 40 + 25 + 15 + 5 = 85 % saving = ( 100 - 85 ) = 15 % 15 / 100 × salary = 2700 , salary = 18000 rs . answer : c ."
Answer: c
Python program:
a = 2700 * 100
b = a / 5
Problem: two trucks each 250 m long are running in opposite directions on parallel paths . their speeds are 30 km / hr and 20 km / hr respectively . find the time taken by the slower train to pass the driver of the faster one ?
Options: a ) 77 sec , b ) 66 sec , c ) 48 sec , d ) 55 sec , e ) 36 sec
Rationale: relative speed = 20 + 30 = 50 km / hr . 50 * 5 / 18 = 125 / 9 m / sec . distance covered = 250 + 250 = 500 m . required time = 500 * 9 / 125 = 36 sec . answer : e
Answer: e
Python program:
a = 250 * 2
b = 30 + 20 
c = b * const_0_2778
d = a / c
Problem: if a * b * c = 130 , b * c * d = 65 , c * d * e = 1000 and d * e * f = 150 the ( a * f ) / ( c * d ) = ?
Options: a ) 1 / 2 , b ) 1 / 4 , c ) 3 / 4 , d ) 1 / 3 , e ) none of these
Rationale: "explanation : a â ˆ — b â ˆ — c / b â ˆ — c â ˆ — d = 130 / 65 = > a / d = 2 d â ˆ — e â ˆ — f / c â ˆ — d â ˆ — e = 150 / 1000 = > f / c = 1 / 4 a / d * f / c = 2 * 15 / 10 = 1 / 3 answer : d"
Answer: d
Python program:
a = 130 * 150
b = 1000 * 65
c = a / b
Problem: two numbers are less than third number by 25 % and 37 % respectively . how much percent is the second number less than by the first
Options: a ) 6 % , b ) 8 % , c ) 9 % , d ) 11 % , e ) 12 %
Rationale: let the third number is x . then first number = ( 100 - 25 ) % of x = 75 % of x = 75 x / 100 second number is ( 63 x / 100 ) difference = 75 x / 100 - 63 x / 100 = 3 x / 25 so required percentage is , difference is what percent of first number ( 3 x / 25 * 100 / 75 x * 100 ) % = 6 % answer : a
Answer: a
Python program:
a = 37 - 25
b = 100 - 25
c = a / b
d = c * 100
e = d - 10
Problem: for any integer k greater than 1 , the symbol k * denotes the product of all the fractions of the form 1 / t , where t is an integer between 1 and k , inclusive . what is the value of 6 * / 4 * ?
Options: a ) 5 , b ) 5 / 4 , c ) 4 / 5 , d ) 1 / 4 , e ) 1 / 5
Rationale: "when dealing with ' symbolism ' questions , it often helps to ' play with ' the symbol for a few moments before you attempt to answer the question that ' s asked . by understanding how the symbol ' works ' , you should be able to do the latter calculations faster . here , we ' re told that k * is the product of all the fractions of the form 1 / t , where t is an integer between 1 and k , inclusive . based on this definition . . . . if . . . . k = 2 k * = ( 1 / 1 ) ( 1 / 2 ) = 1 / 2 if . . . . k = 3 k * = ( 1 / 1 ) ( 1 / 2 ) ( 1 / 3 ) = 1 / 6 we ' re asked to find the value of 5 * / 4 * now that we know how the symbol ' works ' , solving this problem should n ' t be too difficult . you can actually choose to do the math in a couple of different ways . . . . 5 * = ( 1 / 1 ) ( 1 / 2 ) ( 1 / 3 ) ( 1 / 4 ) ( 1 / 5 ) do n ' t calculate this just yet though . . . . since we ' re dividing by 4 * , many of those fractions will ' cancel out . ' 4 * = ( 1 / 1 ) ( 1 / 2 ) ( 1 / 3 ) ( 1 / 4 ) we ' re looking for the value of : ( 1 / 1 ) ( 1 / 2 ) ( 1 / 3 ) ( 1 / 4 ) ( 1 / 5 ) / ( 1 / 1 ) ( 1 / 2 ) ( 1 / 3 ) ( 1 / 4 ) since the first four fraction in the numerator and denominator cancel out , we ' re left with just one fraction : 1 / 4 d"
Answer: d
Python program:
a = 1 / 3
b = a / 3
c = 1 + 4 
d = b / c
Problem: if @ is a binary operation defined as the difference between an integer n and the product of n and 5 , then what is the largest positive integer n such that the outcome of the binary operation of n is less than 10 ?
Options: a ) 1 , b ) 2 , c ) 3 , d ) 4 , e ) 5
Rationale: "the product of n and 5 = 5 n . . the difference between an integer n and the product of n and 5 = 5 n - n = 4 n . . the outcome of the binary operation of n is less than 10 ? so 4 n < 10 . . . max value that n can take as an integer is 2 answer : b"
Answer: b
Python program:
a = 5 - 1
b = 10 / a
c = math.floor(b)
Problem: how many seconds will a 400 meter long train take to cross a man walking with a speed of 3 km / hr in the direction of the moving train if the speed of the train is 63 km / hr ?
Options: a ) 287 , b ) 288 , c ) 900 , d ) 277 , e ) 121
Rationale: "let length of tunnel is x meter distance = 400 + x meter time = 1 minute = 60 seconds speed = 78 km / hr = 78 * 5 / 18 m / s = 65 / 3 m / s distance = speed * time 400 + x = ( 65 / 3 ) * 60 400 + x = 20 * 65 = 1300 x = 1300 - 400 = 900 meters answer : c"
Answer: c
Python program:
a = 63 - 3
b = a * const_0_2778
c = 400 / b
d = c - 1
e = d * 10
f = e * 2
Problem: if a and b are the roots of the equation x 2 - 8 x + 8 = 0 , then the value of a 2 + b 2 is :
Options: a ) 36 , b ) 48 , c ) 17 , d ) 6 , e ) 5
Rationale: "sol . ( b ) the sum of roots = a + b = 8 product of roots = ab = 8 now , a 2 + b 2 = ( a + b ) 2 - 2 ab = 64 - 16 = 48 answer b"
Answer: b
Python program:
a = 8 ** 2
b = 4 * 8
c = a - b
d = math.sqrt(c)
e = 8 - d
f = e / 2
g = f ** 2
h = 8 ** 2
i = 4 * 8
j = h - i
k = math.sqrt(j)
l = 8 + k 
m = l / 2
n = m ** 2
o = g + n
Problem: evaluate : 45678 * 8 * 4 * 8 = ?
Options: a ) 730848 , b ) 705265 , c ) 730846 , d ) 730596 , e ) 731848
Rationale: "according to order of operations , 8 ? 4 ? 8 ( division and multiplication ) is done first from left to right 8 / 4 = 2 * 8 = 16 hence 45678 * 8 * 4 * 8 = 45678 * 16 = 730848 correct answer a"
Answer: a
Python program:
a = 8 * 4
b = a * 8
c = 45678 - b
Problem: what is the total number of positive integers that are less than 200 and that have no positive factor in common with 200 other than 1 ?
Options: a ) 60 , b ) 70 , c ) 80 , d ) 90 , e ) 100
Rationale: "since 200 = 2 ^ 3 * 5 ^ 2 then a number can not have 2 and / or 5 as a factor . the odd numbers do not have 2 as a factor and there are 100 odd numbers from 1 to 200 . we then need to eliminate the 20 numbers that end with 5 , that is 5 , 15 , 25 , . . . , 195 . there are a total of 100 - 20 = 80 such numbers between 1 and 200 . the answer is c ."
Answer: c
Python program:
a = 200 - 1
b = 200 - 2
c = b - 2
d = c / 2
e = d + 1 
f = 200 / 100
g = 200 - f
h = 200 / 100
i = g - h
j = 200 / 100
k = i / j
l = k + 1 
m = e + l 
n = 200 - 10
o = n - 10
p = o / 10
q = p + 1 
r = m - q
s = a - r
Problem: it costs $ 6 for the first 1 / 4 hour to use the copier at kinkos . after the first ¼ hour it costs $ 8 per hour . if a certain customer uses the copier for 4 hours and 25 minutes , how much will it cost him ?
Options: a ) $ 23.45 , b ) $ 65.33 , c ) $ 40 , d ) $ 38.27 , e ) $ 39.33
Rationale: 4 hrs 25 min = 265 min first 15 min - - - - - - > $ 6 time left is 250 min . . . now , 60 min costs $ 8 1 min costs $ 8 / 60 250 min costs $ 8 / 60 * 250 = > $ 33.33 so , total cost will be $ 33.33 + $ 6 = > $ 39.33 the answer will be ( e ) $ 39.33
Answer: e
Python program:
a = 25 + 8 
b = a + 6 
c = 25 + 8 
d = c / 100
e = b + d
Problem: population of a city in 20004 was 1300000 . if in 2005 there isan increment of 15 % , in 2006 there is a decrements of 35 % and in 2007 there is an increment of 45 % , then find the population of city at the end of the year 2007
Options: a ) 354354 , b ) 545454 , c ) 465785 , d ) 456573 , e ) 2818075 / 2
Rationale: "required population = p ( 1 + r 1 / 100 ) ( 1 - r 2 / 100 ) ( 1 + r 3 / 100 ) = p ( 1 + 15 / 100 ) ( 1 - 35 / 100 ) ( 1 + 45 / 100 ) = 2818075 / 2 e"
Answer: e
Python program:
a = 15 / 100
b = 1 + a 
c = 35 / 100
d = 1 - c
e = b * d
f = 35 / 100
g = 1 + f 
h = e * g
i = 1300000 * h
Problem: a man invested rs . 50000 at the rate of 5 % p . a . for the first 3 years , 8 % p . a . for the next 5 years and 10 % p . a . for the period beyond 8 years . at the end of 11 years , he want to distribute total money among his 4 sons , how much money will each son get ?
Options: a ) 30000 , b ) 25375 , c ) 28680 , d ) 32000 , e ) 23125
Rationale: let the interest be i . then , ( 50000 × 3 × 5 / 100 ) + ( 50000 × 5 × 8 / 100 ) + ( 50000 × 3 × 10 / 100 ) = i ⇒ 7500 + 20000 + 15000 = i ⇒ i = 42500 total money = 42500 + 50000 = 92500 each son will get = 92500 / 4 = 23125 answer : e
Answer: e
Python program:
a = 10 * 8
b = a * 11
c = b * 11
d = c * 3
e = 50000 - d
f = 10 * 8
g = f * 11
h = g * 3
i = e + h
Problem: a , b and c rents a pasture for rs . 841 . a put in 12 horses for 8 months , b 16 horses for 9 months and 18 horses for 6 months . how much should a pay ?
Options: a ) 270 , b ) 279 , c ) 226 , d ) 231 , e ) 232
Rationale: "12 * 8 : 16 * 9 = 18 * 6 8 : 12 : 9 8 / 29 * 841 = 232 answer : e"
Answer: e
Python program:
a = 12 * 8
b = 16 * 9
c = a + b 
d = 18 * 6
e = c + d 
f = 841 / e
g = 16 * 9
h = f * g
Problem: what is the probability that the sum of two dice will yield a 7 , and then when both are thrown again , their sum will again yield a 7 ? assume that each die has 6 sides with faces numbered 1 to 6 .
Options: a ) 1 / 144 , b ) 1 / 36 , c ) 1 / 12 , d ) 1 / 6 , e ) 1 / 3
Rationale: "in order to get the sum of the two dices to be 7 , there are six combinations that satisfy this requirement . 1 + 6 = 7 2 + 5 = 7 3 + 4 = 7 4 + 3 = 7 5 + 2 = 7 6 + 1 = 7 each combination has 1 / 36 of probability of occurrence , or in total 6 / 36 for the six combinations , which is 1 / 6 . in order to get the probability of this occurring twice in a row we multiply 1 / 6 * 1 / 6 and we get 1 / 36 . the answer is b ."
Answer: b
Python program:
a = 6 ** 2
b = 6 / a
c = 6 ** 2
d = 6 / c
e = b * d
Problem: one fast typist type some matter in 2 hrs and another slow typist type the same matter in 3 hrs . if both do combine in how much time they will take to finish .
Options: a ) 10 , b ) 11 , c ) 12 , d ) 13 , e ) 14
Rationale: fast ' s 1 hr work = 1 / 2 slow ' s 1 hr work = 1 / 3 1 / 2 + 1 / 3 = 5 / 6 they ll finish in 6 / 5 hrs = 1 1 / 5 = = > 1 hr 12 mins answer : c
Answer: c
Python program:
a = 1 / 2
b = 1 / 3
c = a + b 
d = 1 / c
e = d * 10
Problem: how many internal diagonals does a nonagon ( nine sided polygon ) have ?
Options: a ) 25 , b ) 27 , c ) 40 , d ) 56 , e ) 80
Rationale: "number of diagonals in any polygon can be found using this formula : n ( n - 3 ) / 2 here n = 9 no . of diagonals = 9 ( 9 - 3 ) / 2 = 27 ans b"
Answer: b
Python program:
a = 2 * 4
b = a - 3
c = 2 * 4
d = c / 2
e = b * d
Problem: if a lends rs . 3200 to b at 12 % per annum and b lends the same sum to c at 14.5 % per annum then the gain of b in a period of 5 years is ?
Options: a ) 157.78 , b ) 157.98 , c ) 400 , d ) 420 , e ) 430
Rationale: "( 3200 * 2.5 * 5 ) / 100 = > 400 answer : c"
Answer: c
Python program:
a = 3200 * 14
b = a * 5
c = b / 100
d = 3200 * 12
e = d * 5
f = e / 100
g = c - f
Problem: country x taxes each of its citizens an amount equal to 12 percent of the first $ 40,000 of income , plus 20 percent of all income in excess of $ 40,000 . if a citizen of country x is taxed a total of $ 8,000 , what is her income ?
Options: a ) $ 40,000 , b ) $ 56,000 , c ) $ 64,000 , d ) $ 66,667 , e ) $ 80,000
Rationale: "equation is correct , so math must be a problem . 0.12 * 40,000 + 0.2 * ( x - 40,000 ) = 8,000 - - > 4,800 + 0.2 x - 8,000 = 8,000 - - > 0.2 x = 11,200 - - > x = 56,000 . answer : b ."
Answer: b
Python program:
a = 4 * 10
b = a * 1000
c = 4 * 2
d = c * 1000
e = 12 / 100
f = 4 * 10
g = f * 1000
h = e * g
i = d - h
j = 20 / 100
k = i / j
l = b + k
Problem: in a kilometer race , a beats b by 54 meters or 12 seconds . what time does a take to complete the race ?
Options: a ) 212 , b ) 190 , c ) 277 , d ) 181 , e ) 122
Rationale: "time taken by b run 1000 meters = ( 1000 * 12 ) / 54 = 222 sec . time taken by a = 224 - 12 = 212 sec . answer : a"
Answer: a
Python program:
a = 1 * 1000
b = 54 / 12
c = a / b
d = c - 12
Problem: find the average of all prime numbers between 60 and 90
Options: a ) 45 , b ) 55 , c ) 69 , d ) 65 , e ) 77
Rationale: "prime numbers between 60 and 90 are 67 , 71 , 73 , 79 , 83 , 89 required average = ( 67 + 71 + 73 + 79 + 83 + 89 ) / 6 = 462 / 6 = 77 answer is e"
Answer: e
Python program:
a = 60 + 1 
b = 60 + 1 
c = b + 2 
d = a + c 
e = 90 - 60
f = 90 - 2
g = e + f 
h = d + g 
i = h / 60
Problem: 5 letters have to be put in 5 different envelopes numbered 1 through 5 such that each of the letters go into only 1 envelope . the letter is said to be put in correct position if for example letter 1 goes into envelope 1 . now what is the probability that all letters be put into wrong envelopes ?
Options: a ) 1 / 3 , b ) 2 / 3 , c ) 11 / 120 , d ) 11 / 30 , e ) 76 / 120
Rationale: this q is based on derangement , a permutation in which all elements are in the wrong position . number of derangements = n ! ( 12 ! − 13 ! + 14 ! + . . . + ( ( − 1 ) n ) n ! ) n ! ( 12 ! − 13 ! + 14 ! + . . . + ( ( − 1 ) n ) n ! ) . . of course it can be derived but thats not required . . since there are 5 letters and 5 envelopes : - derangements = 5 ! ( 12 ! − 13 ! + 14 ! − 15 ! ) derangements = 5 ! ( 12 ! − 13 ! + 14 ! − 15 ! ) = > 120 ( 1 / 2 − 1 / 6 + 1 / 24 − 1 / 120 ) = 60 − 20 + 5 − 1 = 44.120 ( 1 / 2 − 1 / 6 + 1 / 24 − 1 / 120 ) = 60 − 20 + 5 − 1 = 44 . total possible ways = 5 ! = 120 . therefore required prob , p = 44 / 120 = 11 / 30 . ans d
Answer: d
Python program:
a = math.factorial(2)
b = 1/(a)
c = math.factorial(3)
d = 1/(c)
e = b - d
f = math.factorial(4)
g = 1/(f)
h = e + g 
i = math.factorial(5)
j = 1/(i)
k = h - j
Problem: a rectangular lawn of dimensions 70 m * 60 m has two roads each 10 m wide running in the middle of the lawn , one parallel to the length and the other parallel to the breadth . what is the cost of traveling the two roads at rs . 3 per sq m ?
Options: a ) s . 3988 , b ) s . 3900 , c ) s . 3228 , d ) s . 3922 , e ) s . 3600
Rationale: "area = ( l + b – d ) d ( 70 + 60 – 10 ) 10 = > 1200 m 2 1200 * 3 = rs . 3600 answer : e"
Answer: e
Python program:
a = 70 + 60 
b = a - 10
c = b * 10
d = c * 3
Problem: the distance from city a to city b is 220 miles . while driving from city a to city b , bob drives at a constant speed of 40 miles per hour . alice leaves city a 30 minutes after bob . what is the minimum constant speed in miles per hour that alice must exceed in order to arrive in city b before bob ?
Options: a ) 44 , b ) 48 , c ) 50 , d ) 52 , e ) 54
Rationale: "the time it takes bob to drive to city b is 220 / 40 = 5.5 hours . alice needs to take less than 5 hours for the trip . alice needs to exceed a constant speed of 220 / 5 = 44 miles per hour . the answer is a ."
Answer: a
Python program:
a = 220 / 40
b = 30 / const_60
c = a - b
d = 220 / c
Problem: one fourth of a solution that was 10 % sugar by weight was replaced by a second solution resulting in a solution that was 18 percent sugar by weight . the second solution was what percent sugar by weight ?
Options: a ) 34 % , b ) 24 % , c ) 42 % , d ) 18 % , e ) 8.5 %
Rationale: "instead of using complex calculations and remembering formulae , why dont u directly get to weighted average . 3 parts of 10 % + 1 part of x ( unknown ) % = 4 parts of 18 % = > x % = 72 % - 30 % = 42 % ans c it is ."
Answer: c
Python program:
a = 18 / 100
b = 100 * a
c = 1 / 4
d = c * 100
e = 100 - d
f = 10 / 100
g = e * f
h = b - g
i = 1 / 4
j = i * 100
k = h / j
l = k * 100
Problem: the average salary / head of all the workers in a workshop is rs . 700 , if the average salary / head of 5 technician is rs . 800 and the average salary / head of the rest is rs . 650 , the total no . of workers in the work - shop is ?
Options: a ) 18 , b ) 19 , c ) 17 , d ) 16 , e ) 15
Rationale: let the total number of workers be y . so sum of salary for all workers = sum of salary of 5 technician + sum of salary for other y - 5 workers . 5 x 800 + 650 ( y - 5 ) = 700 y ⇒ 4000 + 650 y - 3250 = 700 y ⇒ 50 y = 750 ∴ y = 15 so total number of workers = 15 e
Answer: e
Python program:
a = 5 * 800
b = 650 * 5
c = a - b
d = 700 - 650
e = c / d
Problem: there are 9 executives , including the ceo and cfo , that are asked to form a small team of 5 members . however , the ceo and cfo may not both be assigned to the team . given this constraint , how many ways are there to form the team ?
Options: a ) 85 , b ) 87 , c ) 89 , d ) 91 , e ) 93
Rationale: "the total number of ways to form a team of 5 is 9 c 5 = 126 . we need to subtract the number of teams that have both the ceo and the cfo . the number of teams with both the ceo and cfo is 7 c 3 = 35 . the number of ways to form an acceptable team is 126 - 35 = 91 . the answer is d ."
Answer: d
Python program:
a = 9 - 5
b = math.factorial(a)
c = 5 * 3
d = c + 3 
e = b - d