euclaise/mathqa_programs huggingface dataset:
Problem: jane and thomas are among the 7 people from which a committee of 4 people is to be selected . how many different possible committees of 4 people can be selected from these 7 people if at least one of either jane or thomas is to be selected ?
Options: a ) 30 , b ) 45 , c ) 55 , d ) 65 , e ) 70
Rationale: "the total number of ways to choose 4 people from 7 is 7 c 4 = 35 . the number of committees without jane or thomas is 5 c 4 = 5 . there are 35 - 5 = 30 possible committees which include jane and / or thomas . the answer is a ."
Answer: a
Python program:
a = math.comb(7, 1)
b = math.comb(7, 1)
c = a + b 
d = math.comb(4, 1)
e = c + d
Problem: jack , jill , and sandy each have one try to make a basket from half court . if their individual probabilities of making the basket are 1 / 6 , 1 / 7 , and 1 / 8 respectively , what is the probability that jack and jill will make a basket but sandy will miss ?
Options: a ) 1 / 8 , b ) 1 / 16 , c ) 1 / 48 , d ) 1 / 96 , e ) 1 / 168
Rationale: "the probability that jack and jill will make a basket but sandy will miss is 1 / 6 * 1 / 7 * 7 / 8 = 1 / 48 . the answer is c ."
Answer: c
Python program:
a = 1 / 7
b = 1 / 8
c = a * b
d = 1 / 6
e = 1 - d
f = c * e
Problem: you hold some gold in a vault as an investment . over the past year the price of gold increases by 42 % . in order to keep your gold in the vault , you must pay 4 % of the total value of the gold per year . what percentage has the value of your holdings changed by over the past year .
Options: a ) 38 % , b ) 46 % , c ) 47.68 % , d ) 44.32 % , e ) 36.32 %
Rationale: "( 100 % + 42 % ) * ( 100 % - 4 % ) = 1.42 * 0.96 = 136.32 % an increase of 36.32 % your gold holdings have increased in value by 36.32 % . the answer is e"
Answer: e
Python program:
a = 42 / 4
b = 42 - a
Problem: calculate how many seconds it eill take for 4 bells to toll together again , given that they begin to toll together respectively at the intervals of 2 , 5 , 8 and 11 seconds . ?
Options: a ) 440 , b ) 420 , c ) 410 , d ) 442 , e ) 422
Rationale: "lcm of 2 , 5 , 8 and 11 is 440 lcm = 440 answer : a"
Answer: a
Python program:
a = 2 * 5
b = 8 * a
c = 3 * b
Problem: the sum of the ages of 5 children born at the intervals of 1 year each is 50 years . what is the age of the youngest child ?
Options: a ) 22 , b ) 8 , c ) 10 , d ) 99 , e ) 38
Rationale: "let x = the youngest child . each of the other four children will then be x + 1 , x + 2 , x + 3 , x + 4 . we know that the sum of their ages is 50 . so , x + ( x + 1 ) + ( x + 2 ) + ( x + 3 ) + ( x + 4 ) = 50 therefore the youngest child is 8 years old answer : b"
Answer: b
Python program:
a = 5 / 1
b = 50 / a
c = 5 - 1
d = c * 1
e = b - d
f = e / 1
Problem: if 15 machine can finish a job in 36 days , then how many more machines would be needed to finish the job in one - fourth less time ?
Options: a ) a . 5 , b ) b . 8 , c ) c . 10 , d ) d . 12 , e ) e . 16
Rationale: "you might think of this in a management context - we can use the principle of ' person - hours ' to solve any problem where we have identical workers . so , using simpler numbers , suppose you know that 6 identical employees , working simultaneously , would finish a job in 5 hours . then that job requires 6 * 5 = 30 total hours of person - work . if instead you wanted the job done in 3 hours , you ' d assign 30 / 3 = 10 employees to do the job , because you want to get a total of 30 hours of work from the employees . we can solve this problem identically . if 15 machines ( identical ones , i assume ) work simultaneously for 36 days , they will do a total of 15 * 36 machine - days of work . so the job requires 15 * 36 days of machine work in total . we instead want the job done in 1 / 4 less time , so in 27 days . so we ' ll need 15 * 36 / 27 = 20 machines , or 5 additional machines . a"
Answer: a
Python program:
a = 15 * 36
b = 3 / 4
c = b * 36
d = a / c
e = d - 15
Problem: if a randomly selected non - negative single digit integer is added to { 2 , 3 , 6 , 8 } . what is the probability that the median of the set will increase but the range still remains the same ?
Options: a ) 0.2 , b ) 0.3 , c ) 0.4 , d ) 0.5 , e ) 0.6
Rationale: "we are selecting from non - negative single digit integers , so from { 0 , 1 , 2 , 3 , 4 , 5 , 6 , 7 , 8 , 9 } . these 10 digits represent the total number of outcomes . hence , the total number of outcomes is 10 . we need to find the probability that the median of the set will increase but the range still remains the same . the median of the set is ( 3 + 6 ) / 2 = 4.5 , thus the number selected must be 5 or greater . for the range to remain the same , the number must be between 2 and 8 inclusive . to satisfy both conditions , the number selected must be 5 , 6 , 7 , or 8 . the probability is 4 / 10 = 0.4 the answer is c ."
Answer: c
Python program:
a = 4 / 10
Problem: in what time will a train 140 m long cross an electric pole , it its speed be 108 km / hr ?
Options: a ) 2.5 , b ) 4.7 , c ) 2.9 , d ) 2.3 , e ) 2.1
Rationale: "speed = 108 * 5 / 18 = 30 m / sec time taken = 140 / 30 = 4.7 sec . answer : b"
Answer: b
Python program:
a = 108 * const_0_2778
b = 140 / a
Problem: a small water pump would take 2 hours to fill an empty tank . a larger pump would take 1 / 3 hour to fill the same tank . how many hours would it take both pumps , working at their respective constant rates , to fill the empty tank if they began pumping at the same time ?
Options: a ) 3 / 7 , b ) 2 / 7 , c ) 1 / 4 , d ) 2 / 3 , e ) 5 / 7
Rationale: "rate of the small pump is 1 / 2 tank / hour rate of the larger pump is 1 / ( 1 / 3 ) or 3 tank / hour ; combined rate of the two pumps is 1 / 2 + 3 = 7 / 2 tank / hour , together they will fill the empty tank in 1 / ( 7 / 2 ) = 2 / 7 hours ( time = job / rate ) . answer : b"
Answer: b
Python program:
a = 1/(2)
b = a + 3 
c = 1/(b)
Problem: in a certain company 20 % of the men and 40 % of the women attended the annual company picnic . if 45 % of all the employees are men . what % of all the employee went to the picnic ?
Options: a ) 31 % , b ) 34 % , c ) 35 % , d ) 36 % , e ) 37 %
Rationale: "total men in company 45 % means total women in company 55 % ( assume total people in company 100 % ) no of men employees attended picnic = 45 x ( 20 / 100 ) = 9 no of women employees attend picnic = 55 x ( 40 / 100 ) = 22 total percentage of employees attend the picnic = 9 + 22 = 31 % answer : a"
Answer: a
Python program:
a = 45 / 100
b = 20 / 100
c = a * b
d = 100 - 45
e = d / 100
f = 40 / 100
g = e * f
h = c + g 
i = h * 100
Problem: the ratio by weight , measured in pounds , of books to clothes to electronics in a suitcase initially stands at 5 : 4 : 2 . someone removes 7 pounds of clothing from the suitcase , thereby doubling the ratio of books to clothes . how many pounds do the electronics in the suitcase weigh ?
Options: a ) 6 , b ) 7 , c ) 8 , d ) 9 , e ) 10
Rationale: "the weights of the items in the suitcase are 5 k , 4 k , and 2 k . if removing 7 pounds of clothes doubles the ratio of books to clothes , then 7 pounds represents half the weight of the clothes . 2 k = 7 pounds and then k = 3.5 pounds . the electronics weigh 2 ( 3.5 ) = 7 pounds . the answer is b ."
Answer: b
Python program:
a = 5 + 4 
b = a + 2 
c = b * 7
d = negate / (
e = 5 + 4 
f = e + 2 
g = f * 2
h = 5 + 4 
i = h + 2 
j = i * 4
k = g - j
l = 2 * d
Problem: martin bought 10 concert tickets , some at the full price of $ 2.00 per ticket , and some at a discounted price of $ 1.60 per ticket . if he spent a total of $ 17.20 , how many discounted tickets did he buy ?
Options: a ) 3 , b ) 4 , c ) 5 , d ) 6 , e ) 7
Rationale: "let x be the number of tickets he bought at $ 2 per ticket . then 2 x + ( 10 - x ) 1.6 = 17.2 0.4 x = 1.2 = > x = 3 discounted tickets = 10 - x = 7 ans : e"
Answer: e
Python program:
a = 10 * 2
b = 1 * 60
c = a - b
Problem: if 625 ^ ( - x ) + 25 ^ ( - 2 x ) + 5 ^ ( - 4 x ) = 10 , what is the value of x ?
Options: a ) - 4 , b ) - 1 / 4 , c ) 0 , d ) 1 / 4 , e ) 4
Rationale: "we ' re told that 625 ^ ( - x ) + 25 ^ ( - 2 x ) + 5 ^ ( - 4 x ) = 15 . we ' re asked for the value of x . since each of the calculated terms must be positive ( regardless of what the exponent is ) , we can use thebasesto our advantage . . . . . with answer a , we ' d have 625 ^ 4 , which is much bigger than 15 ( and we ' d be adding to that big number ) . eliminate a . with answer e , we ' d have 625 ^ ( - 4 ) , which would create a tiny fraction ( and we ' d add some other fractions to it , so the total would be much too small ) . eliminate e . with answer d , we ' d have 625 ^ ( - 1 / 4 ) , which will also be a fraction ( just not as tiny as the one in answer e ) , but the total would still be too small . eliminate d . with answer c , anything to the ' 0 power ' is 1 , so we ' d have 1 + 1 + 1 = 3 . this is not 15 . eliminate c . c"
Answer: c
Python program:
a = 1 / 4
Problem: if a # b = ab – b + b ^ 2 , then 2 # 3 =
Options: a ) 2 , b ) 8 , c ) 12 , d ) 21 , e ) 35
Rationale: "solution - simply substitute 2 and 3 in equation in the place of a and b respectively . 2 # 3 = 2 * 3 - 3 + 3 ^ 2 = 6 - 3 + 9 = 12 . ans c"
Answer: c
Python program:
a = 2 * 3
b = a - 3
c = 3 ** 2
d = b + c
Problem: andy solves problems 70 to 125 inclusive in a math exercise . how many problems does he solve ?
Options: a ) 56 , b ) 52 , c ) 51 , d ) 50 , e ) 49
Rationale: 125 - 70 + 1 = 56 ' a ' is the answer
Answer: a
Python program:
a = 125 - 70
b = a + 1
Problem: share rs . 4200 among john , jose & binoy in the ration 2 : 4 : 6 . find the amount received by john ?
Options: a ) 900 , b ) 980 , c ) 1200 , d ) 1240 , e ) 1400
Rationale: "amount received by sanjay . 4 / 12 x 4200 = 1400 = ( related ratio / sum of ratio ) x total amount so , the amount received by sanjay is 1400 . e"
Answer: e
Python program:
a = 4200 / 2
b = 4200 / 6
c = a - b
Problem: if k is a non - negative integer and 21 ^ k is a divisor of 435,961 then 7 ^ k - k ^ 7 =
Options: a ) 0 , b ) 1 , c ) 42 , d ) 118 , e ) 242
Rationale: "4 + 3 + 5 + 9 + 6 + 1 = 28 , so this number is not divisible by 3 and thus not divisible by 21 . therefore , k = 0 7 ^ k - k ^ 7 = 1 - 0 = 1 the answer is b ."
Answer: b
Python program:
a = 1 - 1
b = 7 ** a
c = 1 - 1
d = c ** 7
e = b - d
Problem: maxwell leaves his home and walks toward brad ' s house at the same time that brad leaves his home and runs toward maxwell ' s house . if the distance between their homes is 60 kilometers , maxwell ' s walking speed is 4 km / h , and brad ' s running speed is 6 km / h , what is the distance traveled by brad ?
Options: a ) 16 , b ) 36 , c ) 20 , d ) 24 , e ) 30
Rationale: "time taken = total distance / relative speed total distance = 60 kms relative speed ( opposite side ) ( as they are moving towards each other speed would be added ) = 6 + 4 = 10 kms / hr time taken = 60 / 10 = 6 hrs distance traveled by brad = brad ' s speed * time taken = 6 * 6 = 36 kms . . . answer - b"
Answer: b
Python program:
a = 4 + 6 
b = 60 / a
c = 4 * b
Problem: a train 90 meters long completely crosses a 200 meters long bridge in 36 seconds . what is the speed of the train is ?
Options: a ) 29 , b ) 40 , c ) 25 , d ) 66 , e ) 09
Rationale: "s = ( 90 + 200 ) / 36 = 290 / 36 * 18 / 5 = 29 answer : a"
Answer: a
Python program:
a = 90 + 200 
b = a / 1000
c = 36 / 3600
d = b / c
Problem: a circular plate with a diameter of 10 inches is kept on another plate of 12 inches diameter . what fraction of the big plate ' s surface is not covered by the small plate ?
Options: a ) 11 / 36
b ) 23 / 10
c ) 5 / 14
d ) 22 / 11
e ) 3 / 4
Rationale: the questions asks us to find the surface which is not covered by the plate i . e . , area of the surface not covered . where as circumference is the length along the edge of the circle , 2 * pi * r implies the length of the curve pi * r ^ 2 implies area enclosed by that curve . . hence area of the circle is considered for this problem area of the big plate = pi * r ^ 2 , where r = 6 = > pi * 36 area of the small plate = pi * 25 surface not covered by the plate = pi * 36 - pi * 25 = pi * 11 fraction of big plate ' s surface is not covered by small plate = pi * 11 / total area of the big plate = > pi * 11 / pi * 36 answer a
Answer: a
Python program:
a = 12 / 2
b = circle_area - (
c = 10 / 2
d = b / circle_area
Problem: a contractor undertakes to do a job within 100 days and hires 10 people to do it . after 20 days , he realizes that one fourth of the work is done so he fires 2 people . in how many more days b will the work get over ?
Options: a ) 60 , b ) 70 , c ) b = 75 , d ) b = 80 , e ) 100
Rationale: "we can also use the concept of man - days here 100 days - - > 10 men so the job includes 100 * 10 = 1000 man - days after 20 days 1 / 4 of job is completed so 1 / 4 x 1000 man - days = 250 man - days job is done now the balance job = 1000 - 250 = 750 man - days worth of job since 2 men are fired so b / l men = 8 therefore total no . of days of job = 750 man - day / 8 days = 375 / 4 = 94 days ( approx . ) now since this is total and ques . is asking for additional no . of days , so 94 - 20 = 74 days the nearest approx . to answer is 75 ans : c ( 75 days )"
Answer: c
Python program:
a = 10 * 20
b = a / const_0_25
c = 1 - const_0_25
d = b * c
e = 10 - 2
f = d / e
Problem: if the cost price is 25 % of selling price . then what is the profit percent
Options: a ) 238 , b ) 278 , c ) 300 , d ) 166 , e ) 129
Rationale: "explanation : let the s . p = 100 then c . p . = 25 profit = 75 profit % = ( 75 / 25 ) * 100 = 300 % answer : c"
Answer: c
Python program:
a = 100 - 25
b = a / 25
c = b * 100
Problem: a man rows downstream 32 km and 14 km upstream . if he takes 6 hours to cover each distance , then the velocity ( in kmph ) of the current is :
Options: a ) 1.5 kmph , b ) 1.75 kmph , c ) 2 kmph , d ) 3 kmph , e ) none
Rationale: sol . rate downstream = [ 32 / 6 ] kmph ; rate upstream = [ 14 / 6 ] kmph . ∴ velocity of current = 1 / 2 [ 32 / 6 - 14 / 6 ] kmph = 3 / 2 kmph = 1.5 kmph . answer a
Answer: a
Python program:
a = 32 / 6
b = 14 / 6
c = a - b
d = c / 2
Problem: the average weight of 10 person ' s increases by 4 kg when a new person comes in place of one of them weighing 70 kg . what is the weight of the new person ?
Options: a ) 85 , b ) 86.5 , c ) 90 , d ) 88.5 , e ) 110
Rationale: "total increase in weight = 10 x 4 = 40 if x is the weight of the new person , total increase in weight = x − 70 = > 40 = x - 70 = > x = 40 + 70 = 110 answer : e"
Answer: e
Python program:
a = 10 * 4
b = a + 70
Problem: the price of rice falls by 20 % . how much rice can be bought now with the money that was sufficient to buy 20 kg of rice previously ?
Options: a ) 5 kg , b ) 15 kg , c ) 25 kg , d ) 30 kg , e ) none
Rationale: "solution : let rs . 100 be spend on rice initially for 20 kg . as the price falls by 20 % , new price for 20 kg rice , = ( 100 - 20 % of 100 ) = 80 new price of rice = 80 / 20 = rs . 4 per kg . rice can bought now at = 100 / 4 = 25 kg . answer : option c"
Answer: c
Python program:
a = 100 - 20
b = a / 20
c = 100 / b
Problem: a boat takes 90 minutes less to travel 36 miles downstream than to travel the same distance upstream . if the speed of the boat in still water is 10 mph , the speed of the stream is
Options: a ) 2 mph , b ) 2.5 mph , c ) 3 mph , d ) 4 mph , e ) none
Rationale: "solution speed downstreams = ( 10 + x ) mph . speed upstreams = ( 10 - x ) mph . = 18 kmph . 36 / ( 10 - x ) - 36 / ( 10 + x ) = 90 / 60 = 72 x × 60 = 90 ( 100 - x ² ) x ² + 48 x + 100 = 0 . x = 2 mph . answer a"
Answer: a
Python program:
a = 10 ** 2
b = a * 4
c = 90 / const_60
d = 36 / c
e = d * 2
f = e ** 2
g = b + f 
h = math.sqrt(g)
i = 90 / const_60
j = 36 / i
k = j * 2
l = h - k
m = l / 2
Problem: if 2 + 3 = 10 ; 2 + 5 = 27 ; 2 + 7 = 53 then 2 + 11 = ?
Options: a ) 124 , b ) 129 , c ) 128 , d ) 125 , e ) 120
Rationale: "2 ^ 0 + 3 ^ 2 = 1 + 9 = 10 2 ^ 1 + 5 ^ 2 = 2 + 25 = 27 2 ^ 2 + 7 ^ 2 = 4 + 49 = 53 and 2 ^ 3 + 11 ^ 2 = 8 + 121 = 129 answer : b"
Answer: b
Python program:
a = 2 ** 2
b = 11 ** 2
c = a + b
Problem: if the sides of a cube are in the ratio 7 : 3 . what is the ratio of their diagonals ?
Options: a ) 9 : 4 , b ) 8 : 4 , c ) 7 : 4 , d ) 7 : 3 , e ) 6 : 4
Rationale: "explanation : diagonal of a cube = a √ 3 where a is side a 1 : a 2 = 7 : 3 d 1 : d 2 = 7 : 3 where √ 3 cancelled both side answer : d"
Answer: d
Python program:
a = 7 / 3
Problem: the sum of two consecutive integers is 31 . find the numbers .
Options: a ) 17 , 18 , b ) 7 , 8 , c ) 15 , 16 , d ) 1 , 2 , e ) 8 , 9
Rationale: "n + ( n + 1 ) = 31 2 n + 1 = 31 2 n = 30 n = 15 answer : c"
Answer: c
Python program:
a = 31 - 10
b = a - 2
c = b / 4
d = c + 2 
e = d + 2 
f = e ** 2
g = 31 - 10
h = g - 2
i = h / 4
j = i + 2 
k = j + 2 
l = k + 2 
m = l ** 2
n = f + m 
o = 31 - 10
p = o - 2
q = p / 4
r = q ** 2
s = 31 - 10
t = s - 2
u = t / 4
v = u + 2 
w = v ** 2
x = r + w 
y = n + x
Problem: the average of 4 consecutive odd numbers is 24 . find the largest number
Options: a ) 25 , b ) 27 , c ) 29 , d ) 31 , e ) 32
Rationale: explanation : let the numbers are x , x + 2 , x + 4 , x + 6 , then = > x + ( x + 2 ) + ( x + 4 ) + ( x + 6 ) / 4 = 24 = > 4 x + 12 ) / 4 = 24 = > x + 3 = 24 = > x = 21 so largest number is 21 + 6 = 27 option b
Answer: b
Python program:
a = 4 * 24
b = a / 4
c = b + 3
Problem: what is the smallest integer that is multiple of 8,7 and 20
Options: a ) 141 , b ) 180 , c ) 130 , d ) 122 , e ) 280
Rationale: correct answer : e it is the lcm of 8,7 and 20 which is 280
Answer: e
Python program:
a = 2 * 4
b = 3 + 4 
c = math.lcm(a, b)
d = math.lcm(c, 20)
Problem: by travelling at 40 kmph , a person reaches his destination on time . he covered two - third the total distance in one - third of the total time . what speed should he maintain for the remaining distance to reach his destination on time ?
Options: a ) 20 kmph , b ) 17 kmph , c ) 15 kmph , d ) 14 kmph , e ) 13 kmph
Rationale: "let the time taken to reach the destination be 3 x hours . total distance = 40 * 3 x = 120 x km he covered 2 / 3 * 120 x = 80 x km in 1 / 3 * 3 x = x hours so , the remaining 40 x km , he has to cover in 2 x hours . required speed = 40 x / 2 x = 20 kmph . answer : a"
Answer: a
Python program:
a = 40 * 3
b = 40 * 3
c = b * 2
d = c / 3
e = a - d
f = 3 - 1
g = e / f
Problem: the present population of a town is 260 . population increase rate is 10 % p . a . find the population of town after 1 years ?
Options: a ) 100 , b ) 120 , c ) 200 , d ) 226 , e ) 286
Rationale: "p = 260 r = 10 % required population of town = p * ( 1 + r / 100 ) ^ t = 260 * ( 1 + 10 / 100 ) = 260 * ( 11 / 10 ) = 286 answer is e"
Answer: e
Python program:
a = 260 * 10
b = a / 100
c = 260 + b
Problem: a group of students decided to collect as many paise from each member of group as is the number of members . if the total collection amounts to rs . 3025 . , the number of the member is the group is :
Options: a ) 55 , b ) 67 , c ) 77 , d ) 87 , e ) 97
Rationale: "money collected = ( 30.25 x 100 ) paise = 3025 paise . number of members = square root of 3025 = 55 . answer : option a"
Answer: a
Python program:
a = 3025 * 100
b = math.sqrt(a)
Problem: in 1996 , the property tax of a community is increased by 6 % over the 1995 tax . an additional surcharge of $ 200 is also added for a special project . if the petersons ' 1996 tax totals $ 2108 , find their property tax for the year 1995
Options: a ) 1600 , b ) 1800 , c ) 1900 , d ) 2000 , e ) 2500
Rationale: tax for the year 1996 = 2108 surcharge add : 200 ie 2000 - 200 = 1800 1800 * 6 % = 108 + 2000 = 2108 so the answer is b
Answer: b
Python program:
a = 2108 - 200
b = 6 / 100
c = 1 + b 
d = a / c
Problem: in an election , candidate douglas won 64 percent of the total vote in counties x and y . he won 76 percent of the vote in county x . if the ratio of people who voted in county x to county y is 2 : 1 , what percent of the vote did candidate douglas win in county y ?
Options: a ) 10 % , b ) 25 % , c ) 30 % , d ) 35 % , e ) 40 %
Rationale: "given voters in ratio 2 : 1 let x has 200 votersy has 100 voters for x 76 % voted means 76 * 200 = 152 votes combined for xy has 300 voters and voted 64 % so total votes = 192 balance votes = 192 - 152 = 40 as y has 100 voters so 40 votes means 40 % of votes required ans e"
Answer: e
Python program:
a = 64 / 100
b = 76 / 100
c = 2 / 3
d = b * c
e = a - d
f = 1 / 3
g = e / f
h = g * 100
Problem: how many seconds will a 900 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 ) 500 , d ) 400 , e ) 121
Rationale: "let length of tunnel is x meter distance = 900 + x meter time = 1 minute = 60 seconds speed = 78 km / hr = 78 * 5 / 18 m / s = 65 / 3 m / s distance = speed * time 900 + x = ( 65 / 3 ) * 60 900 + x = 20 * 65 = 1300 x = 1300 - 900 = 400 meters answer : d"
Answer: d
Python program:
a = 63 - 3
b = a * const_0_2778
c = 900 / b
d = c - 1
e = d * 10
f = e * 2
Problem: 16 * 16 * 16 * 16 * 16 = 4 ^ ?
Options: a ) 8 , b ) 6 , c ) 10 , d ) 4 , e ) 3
Rationale: 4 ^ 2 * 4 ^ 2 * 4 ^ 2 * 4 ^ 2 * 4 ^ 2 = 4 ^ ( 2 + 2 + 2 + 2 + 2 ) = 4 ^ 10 answer : 10 option : c
Answer: c
Python program:
a = max(4)
Problem: fox jeans regularly sell for $ 15 a pair and pony jeans regularly sell for $ 18 a pair . during a sale these regular unit prices are discounted at different rates so that a total of $ 8.82 is saved by purchasing 5 pairs of jeans : 3 pairs of fox jeans and 2 pairs of pony jeans . if the sum of the two discount rates is 22 percent , what is the discount rate on pony jeans ?
Options: a ) 9 % , b ) 10 % , c ) 11 % , d ) 12 % , e ) 15 %
Rationale: "let x be the discount on pony jeans . then 0.22 - x is the discount on fox jeans . 3 ( 0.22 - x ) ( 15 ) + 2 x ( 18 ) = 8.82 9.9 - 45 x + 36 x = 8.82 9 x = 1.08 x = 0.12 the answer is d ."
Answer: d
Python program:
a = 22 / 100
b = 22 / 100
c = 18 * 2
d = b * c
e = 8 - 82
f = 15 * 3
g = 18 * 2
h = f - g
i = e / h
j = a - i
k = j * 100
Problem: when average age of 25 members are 0 , how many members greater than 0 ?
Options: a ) 17 , b ) 24 , c ) 21 , d ) 23 , e ) 25
Rationale: "average of 25 numbers = 0 . sum of 25 numbers ( 0 x 25 ) = 0 . it is quite possible that 24 of these numbers may be positive and if their sum is a then 25 th number is ( - a ) answer is 24 ( b )"
Answer: b
Python program:
a = 25 - 1
Problem: sakshi can do a piece of work in 10 days . tanya is 25 % more efficient than sakshi . the number of days taken by tanya to do the same piece of work :
Options: a ) 8 , b ) 16 , c ) 18 , d ) 25 , e ) 10
Rationale: "solution ratio of times taken by sakshi and tanya = 125 : 100 = 5 : 4 . suppose tanya taken x days to do the work . 5 : 4 : : 10 : x ⇒ x = ( 10 x 4 / 5 ) ⇒ x = 8 days . hence , tanya takes 8 days is complete the work . answer a"
Answer: a
Python program:
a = 25 / 100
b = 1 + a 
c = 10 / b
Problem: there were two candidates in an election . winner candidate received 65 % of votes and won the election by 300 votes . find the number of votes casted to the winning candidate ?
Options: a ) 228 , b ) 744 , c ) 255 , d ) 650 , e ) 231
Rationale: "w = 65 % l = 35 % 65 % - 35 % = 30 % 30 % - - - - - - - - 300 65 % - - - - - - - - ? = > 650 answer : d"
Answer: d
Python program:
a = 100 - 65
b = 65 - a
c = b / 100
d = 300 / c
e = d * 65
f = e / 100
Problem: a grocer purchased a quantity of bananas at 3 pounds for $ 0.50 and sold the entire quantity at 4 pounds for $ 1.00 . how many pounds did the grocer purchase if the profit from selling the bananas was $ 6.00 ?
Options: a ) 72 , b ) 60 , c ) 90 , d ) 120 , e ) 240
Rationale: "cost price of 1 pound of bananas = 0.5 / 3 = 1 / 6 selling price of 1 pound of bananas = 1 / 4 profit per pound = ( 1 / 4 - 1 / 6 ) = ( 1 / 12 ) total profit is given as 6 ( 1 / 12 ) * x = 6 x = 72 answer : a"
Answer: a
Python program:
a = 1 / 0
b = 0 / 50
c = a - b
d = 6 / 0