euclaise/mathqa_programs huggingface dataset:
Problem: a certain high school has 500 students . of these students , 40 are taking music , 20 are taking art , and 10 are taking both music and art . how many students are taking neither music nor art ?
Options: a ) 430 , b ) 440 , c ) 450 , d ) 460 , e ) 470
Rationale: we ' re given a series of facts to work with : 1 ) a certain high school has 500 students . 2 ) of these students : x are taking music , y are taking art , and z are taking both music and art . we ' re asked how many students are taking neither music nor art ? let ' s test x = 40 y = 20 z = 10 so , we have 40 students taking music , 20 taking art and 10 taking both music and art . 30 student taking just music 10 student taking just art 10 student taking both music and art total = 50 students we ' re asked for the total number of students who are taking neither course . that is 500 - 50 = 450 . c
Answer: c
Python program:
a = 40 + 20 
b = a - 10
c = 500 - b
Problem: when 1 / 10 percent of 7,000 is subtracted from 1 / 10 of 7,000 , the difference is
Options: a ) 0 , b ) 50 , c ) 450 , d ) 693 , e ) 500
Rationale: we can break this problem into two parts : 1 ) what is 1 / 10 percent of 7,000 ? 2 ) what is 1 / 10 of 7,000 ? to calculate 1 / 10 percent of 7,000 we must first remember to divide 1 / 10 by 100 . so we have : ( 1 / 10 ) / ( 100 ) to divide a number by 100 means to multiply it by 1 / 100 , so we have : 1 / 10 x 1 / 100 = 1 / 1,000 thus , 1 / 10 percent of 7,000 = 1 / 1,000 x 7,000 = 7 . now let ' s concentrate on part 2 . we need to calculate 1 / 10 of 7,000 . to do this we simply multiply 1 / 10 by 7,000 . 1 / 10 x 7,000 = 700 the answer to part 1 is 7 , and the answer to part 2 is 700 . their difference is 700 – 7 = 693 . answer d .
Answer: d
Python program:
a = 3 + 4 
b = a * 1000
c = 1 / 10
d = b * c
e = 1 / 10
f = e / 100
g = 3 + 4 
h = g * 1000
i = f * h
j = d - i
Problem: what sum of money will produce rs . 210 as simple interest in 4 years at 3 1 / 2 percent ?
Options: a ) rs . 2500 , b ) rs . 1500 , c ) rs . 1400 , d ) rs . 1600 , e ) rs . 1300
Rationale: 210 = ( p * 4 * 7 / 2 ) / 100 p = 1500 answer : b
Answer: b
Python program:
a = 1 / 2
b = 3 + a 
c = 4 * b
d = c / 100
e = 210 / d
Problem: while driving from a - ville to b - town , harriet drove at a constant speed of 90 kilometers per hour . upon arriving in b - town , harriet immediately turned and drove back to a - ville at a constant speed of 160 kilometers per hour . if the entire trip took 5 hours , how many minutes did it take harriet to drive from a - ville to b - town ?
Options: a ) 138 , b ) 148 , c ) 150 , d ) 162 , e ) 192
Rationale: 5 hr = 300 min . if harriet spend equal hrs on each leg she will spend 150 min on each . since speed a - b is less than speed b - a and distance on each leg is the same , time spent on a - b is more than 150 min , which mean we can eliminate ans . a , b and c . now let plug in ans . d or e and verify which one give same distance on each leg . d . t = 162 min * leg a - b - - - > d = 90.192 / 60 = 17280 / 60 * leg b - a - - - - > d = 160 * 108 / 60 = 17280 / 60 so the correct ans . ise
Answer: e
Python program:
a = 90 * 5
b = 90 + 160 
c = a / b
d = 5 - c
e = d * const_60
Problem: the milk level in a rectangular box measuring 64 feet by 25 feet is to be lowered by 6 inches . how many gallons of milk must be removed ? ( 1 cu ft = 7.5 gallons )
Options: a ) 100 , b ) 250 , c ) 750 , d ) 5625 , e ) 6000
Rationale: 6 inches = 1 / 2 feet ( there are 12 inches in a foot . ) , so 64 * 25 * 1 / 2 = 800 feet ^ 3 of milk must be removed , which equals to 800 * 7.5 = 6000 gallons . answer : e .
Answer: e
Python program:
a = 64 * 25
b = 1 / 2
c = a * b
d = c * 7
Problem: a computer store offers employees a 20 % discount off the retail price . if the store purchased a computer from the manufacturer for $ 1000 dollars and marked up the price 20 % to the final retail price , how much would an employee save if he purchased the computer at the employee discount ( 20 % off retail price ) as opposed to the final retail price .
Options: a ) $ 1,000 , b ) $ 960 , c ) $ 240 , d ) $ 200 , e ) $ 150
Rationale: "cost price = 1000 profit = 20 % = 20 % of 1000 = 200 selling price = cp + profit sp = 1200 a discount of 20 % to employees means 20 % off on 1200 so 20 % of 1200 = 240 so a employee thinks he saved 240 . . answer : c"
Answer: c
Python program:
a = 1000 * 20
b = a / 100
c = b + 1000 
d = 1000 / 100
e = d * 2
f = c / e
Problem: i sold a book at a profit of 10 % . had i sold it for $ 90 more , 15 % would have been gained . find the cost price ?
Options: a ) $ 1800 , b ) $ 2500 , c ) $ 3000 , d ) $ 3120 , e ) $ 1540
Rationale: "115 % of cost - 110 % of cost = $ 90 5 % of cost = $ 90 cost = 90 * 100 / 5 = $ 1800 answer is a"
Answer: a
Python program:
a = 90 * 10
b = 15 - 10
c = a / b
d = c * 100
e = d / 10
Problem: reena took a loan of $ . 1200 with simple interest for as many years as the rate of interest . if she paid $ 972 as interest at the end of the loan period , what was the rate of interest ?
Options: a ) 3.6 , b ) 6 , c ) 18 , d ) can not be determined , e ) none of these
Rationale: "let rate = r % and time = r years . then , 1200 x r x r / 100 = 972 12 r 2 = 972 r 2 = 81 r = 9 . answer : e"
Answer: e
Python program:
a = 972 * 100
b = a / 1200
c = math.sqrt(b)
Problem: 7 , 10 , 8 , 11 , 9 , 12 , ___
Options: a ) 10 , b ) 11 , c ) 12 , d ) 13 , e ) 14
Rationale: "10 = 7 + 3 8 = 10 - 2 11 = 8 + 3 9 = 11 - 2 12 = 9 + 3 similarly 12 - 2 = 10 answer : a"
Answer: a
Python program:
a = negate - (
Problem: how much more would rs . 20000 fetch , after two years , if it is put at 20 % p . a . compound interest payable half yearly than if is put at 20 % p . a . compound interest payable yearly ?
Options: a ) a ) rs . 6 , 602.50 , b ) b ) rs . 6 , 601.50 , c ) c ) rs . 6 , 603.50 , d ) d ) rs . 6 , 604.50 , e ) e ) rs . 6 , 605.50
Rationale: "20000 ( 11 / 10 ) 4 - 20000 ( 6 / 5 ) 2 = 6 , 602.50 answer : a"
Answer: a
Python program:
a = 20 / 100
b = a / 2
c = 1 + b 
d = c ** 4
e = d * 20000
f = 20 / 100
g = f + 1 
h = g ** 2
i = h * 20000
j = e - i
Problem: how much interest will $ 10,000 earn in 9 months at an annual rate of 10 % ?
Options: a ) $ 250 , b ) $ 350 , c ) $ 450 , d ) $ 60 , e ) $ 650
Rationale: "soln : - 9 months = 3 / 4 of year ; 10 % = 10 / 100 = 1 / 10 ; $ 10,000 ( principal ) * 3 / 50 ( interest rate ) * 1 / 10 ( time ) = $ 60 . answer : d"
Answer: d
Python program:
a = 100 ** 2
b = 10 / 100
c = a * b
d = 3 / 10
e = c * d
Problem: a new home buyer pays 4 % annual interest on her first mortgage and 9 % annual interest on her second mortgage . if she borrowed a total of $ 320,000 , 80 % of which was in the first mortgage , what is her approximate monthly interest payment ?
Options: a ) $ 1,333 , b ) $ 1,733 , c ) $ 3,466 , d ) $ 13,333 , e ) $ 20,796
Rationale: "making the numbers a little easy looking : monthly payment = 320,000 * ( 80 / 100 * 4 / 100 + 20 / 100 * 9 / 100 ) / 12 = 3200 / 12 * ( 3.2 + 1.8 ) = 16000 / 12 = 1333 answer : a"
Answer: a
Python program:
a = 4 * 2
b = 9 - a
Problem: a dog takes 5 leaps for every 8 leaps of a hare . if one leap of the dog is equal to 4 leaps of the hare , the ratio of the speed of the dog to that of the hare is :
Options: a ) 5 : 8 , b ) 5 : 3 , c ) 5 : 2 , d ) 5 : 9 , e ) 2 : 5
Rationale: "explanation : dog : hare = ( 5 * 4 ) leaps of hare : 8 leaps of hare = 20 : 8 - - > 10 : 4 - - > 5 : 2 answer : c"
Answer: c
Python program:
a = 5 * 4
b = a / 8
Problem: by selling 200 apples , a fruit - seller gains the selling price of 50 apples . find the gain percent ?
Options: a ) 33.33 % , b ) 35 % , c ) 27.75 % , d ) 35.75 % , e ) 32.25 %
Rationale: sp = cp + g 200 sp = 200 cp + 50 sp 150 sp = 200 cp 150 - - - 50 cp 100 - - - ? = > 33.33 % answer : a
Answer: a
Python program:
a = 200 - 50
b = 50 / a
c = b * 100
Problem: a , b and c can do a piece of work in 24 days , 30 days and 40 days respectively . they began the work together but c left 8 days before the completion of the work . in how many days was the work completed ?
Options: a ) 12 days , b ) 16 days , c ) 18 days , d ) 11 days , e ) 38 days
Rationale: "one day work of a , b and c = 1 / 24 + 1 / 30 + 1 / 40 = 1 / 10 work done by a and b together in the last 8 days = 8 * ( 1 / 24 + 1 / 30 ) = 3 / 5 remaining work = 2 / 5 the number of days required for this initial work = 4 days . the total number of days required = 8 + 4 = 12 days . answer : a"
Answer: a
Python program:
a = 1 / 24
b = 1 / 30
c = a + b 
d = c * 8
e = 1 - d
f = 2 + 3 
g = 2 * 8
h = f * g
i = 1 / h
j = 1 / 24
k = 1 / 30
l = j + k 
m = i + l 
n = e / m
o = n + 8
Problem: a man whose bowling average is 12.4 , takes 4 wickets for 26 runs and there by decreases his average by 0.4 . the number of wickets taken by him before his last match is ?
Options: a ) 53 , b ) 54 , c ) 55 , d ) 56 , e ) 57
Rationale: "12.4 * x + 26 = ( 4 + x ) 12 solve equation x = 55 answer : c"
Answer: c
Python program:
a = math.floor(12, 4)
b = a * 4
c = b - 26
d = math.floor(12, 4)
e = 12 - 4
f = c / e
Problem: an engine moves at the speed of 60 kmph without any coaches attached to it . speed of the train reduces at the rate that varies directly as the square root of the number of coaches attached . when 9 coaches are attached speed decreases to 48 kmph . what will be the speed of train when 25 coaches are attached .
Options: a ) 35 , b ) 28 , c ) 40 , d ) 44 , e ) 42
Rationale: 1 . no . of coaches = 9 sqr root = 3 speed decreases by 12 12 = k * 3 k = 4 no . of coaches = 25 swr root = 5 decrease = 5 * 4 = 20 new speed = 60 - 20 = 40 c
Answer: c
Python program:
a = math.sqrt(25)
b = 60 - 48
c = math.sqrt(9)
d = b / c
e = a * d
f = 60 - e
Problem: a survey was sent to 80 customers , 12 of whom responded . then the survey was redesigned and sent to another 63 customers , 10 of whom responded . by approximately what percent did the response rate increase from the original survey to the redesigned survey ?
Options: a ) 2 % , b ) 5 % , c ) 14 % , d ) 28 % , e ) 63 %
Rationale: "rate of first survey = 12 / 80 rate of second survey = 10 / 63 % response rate increase ( 10 / 63 - 12 / 80 ) / ( 12 / 80 ) = 5 % answer is b = 5 %"
Answer: b
Python program:
a = 10 / 63
b = 12 / 80
c = a - b
d = c * 100
e = math.floor(d)
Problem: a train covers a distance of 12 km in 10 min . if it takes 9 sec to pass a telegraph post , then the length of the train is ?
Options: a ) 298 , b ) 288 , c ) 120 , d ) 776 , e ) 180
Rationale: "speed = ( 12 / 10 * 60 ) km / hr = ( 72 * 5 / 18 ) m / sec = 20 m / sec . length of the train = 20 * 9 = 180 m . answer : e"
Answer: e
Python program:
a = 100 / 0
b = a - 9
c = 100 / 0
Problem: in a mixture of 60 litres the ratio of milk to water is 5 : 1 . additional 20 litres of water is added to the mixture . find the ratio of milk to water in the resulting mixture .
Options: a ) 2 : 3 , b ) 5 : 3 , c ) 1 : 4 , d ) 3 : 2 , e ) 3 : 1
Rationale: "given that milk / water = 5 x / x and 5 x + x = 60 - - > x = 10 . thus milk = 5 x = 50 liters and water = x = 10 liters . new ratio = 50 / ( 20 + 10 ) = 50 / 30 = 5 / 3 . answer is b"
Answer: b
Python program:
a = 5 + 1 
b = 60 / a
c = 60 - b
d = 5 + 1 
e = 60 / d
f = e + 20 
g = c / f
Problem: a train traveling at 72 kmph crosses a platform in 34 seconds and a man standing on the platform in 18 seconds . what is the length of the platform in meters ?
Options: a ) 240 meters , b ) 320 meters , c ) 420 meters , d ) 600 meters , e ) can not be determined
Rationale: "speed of train = 72 * ( 5 / 18 ) = 20 m / s lets consider the man as a stationery point on the platform . crossing the point gives us the length of the train . lt = 20 * 18 = 360 m . crossing the platform gives us the length of trainlength of platform . l ( t + p ) = 20 * 34 = 680 m . so , length of platform = 680 - 360 = 320 m imo , answer b"
Answer: b
Python program:
a = 72 * 1000
b = a / 3600
c = b * 34
d = 72 * 1000
e = d / 3600
f = e * 18
g = c - f
Problem: square abcd is the base of the cube while square efgh is the cube ' s top face such that point e is above point a , point f is above point b etc . what is the distance between the midpoint of edge ab and the midpoint of edge eh if the area of square abcd is 2 ?
Options: a ) 1 / sqrt 2
b ) 1
c ) sqrt 2
d ) sqrt 3
e ) 2 sqrt 3
Rationale: distance from mid point of ab to ad = sqrt [ ( 1 / sqrt 2 ) ^ 2 + ( 1 / sqrt 2 ) ^ 2 ] = 1 the distance between the midpoint of edge ab and the midpoint of edge eh = sqrt [ 1 ^ 2 + ( sqrt 2 ) ^ 2 ] = sqrt 3 . answer : d
Answer: d
Python program:
a = 1 + 2 
b = math.sqrt(a)
Problem: in an ngo the daily average wages of 20 illiterate employees is decreased from rs . 25 to rs . 10 , thus the average salary of all the literate and illiterate employees is decreased rs . 10 per day . the no . of educated employees working in the ngo is :
Options: a ) 12 , b ) 11 , c ) 10 , d ) 27 , e ) 22
Rationale: explanation : total employees = \ inline \ frac { ( 25 - 10 ) \ times 20 } { 10 } = 30 hence number of educated employees = 30 - 20 = 10 answer : c ) 10
Answer: c
Python program:
a = 20 - 10
Problem: you have been given a physical balance and 7 weights of 52 , 50 , 48 , 44 , 45 , 46 and 78 kgs . keeping weights on one pan and object on the other , what is the maximum you can weigh less than 183 kgs .
Options: a ) 180 , b ) 181 , c ) 182 , d ) 178 , e ) 168
Rationale: "add the max weights 52 + 50 + 78 = 180 answer : a"
Answer: a
Python program:
a = 50 + 48 
b = a + 44 
c = b + 46
Problem: excluding stoppages , the speed of a train is 45 kmph and including stoppages it is 34 kmph . of how many minutes does the train stop per hour ?
Options: a ) e 982 , b ) 27 , c ) 12 , d ) 14.6 , e ) 28
Rationale: "explanation : t = 11 / 45 * 60 = 14.6 answer : option d"
Answer: d
Python program:
a = 34 / 45
b = const_60 * a
c = const_60 - b
Problem: a , b and c start a business each investing 20,000 . after 5 months a withdrew 5000 , b withdrew 4000 and c invests 6000 more . at the end of the year , a total profit of 69,900 was recorded . find the share of b
Options: a ) 20,000 , b ) 21,000 , c ) 28,200 , d ) 20,500 , e ) none of these
Rationale: "ratio of the capitals of a , b and c = 20000 × 5 + 15000 × 7 : 20000 × 5 + 16000 × 7 : 20000 × 5 + 26000 × 7 = 205000 : 212000 : 282000 = 205 : 212 : 282 . b ’ s share = ( 69900 × 212 ⁄ 699 ) = 21200 ; answer c"
Answer: c
Python program:
a = 12 - 5
b = a * 4000
c = 100 * 100
d = 2 * c
e = d * 5
f = b + e 
g = 100 * 10
h = f / g
Problem: 5 men or 8 women do equal amount of work in a day . a job requires 3 men and 5 women to finish the job in 10 days how many woman are required to finish the job in 14 days .
Options: a ) 10 , b ) 7 , c ) 6 , d ) 12 , e ) 13
Rationale: 1 man can do the work of 8 / 5 = 1.6 women equivalent of 3 * 1.6 + 5 = 9.8 women take 10 days so women needed to do the work in 14 days = [ 10 / 14 ] * 9.8 = 7 answer : b
Answer: b
Python program:
a = 8 / 5
b = a * 3
c = b + 5 
d = c * 10
e = d / 14
Problem: ajay can walk 10 km in 1 hour . in how many hours he can walk 50 km ?
Options: a ) 5 hrs , b ) 10 hrs , c ) 15 hrs , d ) 20 hrs , e ) 30 hrs
Rationale: 1 hour he walk 10 km he walk 50 km in = 50 / 10 * 1 = 5 hours answer is a
Answer: a
Python program:
a = 50 / 10
Problem: factory x ' s bulbs work for over 5000 hours in 75 % of cases , whereas factory y ' s bulbs work for over 5000 hours in 65 % of cases . it is known that factory x supplies 70 % of the total bulbs available . what is the chance that a purchased bulb will work for longer than 5000 hours ?
Options: a ) 76.4 % , b ) 78 % , c ) 77.4 % , d ) 72 % , e ) 73.9 %
Rationale: "for x , 70 % of 75 % will work . for y , 30 % of 65 % will work . * 30 % is the rest of the bulb supply in the market . so , the probability that a purchased bulb will work is : 0.70 ( 0.75 ) = . 525 0.30 ( 0.65 ) = 0.195 the combined probability then is 52.5 + 19.5 = 72 % ans d"
Answer: d
Python program:
a = 75 + 65 
b = a / 2
Problem: the radius of a wheel is 22.4 cm . what is the distance covered by the wheel in making 1500 resolutions ?
Options: a ) 2112 m , b ) 2704 m , c ) 2278 m , d ) 2288 m , e ) 2378 m
Rationale: "in one resolution , the distance covered by the wheel is its own circumference . distance covered in 1500 resolutions . = 1500 * 2 * 22 / 7 * 22.4 = 211200 cm = 2112 m answer : a"
Answer: a
Python program:
a = 3 + 4 
b = a * 3
c = b + 1 
d = 3 + 4 
e = c / d
f = e * 22
g = f * 2
h = g * 1500
i = h / 100
Problem: a 300 meter long train running at the speed of 120 kmph crosses another train running in the opposite direction at the speed of 80 kmph in 9 seconds . what is the lenght of other train .
Options: a ) 210 m , b ) 220 m , c ) 230 m , d ) 240 m , e ) 200 m
Rationale: relative speeds = ( 120 + 80 ) km / hr = 200 km / hr = ( 200 * 5 / 18 ) m / s = ( 500 / 9 ) m / s let length of train be xm x + 300 / 9 = 500 / 9 x = 200 ans is 200 m answer : e
Answer: e
Python program:
a = 120 + 80 
b = a * const_0_2778
c = 9 * b
d = c - 300
Problem: by selling 12 pens for a rupee a woman loses 20 % . how many for a rupee should he sell in order to gain 20 % ?
Options: a ) 12 , b ) 14 , c ) 45 , d ) 8 , e ) 65
Rationale: "d 80 % - - - 12 120 % - - - ? 80 / 120 * 12 = 8"
Answer: d
Python program:
a = 100 - 20
b = 100 / a
c = b / 12
d = 100 - 20
e = 100 / d
f = e / 12
g = f * 20
h = g / 100
i = c + h 
j = 1/(i)
Problem: how many of the positive factors of 26 , 16 and how many common factors are there in numbers ?
Options: a ) 1 , b ) 2 , c ) 3 , d ) 4 , e ) 5
Rationale: "factors of 26 - 1 , 2 , 13 and 26 factors of 16 - 1 , 2 , 4 , 8 and 16 comparing both , we have three common factors of 45,16 - 2 answer : b"
Answer: b
Python program:
a = 16 / 26
Problem: find unit digit of n when n = 63 ^ 1 ! + 2 ! + . . . + 63 ! + 18 ^ 1 ! + 2 ! + . . . + 18 ! + 37 ^ 1 ! + 2 ! + . . . 37 !
Options: a ) 2 , b ) 4 , c ) 6 , d ) 8 , e ) 0
Rationale: 3,8 and 7 have a power cycle of 4 , i . e . the units digit in each case will repeat after every 4 th power . for eg : 3 ^ 1 = 3 , 3 ^ 2 = 9 , 3 ^ 3 = 27 , 3 ^ 4 = 81 , 3 ^ 5 = 243 all the powers given ( 1 ! + 2 ! + . . . . ) , are multiples of 4 . it is so because the last 2 digits of the total sum will be 00 , for each one of them , which make them divisible by 4 . thus , the given problem boils down to 3 ^ 4 + 8 ^ 4 + 7 ^ 4 = 1 + 6 + 1 = 8 thus , the units digit is 8 . answer : d
Answer: d
Python program:
a = 63 + 18 
b = a + 37 
c = b - 100
d = c - 10
Problem: 6 students are equally divided into 3 groups , then , the 3 groups were assigned to 3 different topics . how many different arrangements w are possible ?
Options: a ) 30 , b ) 60 , c ) 90 , d ) 180 , e ) 540
Rationale: 90 is the number of ways you can assign 3 teams formed out of 12 people to 3 different tasks . but now you can order the 3 tasks in 3 ! ways . t 1 t 2 t 3 or t 2 t 1 t 3 . . . . etc etc . i was confused between 90 and 540 but since question used the wordarrangementsdecided to go with complete arrangements w including the order of tasks . could you explain the highlighted step . . . i ' m getting 90 = 15 * 3 ! suppose the students are numbered 12 , 34 , 56 and tasks are x , y and z one of the 15 possible ways of forming teams is 12 , 34 , 56 . these teams can be assigned to 3 tasks in 3 ! = 6 ways x - - y - - z 12 - - 34 - - 56 12 - - 56 - - 34 34 - - 12 - - 56 34 - - 56 - - 12 56 - - 12 - - 34 56 - - 34 - - 12 so the answer should be 15 * 6 = 90 but now you can fruther decide which task you want to perform first x y or z . . = c
Answer: c
Python program:
a = math.factorial(6)
b = 6 - 2
c = math.factorial(b)
d = a / c
e = d / 2
f = math.factorial(3)
g = e * f
Problem: find the value of ( √ 1.5 ) / ( √ 0.81 ) + ( √ 1.44 ) / ( √ 0.49 ) is
Options: a ) 195 / 63 , b ) 145 / 63 , c ) 155 / 63 , d ) 125 / 63 , e ) 3.075
Rationale: "( √ 1.5 ) / ( √ 0.81 ) + ( √ 1.44 ) / ( √ 0.49 ) = > 3.075 answer is e ."
Answer: e
Python program:
a = math.sqrt(1)
b = math.sqrt(0)
c = a / b
d = math.sqrt(1)
e = math.sqrt(0)
f = d / e
g = c + f
Problem: a completes a piece of work in 3 / 4 of the time in b does , b takes 4 / 5 of the time in c does . they got a profit of rs . 40000 how much b gets ?
Options: a ) 12765 , b ) 121227 , c ) 26887 , d ) 19977 , e ) 26992
Rationale: assume c takes 20 days . now b takes 4 / 5 ( 20 ) = 16 days . a takes 3 / 4 ( 16 ) = 12 now their efficiencies ratio = 1 / 20 : 1 / 16 : 1 / 12 = 12 : 15 : 20 b ' s share in the profit of rs . 40000 = 15 / 47 ( 40000 ) = rs . 12765 answer : a
Answer: a
Python program:
a = 1000 + 1000 
b = 40000 / 4
c = a + b 
d = const_60 * 10
e = d + 100 
f = const_60 + 5 
g = e + f 
h = c + g
Problem: the sum of two consecutive number is 87 . which is the larger number ?
Options: a ) 42 , b ) 43 , c ) 44 , d ) 45 , e ) 46
Rationale: "let consecutive number be x , x + 1 therefore sum of the consecutive number is x + x + 1 = 87 2 x + 1 = 87 2 x = 86 x = 43 therefore larger number is x + 1 = 44 answer : c"
Answer: c
Python program:
a = 87 - 10
b = a - 2
c = b / 4
d = c + 2 
e = d + 2 
f = e ** 2
g = 87 - 10
h = g - 2
i = h / 4
j = i + 2 
k = j + 2 
l = k + 2 
m = l ** 2
n = f + m 
o = 87 - 10
p = o - 2
q = p / 4
r = q ** 2
s = 87 - 10
t = s - 2
u = t / 4
v = u + 2 
w = v ** 2
x = r + w 
y = n + x
Problem: right triangle pqr is to be constructed in the xy - plane so that the right angle is at p and pr is parallel to the x - axis . the x and y coordinates of p , q and r are to be integers that satisfy the inequalitites - 4 ≤ x ≤ 5 and 6 ≤ y ≤ 16 . how many different triangles with these properties could be constructed ?
Options: a ) 110 , b ) 1100 , c ) 9900 , d ) 10000 , e ) 12100
Rationale: total values for x = 10 ; y = 11 x 1 , y 1 = 10 * 11 . . . . . . . . . . . . . . . . . . . . . . . coordinates of 1 st pnt x 2 , y 2 = 9 * 1 ( y 2 = y 1 ) . . . . . . . . . . . . . . . coordinates of 2 nd pnt y coordinates will be same as that of 1 st pnt bcoz it is parallel to x axis x 3 , y 3 = 1 * 10 ( x 2 = x 3 ) . . . . . . . . . . coordinates of 3 rd pt . x coordinates will be same as that of 2 nd point bcoz to make a right angle it has to be parallel to y axis tot ways = 10 * 11 * 9 * 1 * 1 * 10 = 9900 ans : c
Answer: c
Python program:
a = 10 - 1
b = 6 + 4 
c = 16 - 5
d = b * c
e = a * d
f = e * 10
Problem: when a student joe , weighing 40 kg , joins a group of students whose average weight is 30 kg , the average weight goes up by 1 kg . subsequently , if two students , excluding joe , leave the group the average weight comes back to 30 kg . what is the difference between the average weight of the two students who left and the weight of joe ?
Options: a ) 5 kg , b ) 11 kg , c ) 30 kg , d ) 36.5 kg , e ) 71 kg
Rationale: "after two persons leave the group the average remains the same . that means the weight of the two persons = 40 + 30 = 70 so , the average the two persons = 35 that gives the answer 40 - 35 = 5 answer a"
Answer: a
Python program:
a = 30 + 1 
b = 40 - a
c = 30 * b
d = c + 40 
e = 30 + 1 
f = 40 - e
g = f - 1
h = g * 30
i = d - h
j = i / 2
k = 40 - j
Problem: a certain clock marks every hour by striking a number of times equal to the hour , and the time required for a stroke is exactly equal to the time interval between strokes . at 6 : 00 the time lapse between the beginning of the first stroke and the end of the last stroke is 33 seconds . at 12 : 00 , how many seconds elapse between the beginning of the first stroke and the end of the last stroke ?
Options: a ) a . 72 , b ) b . 50 , c ) c . 48 , d ) d . 69 , e ) e . 44
Rationale: "at 6 : 00 it ' ll chime 6 times . if we assume that the time taken to chime is x , then time between chimes is also x . so you have 6 chimes , which is 6 x and 5 time intervals between chimes . this means that 11 x = 33 seconds . thus x = 3 seconds . by a similar logic , at 12 : 00 , there are 12 chimes and 11 intervals so the total time is ( 12 + 11 ) x = 23 x = 69 seconds . answer d"
Answer: d
Python program:
a = 1 + 4 
b = 6 + a 
c = 33 / b
d = 1 + 4 
e = 6 + d 
f = 12 + e 
g = c * f