euclaise/mathqa_programs huggingface dataset:
Problem: in a school with 5 classes , each class has 2 students less than the previous class . how many students are there in the largest class if the total number of students at school is 140 ?
Options: a ) 28 , b ) 29 , c ) 30 , d ) 31 , e ) 32
Rationale: "let x be the number of students in the largest class . then x + ( x - 2 ) + ( x - 4 ) + ( x - 6 ) + ( x - 8 ) = 140 5 x - 20 = 140 5 x = 160 x = 32 the answer is e ."
Answer: e
Python program:
a = 2 + 2 
b = 2 + a 
c = 2 + 2 
d = c + 2 
e = b + d 
f = 2 + 2 
g = f + 2 
h = g + 2 
i = e + h 
j = 140 - i
k = j / 5
l = 2 + 2 
m = l + 2 
n = m + 2 
o = k + n
Problem: a chemical supply company has 60 liters of a 45 % hno 3 solution . how many liters of pure undiluted hno 3 must the chemists add so that the resultant solution is a 50 % solution ?
Options: a ) 6 , b ) 15 , c ) 20 , d ) 24 , e ) 30
Rationale: "60 liters of a 45 % hno 3 solution means hno 3 = 27 liters in 60 liters of the solution . now , let x be the pure hno 3 added . as per question , 27 + x = 50 % of ( 60 + x ) or x = 6 . hence , a"
Answer: a
Python program:
a = 60 / 2
b = 60 * 45
c = b / 100
d = a - c
e = d * 2
Problem: a furniture store owner decided to drop the price of her recliners by 20 % to spur business . by the end of the week she had sold 40 % more recliners . what is the percentage increase of the gross ?
Options: a ) 10 % , b ) 15 % , c ) 11.2 % , d ) 7 % , e ) 13 %
Rationale: "say a recliner is actually worth $ 100 if she sells 100 recliners then she earns $ 10000 after the discount of 20 % , she will earn $ 80 per recliner and she sells 40 % more ie . , 140 recliners hence her sales tields 140 * 80 = $ 11200 increase in sales = 11200 - 10000 = $ 1120 so % increase = 1120 * 100 / 10000 = 11.20 % c is the answer"
Answer: c
Python program:
a = 20 / 100
b = 1 - a
c = 40 / 100
d = 1 + c 
e = b * d
f = e * 100
g = f - 100
Problem: company c produces toy trucks at a cost of $ 5.00 each for the first 100 trucks and $ 3.50 for each additional truck . if 500 toy trucks were produced by company c and sold for $ 8.00 each , what was company c ’ s gross profit ?
Options: a ) $ 2,250 , b ) $ 2,500 , c ) $ 2,100 , d ) $ 2,150 , e ) $ 2,700
Rationale: cost of 500 trucks : ( 100 * 5 ) + ( 400 * 3.5 ) = 500 + 1400 = $ 1900 revenue : 500 * 8 = $ 4000 profit : 4000 - 1900 = $ 2100 option c is correct
Answer: c
Python program:
a = 500 * 8
b = 5 * 100
c = a - b
d = 500 - 100
e = d * 3
f = c - e
g = f / 1000
h = math.floor(g)
Problem: rs 50000 is divided into two parts one part is given to a person with 10 % interest and another part is given to a person with 20 % interest . at the end of first year he gets profit 7000 find money given by 10 % ?
Options: a ) 30000 , b ) 40000 , c ) 50000 , d ) 60000 , e ) 70000
Rationale: "let first parrt is x and second part is y then x + y = 50000 - - - - - - - - - - eq 1 total profit = profit on x + profit on y 7000 = ( x * 10 * 1 ) / 100 + ( y * 20 * 1 ) / 100 70000 = x + 2 y - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - eq 2 70000 = 50000 + y so y = 20000 then x = 50000 - 20000 = 30000 first part = 30000 answer : a"
Answer: a
Python program:
a = 50000 * 20
b = a / 100
c = b - 7000
d = 10 / 100
e = c / d
Problem: excluding stoppages , the average speed of a bus is 60 km / hr and including stoppages , the average speed of the bus is 20 km / hr . for how many minutes does the bus stop per hour ?
Options: a ) 22 , b ) 88 , c ) 77 , d ) 40 , e ) 99
Rationale: "in 1 hr , the bus covers 60 km without stoppages and 20 km with stoppages . stoppage time = time take to travel ( 60 - 20 ) km i . e 40 km at 60 km / hr . stoppage time = 40 / 60 hrs = 40 min . answer : d"
Answer: d
Python program:
a = 1 * const_60
b = 20 / 60
c = b * const_60
d = a - c
Problem: laxmi and prasanna set on a journey . laxmi moves northwards at a speed of 25 kmph and prasanna moves southward at a speed of 35 kmph . how far will be prasanna from laxmi after 60 minutes ?
Options: a ) 11 , b ) 50 , c ) 60 , d ) 27 , e ) 18
Rationale: "explanation : we know 60 min = 1 hr total northward laxmi ' s distance = 25 kmph x 1 hr = 25 km total southward prasanna ' s distance = 35 kmph x 1 hr = 35 km total distance between prasanna and laxmi is = 25 + 35 = 60 km . answer : c"
Answer: c
Python program:
a = 25 + 35
Problem: john was thrice as old as tom 6 years ago . john will be 15 / 13 times as old as tom in 6 years . how old is tom today ?
Options: a ) 5 , b ) 7 , c ) 9 , d ) 11 , e ) 13
Rationale: j - 6 = 3 ( t - 6 ) , so j = 3 t - 12 j + 6 = 15 / 13 * ( t + 6 ) 13 j + 78 = 15 t + 90 13 ( 3 t - 12 ) + 78 = 15 t + 90 24 t = 168 t = 7 the answer is b .
Answer: b
Python program:
a = 15 / 13
b = 6 * a
Problem: a shopkeeper buys two articles for rs . 1000 each and then sells them , making 50 % profit on the first article and 50 % loss on second article . find the net profit or loss percent ?
Options: a ) 500 , b ) 768 , c ) 276 , d ) 280 , e ) 279
Rationale: "profit on first article = 50 % of 1000 = 500 . this is equal to the loss he makes on the second article . that , is he makes neither profit nor loss . answer : a"
Answer: a
Python program:
a = 100 - 50
b = 100 / a
c = b * 1000
d = 100 + 50 
e = 100 / d
f = e * 1000
g = c + f 
h = 1000 + 1000 
i = g - h
j = i * 100
k = 100 - 50
l = 100 / k
m = l * 1000
n = 100 + 50 
o = 100 / n
p = o * 1000
q = m + p 
r = j / q
s = r * 100
Problem: a can complete a project in 10 days and b can complete the same project in 30 days . if a and b start working on the project together and a quits 10 days before the project is completed , in how many days will the project be completed ?
Options: a ) 18 days , b ) 15 days , c ) 26.67 days , d ) 16 days , e ) 12 days
Rationale: "let x = the number of days taken to complete the project . the amount of work done by a is ( x - 10 ) * ( 1 / 20 ) . the amount of work done by b is ( x ) * ( 1 / 30 ) . ( 1 / 10 ) * ( x - 10 ) + ( 1 / 30 ) * ( x ) = 1 ( x / 10 ) + ( x / 30 ) - 1 ) = 1 4 x / 30 = 2 x = 15 therefore , the answer is b : 15 ."
Answer: b
Python program:
a = 1 / 30
b = a * 10
c = 1 - b
d = 1 / 10
e = 1 / 30
f = d + e 
g = c / f
h = g + 10
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 ( 8 / 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 ) 11 / 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 8 / 8 * c : ( b + c ) / 2 = ( 8 / 8 ) * c b = ( 1 ) * c for set r , consisting of numbers ( a , a + 1 , . . . c ) , the median needs to be found : a = b / 2 = ( 1 * c ) / 2 = ( 1 / 2 ) * c median = ( a + c ) / 2 = ( 1 / 2 * c + c ) / 2 = ( 3 / 2 ) * c / 2 = ( 3 / 4 ) * c ( answer e )"
Answer: e
Python program:
a = 8 / 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: a car traveling at a certain constant speed takes 10 seconds longer to travel 1 km than it would take to travel 1 km at 80 km / hour . at what speed , in km / hr , is the car traveling ?
Options: a ) 70 , b ) 72 , c ) 74 , d ) 65 , e ) 78
Rationale: time to cover 1 kilometer at 80 kilometers per hour is 1 / 80 hours = 3,600 / 80 seconds = 45 seconds ; time to cover 1 kilometer at regular speed is 45 + 10 = 55 seconds = 55 / 3,600 hours = 1 / 65 hours ; so , we get that to cover 1 kilometer 1 / 65 hours is needed - - > regular speed 65 kilometers per hour ( rate is a reciprocal of time or rate = distance / time ) . answer : d
Answer: d
Python program:
a = 1 / 80
b = 3600 * a
c = b + 10 
d = c / 3600
e = 1 / d
Problem: a bus trip of 210 miles would have taken 1 hour less if the average speed v for the trip had been greater by 5 miles per hour . what was the average speed v , in miles per hour , for the trip ?
Options: a ) 25 , b ) 30 , c ) 35 , d ) 40 , e ) 45
Rationale: "the time is the distance / speed . the time difference is 1 hour . 210 / v - 210 / ( v + 5 ) = 1 210 ( v + 5 ) - 210 v = ( v ) ( v + 5 ) 1050 = ( v ) ( v + 5 ) 30 * 35 = ( v ) ( v + 5 ) v = 30 mph the answer is b ."
Answer: b
Python program:
a = 210 * 5
b = a * 4
c = 5 ** 2
d = b + c 
e = math.sqrt(d)
f = e - 5
g = f / 2
Problem: if the 5 th date of a month is tuesday , what date will be 3 days after the 3 rd friday in the month ?
Options: a ) 17 , b ) 18 , c ) 20 , d ) 22 , e ) 33
Rationale: b 18 5 th date of a month is tuesday friday will be on = 5 + 3 = 8 th of a month 1 st friday is on 1 st of a month 2 nd friday is on 8 th of a month 3 rd friday will be on 15 th of a month 3 days after 15 th = 15 + 3 = 18
Answer: b
Python program:
a = 5 * 3
b = a + 3
Problem: what is the dividend . divisor 19 , the quotient is 9 and the remainder is 5 ?
Options: a ) a ) 130 , b ) b ) 134 , c ) c ) 148 , d ) d ) 176 , e ) e ) 160
Rationale: "d = d * q + r d = 19 * 9 + 5 d = 171 + 5 d = 176 answer d"
Answer: d
Python program:
a = 19 * 9
b = a + 5
Problem: 30 % of a number is more than 60 % of 150 by 120 . find the number ?
Options: a ) 770 , b ) 712 , c ) 720 , d ) 740 , e ) 700
Rationale: "( 30 / 100 ) * x – ( 60 / 100 ) * 650 = 190 2 / 7 x = 210 x = 700 answer : e"
Answer: e
Python program:
a = 150 * 60
b = a / 100
c = b + 120 
d = c * 100
e = d / 30
Problem: given f ( x ) = 3 x – 5 , for what value of x does 2 * [ f ( x ) ] + 5 = f ( 3 x – 6 )
Options: a ) 0 , b ) 4 , c ) 6 , d ) 7 , e ) 13
Rationale: "answer = c = 6 f ( x ) = 3 x – 5 2 * [ f ( x ) ] + 5 = f ( 3 x – 6 ) 2 ( 3 x - 5 ) + 5 = 3 ( 3 x - 6 ) - 5 6 x - 5 = 9 x - 23 x = 6"
Answer: c
Python program:
a = 2 * 5
b = a + 5 
c = 3 * 3
d = c + 5 
e = b - d
f = 2 * 3
g = 3 * 1
h = f - g
i = e / h
Problem: one day a car rental agency rented 3 / 4 of its cars , including 2 / 3 of its cars with cd players . if 3 / 5 of its cars have cd players , what percent of the cars that were not rented had cd players ?
Options: a ) 1 / 2 , b ) 2 / 3 , c ) 3 / 4 , d ) 4 / 5 , e ) 5 / 6
Rationale: "the cars with cd players which were not rented is ( 1 / 3 ) ( 3 / 5 ) = 1 / 5 of all the cars . the cars which were not rented is 1 / 4 of all the cars . the percent of non - rented cars which had cd players is ( 1 / 5 ) / ( 1 / 4 ) = 4 / 5 the answer is d ."
Answer: d
Python program:
a = 4 * 2
b = a * 3
c = 4 * b
d = c / 3
e = 4 * 2
f = e * 3
g = 4 * f
h = g / 3
i = h * 4
j = i / 2
k = d - j
l = 4 * 2
m = l * 3
n = 4 * 2
o = n * 3
p = 3 * o
q = p / 4
r = m - q
s = k / r
t = s * 100
Problem: a train speeds past a pole in 15 seconds and a platform 100 m long in 25 seconds . its length is ?
Options: a ) 128 , b ) 177 , c ) 199 , d ) 178 , e ) 150
Rationale: "let the length of the train be x meters and its speed be y m / sec . they , x / y = 15 = > y = x / 15 x + 100 / 25 = x / 15 x = 150 m . answer : e"
Answer: e
Python program:
a = 2 - 1
b = 100 * a
Problem: an investor deposited $ 5,000 to open a new savings account that earned 12 percent annual interest , compounded quarterly . if there were no other transactions in the account , what was the amount of money in the account 6 months after the account was opened ?
Options: a ) $ 5300.50 , b ) $ 5304.50 , c ) $ 5405.50 , d ) $ 5604.50 , e ) $ 5805.50
Rationale: "the amount in the account after 6 months is 1.03 * 1.03 ( $ 5,000 ) = $ 5304.50 . the answer is b ."
Answer: b
Python program:
a = 2 + 3 
b = a * 100
c = 2 + 3 
d = c * 2
e = b * d
f = 12 / 4
g = f / 100
h = g + 1 
i = h ** 2
j = e * i
Problem: a and b can do a work in 8 days , b and c can do the same work in 12 days . a , b and c together can finish it in 6 days . a and c together will do it in ?
Options: a ) 8 , b ) 4 , c ) 6 , d ) 12 , e ) 10
Rationale: ( a + b + c ) ' s 1 day work = 1 / 6 ; ( a + b ) ' s 1 day work = 1 / 8 ( b + c ) ' s 1 day work = 1 / 12 ( a + c ) ' s 1 day work = ( 2 * 1 / 6 ) - ( 1 / 8 + 1 / 12 ) = ( 1 / 3 - 5 / 24 ) = 1 / 8 so , a and c together will do the work in 8 days . answer a
Answer: a
Python program:
a = 8 / 2
b = a + 2 
c = 8 * b
d = c / 6
Problem: oy started cycling along the boundaries of a square field from corner point a . after half an hour he reached the corner point c , diagonally opposite to a . if his speed was 8 km / hr , the area of the filed in square km is ?
Options: a ) 64
b ) 4
c ) 16
d ) 9
e ) 5
Rationale: explanation : distance covered by roy in 1 / 2 hr = 4 kmtherefore , side of the square = 4 / 2 = 2 kmhence , area = 2 × 2 = 4 square km answer : b
Answer: b
Python program:
a = 8 / 2
b = a / 2
c = b ** 2
Problem: how many 4 - digit numbers are there such that all 3 digits are different and the first digit and last digit is not zero ?
Options: a ) 2128 , b ) 3458 , c ) 4207 , d ) 5184 , e ) 8104
Rationale: all three digits are different and first digit is not zero . so first digit can be filled in 8 ways . and , second digit can be filled in 9 ways . and , third digit can be filled in 9 ways . and , fourth digit can be filled in 8 ways . total ways = 8 * 9 * 9 * 8 = 5184 hence option ( d ) .
Answer: d
Python program:
a = 10 - 1
b = 4 / 2
c = a ** b
d = 10 - 1
e = d - 1
f = 4 / 2
g = e ** f
h = c * g
Problem: the digital sum of a number is the sum of its digits . for how many of the positive integers 24 - 80 inclusive is the digital sum a multiple of 7 ?
Options: a ) 7 , b ) 9 , c ) 14 , d ) 16 , e ) 20
Rationale: "is there other way than just listing ? 25 34 43 52 59 61 68 70 77 9 ways . . b"
Answer: b
Python program:
a = 24 - 7
b = a - 2
Problem: 32 = a + 2 b | a | > 2 if ‘ a ’ and ‘ b ’ are both integers , then what is the smallest possible values of ‘ a ’ that can be used to solve the above equation .
Options: a ) 2 , b ) 3 , c ) 4 , d ) 5 , e ) 6
Rationale: let us understand the meaning of | a | > 2 mod is very easy concept if you solve mod question by considering as a distance . when a mod is written as | x - ( a ) | = b , this means the distance from point ' a ' ( both side left and right of ' a ' on number line ) is b . | x - ( a ) | < b means the distance is between the two extreme distance ( left and right side of ' a ' on number line , considering the max distance is ' b ' from ' a ' - as per this scenario . . . . . hence the value of ' a ' must be between these two extremes . | x - ( a ) | > b means the distance is greater than the distance of ' b ' . . i . e the value of a could be anywhere more than ' b ' ( i . e . current case ) . now come to the question . first its given | a | > 2 = = > a > 2 i . e . a can have any value bigger than 2 ( i . e . 3 , 4 , 5 … ) . now , lets move to equation a + 2 b = 32 = = > b = ( 32 – a ) / 2 = = > b = 16 – ( a / 2 ) . according to question , b is an integer , hence to make ‘ b ’ integer a must be divisible by 2 . minimum possible value of ‘ a ’ that is divisible by 2 is 4 ( a is greater than 2 so the next number that is divisible by 2 is 4 ) . so the answer is c ( value 4 ) .
Answer: c
Python program:
a = 2 * 2
Problem: a salesman ' s income consists of a commission and a base salary of $ 350 per week . over the past 5 weeks , his weekly income totals have been $ 406 , $ 413 , $ 420 , $ 436 and $ 495 . what must his average ( arithmetic mean ) commission be per week over the next two weeks so that his average weekly income is $ 500 over the 7 - week period ?
Options: a ) $ 315 , b ) $ 245 , c ) $ 365 , d ) $ 715 , e ) $ 730
Rationale: total weekly income over 5 weeks = $ 406 + $ 413 + $ 420 + $ 436 + $ 495 = $ 2170 for avg weekly income to be $ 500 over 7 weeks , we need total weekly income over 7 weeks = $ 3500 now , $ 3500 - $ 2170 = $ 1330 from this , we subtract base salary for 2 weeks i . e $ 350 * 2 = $ 700 therefore , commission = $ 1330 - $ 700 = $ 730 for 2 weeks avg weekly commission = $ 315 answer a
Answer: a
Python program:
a = 500 * 7
b = 406 + 413 
c = 436 + 420 
d = b + c 
e = d + 495 
f = a - e
g = f / 2
h = g - 350
Problem: at company x , senior sales representatives visit the home office once every 15 days , and junior sales representatives visit the home office once every 10 days . the number of visits that a junior sales representative makes in a 2 - year period is approximately what percent greater than the number of visits that a senior representative makes in the same period ?
Options: a ) 10 % , b ) 25 % , c ) 33 % , d ) 50 % , e ) 67 %
Rationale: "each 30 - day period , senior representatives visit the home office 2 times while junior representatives visit 3 times , thus 50 % more . the answer is d ."
Answer: d
Python program:
a = 1 + 10 
b = 15 - 10
c = b - 1
d = a * c
Problem: two assembly line inspectors , lauren and steven , inspect widgets as they come off the assembly line . if lauren inspects every fifth widget , starting with the fifth , and steven inspects every third , starting with the third , how many of the 99 widgets produced in the first hour of operation are not inspected by either inspector ?
Options: a ) 35 , b ) 40 , c ) 45 , d ) 50 , e ) 55
Rationale: "widgets inspected by lauren : ( ( 95 - 5 ) / 5 ) + 1 = 18 + 1 = 19 widgets inspected by steven : ( ( 96 - 3 ) / 3 ) + 1 = 31 + 1 = 32 widgets inspected by both : ( ( 90 / 15 ) + 1 = 7 total : 19 + 32 - 7 = 44 hence , widgets not inspected : 99 - 44 = 55 option e"
Answer: e
Python program:
a = 4 + 1 
b = 99 / a
c = math.floor(b)
d = 99 / 4
e = math.floor(d)
f = c + e 
g = 4 + 1 
h = 10 + g 
i = 99 / h
j = math.floor(i)
k = f - j
l = 99 - k
Problem: the guests at a football banquet consumed a total of 411 pounds of food . if no individual guest consumed more than 2.5 pounds of food , what is the minimum number of guests that could have attended the banquet ?
Options: a ) 165 , b ) 161 , c ) 162 , d ) 163 , e ) 164
Rationale: "to minimize one quantity maximize other . 164 * 2.5 ( max possible amount of food a guest could consume ) = 410 pounds , so there must be more than 164 guests , next integer is 165 . answer : a ."
Answer: a
Python program:
a = 411 / 2
b = math.floor(a)
c = b + 1
Problem: in an institute , 60 % of the students are boys and the rest are girls . further 15 % of the boys and 7.5 % of the girls are getting a fee waiver . if the number of those getting a fee waiver is 90 , find the total number of students getting 50 % concessions if it is given that 50 % of those not getting a fee waiver are eligible to get half fee concession ?
Options: a ) 360 , b ) 280 , c ) 320 , d ) 330 , e ) 350
Rationale: solution : let us assume there are 100 students in the institute . then , number of boys = 60 and , number of girls = 40 further , 15 % of boys get fee waiver = 9 boys 7.5 % of girls get fee waiver = 3 girls total = 12 students who gets fee waiver but , here given 90 students are getting fee waiver . so we compare 12 = 90 so , 1 = 90 / 12 = 7.5 now number of students who are not getting fee waiver = 51 boys and 37 girls . 50 % concession = 25.5 boys and 18.5 girls ( i . e . total 44 ) . hence , required students = 44 * 7.5 = 330 . answer : option d
Answer: d
Python program:
a = 60 / 100
b = 15 / 100
c = a * b
d = 60 / 100
e = 1 - d
f = 7 / 5
g = e * f
h = c + g 
i = 90 / h
j = 15 / 100
k = 1 - j
l = 60 / 100
m = k * l
n = m / 2
o = 7 / 5
p = 1 - o
q = 60 / 100
r = 1 - q
s = p * r
t = s / 2
u = n + t 
v = i * u
Problem: if n = 2 ^ 0.15 and n ^ b = 64 , b must equal
Options: a ) 3 / 80 , b ) 3 / 5 , c ) 40 , d ) 5 / 3 , e ) 80 / 3
Rationale: "15 / 100 = 3 / 20 n = 2 ^ 3 / 20 n ^ b = 2 ^ 6 ( 2 ^ 3 / 20 ) ^ b = 2 ^ 6 b = 40 answer : c"
Answer: c
Python program:
a = math.log(64)
b = 2 ** 0
c = math.log(b)
d = a / c
Problem: each of the 9 squares shown is to contain one number chosen from 1 , 2 , 3 , 4 , 5 , 6 , 7 , 8 , and 9 . no number is to be repeated . suppose the sum of the 5 squares aligned vertically on the right is 32 and that the sum of the 5 squares aligned horizontally on the bottom is 20 . what number goes in the shared corner square ?
Options: a ) 3 , b ) 4 , c ) 5 , d ) 6 , e ) 7
Rationale: if x is the number in the corner square , then the sum of all the numbers in the squares is equal to the sum of the numbers in the five squares aligned vertically plus the sum of the numbers in the five squares aligned horizontally minus x . hence , 1 + 2 + · · · + 9 = 32 + 20 − x . the sum on the left is 45 , so x = 52 − 45 = 7 . correct answer e
Answer: e
Python program:
a = 1 + 2 
b = 4 + a
Problem: in an electric circuit , two resistors with resistances x and y are connected in parallel . if r is the combined resistance of these two resistors , then the reciprocal of r is equal to the sum of the reciprocals of x and y . what is r if x is 5 ohms and y is 7 ohms ?
Options: a ) 3 / 5 , b ) 1 / 7 , c ) 12 / 35 , d ) 31 / 12 , e ) 35 / 12
Rationale: "1 / r = 1 / x + 1 / y 1 / r = 1 / 5 + 1 / 7 = 12 / 35 r = 35 / 12 the answer is e ."
Answer: e
Python program:
a = 7 * 5
b = 5 + 7 
c = a / b
Problem: a envelop weight 8.5 gm , if 850 of these envelop are sent with an advertisement mail . how much wieght ?
Options: a ) 6.6 kg , b ) 7.225 kg , c ) 6.7 kg , d ) 6.9 kg , e ) 7.8 kg
Rationale: 850 * 8.5 7225.0 gm 7.225 kg answer : b
Answer: b
Python program:
a = 8 * 5
b = a / 1000
Problem: a can give b 90 meters start and c 200 meters start in a kilometer race . how much start can b give c in a kilometer race ?
Options: a ) 120.88 , b ) 120.13 , c ) 111.22 , d ) 120.0 , e ) 111.12
Rationale: "a runs 1000 m while b runs 910 m and c runs 800 m . the number of meters that c runs when b runs 1000 m , = ( 1000 * 800 ) / 910 = 879.12 m . b can give c = 1000 - 879.12 = 120.88 m . answer : a"
Answer: a
Python program:
a = 100 * 10
b = 100 * 10
c = 100 * 10
d = c - 200
e = b * d
f = 100 * 10
g = f - 90
h = e / g
i = a - h
Problem: a man buys 12 lts of liquid which contains 10 % of the liquid and the rest is water . he then mixes it with 10 lts of another mixture with 30 % of liquid . what is the % of water in the new mixture ?
Options: a ) 80.91 , b ) 76.45 , c ) 77.45 , d ) 74.45 , e ) 73.45
Rationale: 10 % in 12 lts is 1.2 . so water = 12 - 1.2 = 10.8 lts . 30 % of 10 lts = 3 . so water in 2 nd mixture = 10 - 3 = 7 lts . now total quantity = 12 + 10 = 22 lts . total water in it will be 10.8 + 7 = 17.8 lts . % of water = ( 100 * 17.8 ) / 22 = 80.91 . answer : a
Answer: a
Python program:
a = 12 - 10
b = 12 * a
c = 12 - 30
d = 10 * c
e = b + d 
f = 12 + 10 
g = e / f
Problem: a jar contains 6 black and 2 white balls . if you pick two balls at the same time , what ' s the probability that one ball is black and one is white ?
Options: a ) 2 / 7 , b ) 5 / 7 , c ) 4 / 7 , d ) 3 / 15 , e ) 3 / 14
Rationale: "p ( 1 st black , 2 nd white ) = 6 / 8 * 2 / 7 = 12 / 56 ; p ( 1 st white , 2 nd black ) = 2 / 8 * 6 / 7 = 12 / 56 . p = 12 / 56 + 12 / 56 = 24 / 112 = 12 / 56 = 6 / 28 = 3 / 14 . answer : e ."
Answer: e
Python program:
a = 6 + 2 
b = 6 / a
c = 6 + 2 
d = c - 1
e = 2 / d
f = b * e
Problem: if a car had traveled 10 kmh faster than it actually did , the trip would have lasted 30 minutes less . if the car went exactly 30 km , at what speed did it travel ?
Options: a ) 20 kmh , b ) 25 kmh , c ) 30 kmh , d ) 35 kmh , e ) 40 kmh
Rationale: "time = distance / speed difference in time = 1 / 2 hrs 30 / x - 30 / ( x + 10 ) = 1 / 2 substitute the value of x from the options . - - > x = 20 - - > 30 / 20 - 30 / 30 = 3 / 2 - 1 = 1 / 2 answer : a"
Answer: a
Python program:
a = 30 * 10
b = 2 * a
c = b * 4
d = 10 ** 2
e = c + d 
f = math.sqrt(e)
g = f - 10
h = g / 2
Problem: a man is 28 years older than his son . in two years , his age will be twice the age of his son . what is the present age of his son ?
Options: a ) 23 years , b ) 22 years , c ) 21 years , d ) 20 years , e ) 26 years
Rationale: "let present age of the son = x years then , present age the man = ( x + 28 ) years given that , in 2 years , man ' s age will be twice the age of his son â ‡ ’ ( x + 28 ) + 2 = 2 ( x + 2 ) â ‡ ’ x = 26 answer : e"
Answer: e
Python program:
a = 2 * 2
b = a - 2
c = 28 - b
d = 2 - 1
e = c / d