euclaise/mathqa_programs huggingface dataset:
Problem: a large box contains 19 small boxes and each small box contains 25 chocolate bars . how many chocolate bars are in the large box ?
Options: a ) 475 , b ) 350 , c ) 450 , d ) 550 , e ) 650
Rationale: "the number of chocolate bars is equal to 19 * 25 = 475 correct answer a"
Answer: a
Python program:
a = 19 * 25
Problem: a store has 10 bottles of juice , including 6 bottles of apple juice . in the evening , 6 bottles of juice are sold one by one . what is the probability of selling 4 bottles of apple juice among the 6 bottles ? assume that every bottle has an equal chance of being bought .
Options: a ) 2 / 5 , b ) 3 / 5 , c ) 2 / 3 , d ) 1 / 2 , e ) 3 / 7
Rationale: "the total number of ways to sell 6 bottles from 10 is 10 c 6 = 210 . the number of ways to sell 4 bottles of apple juice is 6 c 4 * 4 c 2 = 15 * 6 = 90 p ( selling 4 bottles of apple juice ) = 90 / 210 = 9 / 21 = 3 / 7 the answer is e ."
Answer: e
Python program:
a = math.comb(6, 4)
b = math.comb(10, 6)
c = a / b
Problem: in a class of 50 students , 18 take chorus , 26 take band , and 2 take both chorus and band . how many students in the class are not enrolled in either chorus or band ?
Options: a ) 8 , b ) 12 , c ) 15 , d ) 16 , e ) 18
Rationale: 16 + 2 + 24 + x = 50 42 + x = 50 x = 8 students a )
Answer: a
Python program:
a = 18 - 2
b = 26 - 2
c = a + b 
d = c + 2 
e = 50 - d
Problem: a shopkeeper sold an article offering a discount of 5 % and earned a profit of 34.9 % . what would have been the percentage of profit earned if no discount had been offered ?
Options: a ) 28.5 , b ) 27.675 , c ) 30 , d ) data inadequate , e ) 42
Rationale: "giving no discount to customer implies selling the product on printed price . suppose the cost price of the article is 100 . then printed price = 100 ã — ( 100 + 34.9 ) / ( 100 â ˆ ’ 5 ) = 142 hence , required % profit = 142 â € “ 100 = 42 % answer e"
Answer: e
Python program:
a = 100 + 34 
b = a * 100
c = 100 - 5
d = b / c
e = d - 100
Problem: how long will a boy take to run round a square field of side 30 meters , if he runs at the rate of 12 km / hr ?
Options: a ) 52 sec , b ) 45 sec , c ) 60 sec , d ) 25 sec , e ) 36 sec
Rationale: "speed = 12 km / hr = 12 * 5 / 18 = 10 / 3 m / sec distance = 30 * 4 = 120 m time taken = 120 * 3 / 10 = 36 sec answer is e"
Answer: e
Python program:
a = 30 * 4
b = 1000 / 3600
c = 12 * b
d = a / c
Problem: the number of timeshare condos available at sunset beach is 2 / 5 the number of timeshare condos available at playa del mar . if the total number of timeshare condos available at the two beaches combined is 280 , what is the difference between the number of condos available at sunset beach and the number of condos available at playa del mar ?
Options: a ) 60 , b ) 90 , c ) 120 , d ) 150 , e ) 240
Rationale: "let x be the number of timeshare condos available at playa del mar . then number of timeshare condos available at sunset beach = 3 / 5 x we know , x + 2 / 5 x = 280 hence , x = 200 . so , number of timeshare condos available at playa del mar = 200 the difference between the number of condos available at sunset beach and the number of condos available at playa del mar = x - 2 / 5 x = 2 / 5 x = 3 / 5 ( 200 ) = 120 the correct answer is c"
Answer: c
Python program:
a = 280 * 2
b = a / 5
c = 2 * 5
d = b + c
Problem: the price of a coat in a certain store is $ 500 . if the price of the coat is to be reduced by $ 350 , by what percent is the price to be reduced ?
Options: a ) 70 % , b ) 15 % , c ) 20 % , d ) 25 % , e ) 30 %
Rationale: "price of a coat in a certain store = $ 500 the price of the coat is to be reduced by $ 350 % change = ( final value - initial value ) * 100 / initial value % reduction = ( reduction in price ) * 100 / initial value i . e . % reduction = ( 350 ) * 100 / 500 = 70 % answer : option a"
Answer: a
Python program:
a = 350 / 500
b = a * 100
Problem: ratio of two numbers x and y is 7 : 9 . if x is increased by 20 % and y is increased by 33 then the new ratio becomes 1 : 5 . what is the ratio 2 y : ( x + 4 )
Options: a ) 18 : 11 , b ) 8 : 1 , c ) 11 : 18 , d ) 1 : 8 , e ) 1 : 1
Rationale: let : x = 7 n y = 9 n 8.4 n / ( 9 n + 33 ) = 1 / 5 42 n = 9 n + 33 n = 1 so , x = 7 ; y = 9 2 y / ( x + 4 ) = 18 / 11 answer = a
Answer: a
Python program:
a = 100 + 20 
b = a / 100
c = b * 5
d = 9 / 7
e = c - d
f = 33 / e
g = 9 / 7
h = f * g
i = 2 * h
j = 100 + 20 
k = j / 100
l = k * 5
m = 9 / 7
n = l - m
o = 33 / n
p = o + 4 
q = i / p
Problem: of 70 players on a football team , 52 are throwers . the rest of the team is divided so one third are left - handed and the rest are right handed . assuming that all throwers are right handed , how many right - handed players are there total ?
Options: a ) 54 , b ) 59 , c ) 63 , d ) 64 , e ) 92
Rationale: "total = 70 thrower = 52 rest = 70 - 52 = 18 left handed = 18 / 3 = 6 right handed = 12 if all thrower are right handed then total right handed is 52 + 12 = 64 so d . 64 is the right answer"
Answer: d
Python program:
a = 1 / 3
b = 1 - a
c = 70 - 52
d = b * c
e = d + 52
Problem: a man can row upstream at 15 kmph and downstream at 35 kmph , and then find the speed of the man in still water ?
Options: a ) 65 , b ) 86 , c ) 30 , d ) 78 , e ) 25
Rationale: "us = 15 ds = 35 m = ( 35 + 15 ) / 2 = 25 answer : e"
Answer: e
Python program:
a = 15 + 35 
b = a / 2
Problem: x and y invested in a business . they earned some profit which they divided in the ratio of 2 : 3 . if x invested rs . 40,000 . the amount invested by y is
Options: a ) rs . 45,000 , b ) rs . 50,000 , c ) rs . 60,000 , d ) rs . 80,000 , e ) none
Rationale: "solution suppose y invested rs . y then , 40000 / y = 2 / 3 ‹ = › y = ( 40000 × 3 / 2 ) . ‹ = › y = 60000 . answer c"
Answer: c
Python program:
a = 1 + 4 
b = a * 1000
c = b * 2
d = c / 3
Problem: if the product of two numbers is 82500 and their h . c . f . is 55 , find their l . c . m .
Options: a ) 2574 , b ) 2500 , c ) 1500 , d ) 1574 , e ) none of these
Rationale: "explanation : hcf * lcm = 82500 , because we know product of two numbers = product of hcf and lcm lcm = 82500 / 55 = 1500 option c"
Answer: c
Python program:
a = 82500 / 55
Problem: what is the area of an obtuse angled triangle whose two sides are 8 and 12 and the angle included between the two sides is 150 o ?
Options: a ) 24 sq units
b ) 48 sq units
c ) 24 under root 3
d ) 48 under root 3
e ) such a triangle does not exist
Rationale: explanatory answer if two sides of a triangle and the included angle ' y ' is known , then the area of the triangle = 1 / 2 * ( product of sides ) * sin y substituting the values in the formula , we get 1 / 2 * 8 * 12 * sin 150 o = 1 / 2 * 8 * 12 * 1 / 2 . note : sin 150 o = 1 / 2 area = 24 sq units . choice a
Answer: a
Python program:
a = math.sqrt(3)
b = a / 2
c = 8 * b
d = c + 12 
e = 8 / 2
f = triangle_area - (
Problem: tabby is training for a triathlon . she swims at a speed of 1 mile per hour . she runs at a speed of 8 miles per hour . she wants to figure out her average speed for these two events . what is the correct answer for her ?
Options: a ) 8 mph , b ) 5.25 mph , c ) 3.5 mph , d ) 4.5 mph , e ) 0.5 mph
Rationale: "( 1 mph + 8 mph ) / 2 = 4.5 mph correct option is : d"
Answer: d
Python program:
a = 1 + 8 
b = a / 2
Problem: the average age of boys in a class is 16 years and that of the girls is 15 years . what is the average age for the whole class ?
Options: a ) 15 , b ) 16 , c ) 15.5 , d ) insufficient data , e ) 17
Rationale: explanation : we do not have the number of boys and girls . hence we can not find out the answer . answer : option d
Answer: d
Python program:
a = 16 - 15
Problem: there were totally 100 men . 84 are married . 75 have t . v , 85 have radio , 70 have a . c . how many men have t . v , radio , a . c and also married ?
Options: a ) 11 , b ) 12 , c ) 13 , d ) 14 , e ) 15
Rationale: "100 - ( 100 - 84 ) - ( 100 - 75 ) - ( 100 - 85 ) - ( 100 - 70 ) = 100 - 16 - 25 - 15 - 30 = 100 - 86 = 14 answer : d"
Answer: d
Python program:
a = 100 - 84
b = 100 - 75
c = a + b 
d = 100 - 85
e = c + d 
f = 100 - 70
g = e + f 
h = 100 - g
Problem: excluding stoppages , the average speed of a bus is 60 km / hr and including stoppages , the average speed of the bus is 35 km / hr . for how many minutes does the bus stop per hour ?
Options: a ) 22 , b ) 88 , c ) 24 , d ) 20 , e ) 99
Rationale: "in 1 hr , the bus covers 60 km without stoppages and 35 km with stoppages . stoppage time = time take to travel ( 60 - 35 ) km i . e 25 km at 60 km / hr . stoppage time = 25 / 60 hrs = 24 min . answer : c"
Answer: c
Python program:
a = 1 * const_60
b = 35 / 60
c = b * const_60
d = a - c
Problem: one paper sheet can be used to create 8 paper boats or 6 paper planes . if total exact 80 paper toys are to be made , minimum how many sheets need to be used to make paper boats ?
Options: a ) 5 , b ) 4 , c ) 3 , d ) 2 , e ) 1
Rationale: let us say x sheets are used to create paper boats and y sheets are used to create paper planes . since total 80 paper toys are to be created , 8 x + 6 y = 80 . = > 8 x = 80 - 6 y = > x = 10 - ( 6 / 8 ) y = > x = 10 - ( 3 / 4 ) y to minimize x , we need to maximize y . and y needs to be multiple of 4 . y = 4 , x = 10 - ( 3 / 4 ) 4 = 7 y = 8 , x = 10 - ( 3 / 4 ) 8 = 4 y = 12 , x = 10 - ( 3 / 4 ) 12 = 1 beyond this , x will become negative for greater values of y . so , minimum 1 sheet is required to be used for creating paper boats . answer : e
Answer: e
Python program:
a = 80 / 8
b = a / 10
Problem: the h . c . f . of two numbers is 12 and their l . c . m . is 600 . if one of the number is 60 , find the other ?
Options: a ) 100 , b ) 240 , c ) 120 , d ) 200 , e ) 150
Rationale: "other number = 12 * 600 / 60 = 120 answer is c"
Answer: c
Python program:
a = 12 * 60
Problem: 1604 x 1604 = ?
Options: a ) a ) 2572816 , b ) b ) 3624216 , c ) c ) 3624316 , d ) d ) 3625116 , e ) e ) 3625216
Rationale: "1604 x 1604 = ( 1604 ) 2 = ( 1600 + 4 ) 2 = ( 1600 ) 2 + ( 4 ) 2 + ( 2 x 1600 x 4 ) = 2560000 + 16 + 12800 . = 2572816 . a )"
Answer: a
Python program:
a = 1604 / 1604
b = a * 100
Problem: if abc is a quarter circle and a smaller circle is inscribed in it ; if radius of quarter circle is 1.414 units . find the radius of smaller circle
Options: a ) 0.586
b ) 0.687
c ) 0.784
d ) 0.874
e ) 0.974
Rationale: if r be radius of smaller circle then distance b / n centres = √ 2 * r so , r + r √ 2 = r here , r = 1.414 = √ 2 = > r = ( √ 2 - 1 ) r r = 0 . 586 unit answer : a
Answer: a
Python program:
a = 2 - 1
Problem: a bag of potatoes weighs 16 kg divided by a quarter of its weight . how much does the bag weigh ?
Options: a ) 4 kg , b ) 8 kg , c ) 7 kg , d ) 3 kg , e ) 9 kg
Rationale: b 8 kg 8 kg : 16 / 2
Answer: b
Python program:
a = 16 / 2
Problem: the cost price of a radio is rs . 1590 and it was sold for rs . 1450 , find the loss % ?
Options: a ) 8 % , b ) 12 % , c ) 10 % , d ) 14 % , e ) 21
Rationale: "1590 - - - - 140 100 - - - - ? = > 8 % answer : a"
Answer: a
Python program:
a = 1590 - 1450
b = a / 1590
c = b * 100
Problem: a retailer bought a machine at a wholesale price of $ 90 and later on sold it after a 10 % discount of the retail price . if the retailer made a profit equivalent to 20 % of the whole price , what is the retail price of the machine ?
Options: a ) 81 , b ) 100 , c ) 120 , d ) 135 , e ) 160
Rationale: "my solution : wholesale price = 90 retail price , be = x he provides 10 % discount on retail price = x - 10 x / 100 this retail price = 20 % profit on wholesale price x - 10 x / 100 = 90 + 1 / 5 ( 90 ) x = 120 ; answer : c"
Answer: c
Python program:
a = 90 * 20
b = a / 100
c = 90 + b 
d = c * 100
e = 3 * 3
f = e * 10
g = d / f
Problem: what is the least number should be added to 1056 , so the sum of the number is completely divisible by 27 ?
Options: a ) 21 , b ) 22 , c ) 23 , d ) 24 , e ) 25
Rationale: "( 1056 / 27 ) gives remainder 3 24 + 3 = 27 , so we need to add 24 d"
Answer: d
Python program:
a = 1056 / 27
b = math.floor(a)
c = b + 1 
d = c * 27
e = d - 1056
Problem: if 30 % of the 880 students at a certain college are enrolled in biology classes , how many students at the college are not enrolled in a biology class ?
Options: a ) 620 , b ) 630 , c ) 616 , d ) 600 , e ) 650
Rationale: "we know 37.5 % people study biology , therefore the no of people not studying = 100 - 30 = 70 % > therefore the people not studying biology out of a total 880 people are = 70 % of 880 > ( 70 / 100 ) * 880 = 616 people c"
Answer: c
Python program:
a = 880 / 100
b = 100 - 30
c = a * b
Problem: the average of 9 observations was 9 , that of the 1 st of 5 being 10 and that of the last 5 being 8 . what was the 5 th observation ?
Options: a ) 6 , b ) 9 , c ) 8 , d ) 2 , e ) 3
Rationale: "1 to 9 = 9 * 9 = 81 1 to 5 = 5 * 10 = 50 5 to 9 = 5 * 8 = 40 5 th = 50 + 40 = 90 – 81 = 9 answer : b"
Answer: b
Python program:
a = 10 * 5
b = 9 * 5
c = a + b 
d = 9 * 9
e = c - d
Problem: in a certain company 20 % of the men and 40 % of the women attended the annual company picnic . if 30 % of all the employees are men . what % of all the employee went to the picnic ?
Options: a ) 33 % , b ) 34 % , c ) 35 % , d ) 36 % , e ) 37 %
Rationale: "total men in company 30 % means total women in company 70 % ( assume total people in company 100 % ) no of men employees attended picnic = 30 x ( 20 / 100 ) = 6 no of women employees attended picnic = 70 x ( 40 / 100 ) = 28 total percentage of employees attended the picnic = 6 + 28 = 34 % answer : b"
Answer: b
Python program:
a = 30 / 100
b = 20 / 100
c = a * b
d = 100 - 30
e = d / 100
f = 40 / 100
g = e * f
h = c + g 
i = h * 100
Problem: 30 is what percent of 100 ?
Options: a ) 35 % , b ) 30 % , c ) 45 % , d ) 50 % , e ) 55 %
Rationale: 30 / 100 × 100 = 30 % answer : b
Answer: b
Python program:
a = 30 / 100
b = a * 100
Problem: how many liters of a 40 % iodine solution need to be mixed with 35 liters of a 20 % iodine solution to create a 31 % iodine solution ?
Options: a ) 35 , b ) 42 , c ) 100 , d ) 105 , e ) 140
Rationale: "solution 1 : assume the iodine solution to be mixed = x lts . iodine = 0.4 x lts , water = 0.6 x lts . solution 2 : 35 liters of a 20 % iodine solution iodine = 7 lts , water = 28 lts . total iodine = 0.4 x + 7 total water = 0.6 x + 28 the resultant is a 35 % idoine solution . hence ( 0.4 x + 7 ) / ( x + 35 ) = 31 / 100 40 x + 700 = 31 x + 1085 9 x = 385 x = 42 lts correct option : b"
Answer: b
Python program:
a = 35 * 20
b = a / 100
c = b * 31
d = 35 * 20
e = d / 100
f = e * 20
g = c - f
h = 40 / 100
i = 20 * h
j = 35 * 20
k = j / 100
l = i - k
m = g / l
n = m + 35
Problem: if k ^ 3 is divisible by 180 , what is the least possible value of integer k ?
Options: a ) 12 , b ) 30 , c ) 60 , d ) 90 , e ) 120
Rationale: "180 = 2 ^ 2 * 3 ^ 2 * 5 therefore k must include at least 2 * 3 * 5 = 30 . the answer is b ."
Answer: b
Python program:
a = 180 / 2
b = a / 2
Problem: a clock shows the time as 8 a . m . if the minute hand gains 5 minutes every hour , how many minutes will the clock gain by 6 p . m . ?
Options: a ) 45 minutes , b ) 55 minutes , c ) 35 minutes , d ) 25 minutes , e ) 50 minutes
Rationale: "there are 10 hours in between 8 a . m . to 6 p . m . 10 * 5 = 50 minutes . answer : e"
Answer: e
Python program:
a = 3 + 6 
b = a * 5
Problem: a watch was sold at a loss of 12 % . if it was sold for rs . 140 more , there would have been a gain of 4 % . what is the cost price ?
Options: a ) s . 1000 , b ) s . 875 , c ) s . 1007 , d ) s . 1006 , e ) s . 1002
Rationale: "explanation : 88 % 104 % - - - - - - - - 16 % - - - - 140 100 % - - - - ? = > rs . 875 answer : b"
Answer: b
Python program:
a = 140 * 100
b = 100 + 4 
c = 100 - 12
d = b - c
e = a / d
Problem: a vendor bought toffees at 6 for a rupee . how many for a rupee must he sell to gain 20 % ?
Options: a ) 7 , b ) 6 , c ) 5 , d ) 9 , e ) 1
Rationale: "explanation : c . p . of 6 toffees = re . 1 s . p . of 6 toffees = 120 % of re . 1 = rs . 6 / 5 for rs . 6 / 5 , toffees sold = 6 . for re . 1 . toffees sold = 6 * 5 / 6 = 5 answer : c"
Answer: c
Python program:
a = 20 / 100
b = 1 + a 
c = 6 * b
Problem: ratio between rahul and deepak is 4 : 3 , after 10 years rahul age will be 26 years . what is deepak present age
Options: a ) 12 , b ) 15 , c ) 20 , d ) 22 , e ) 23
Rationale: "explanation : present age is 4 x and 3 x , = > 4 x + 10 = 26 = > x = 4 so deepak age is = 3 ( 4 ) = 12 answer : option a"
Answer: a
Python program:
a = 26 - 10
b = a * 3
c = b / 4
Problem: a man can row downstream at the rate of 10 km / hr and upstream at 4 km / hr . find man ' s rate in still water and the rate of current ?
Options: a ) 9,6 , b ) 7,3 , c ) 9,3 , d ) 6,6 , e ) none of these
Rationale: "explanation : rate of still water = 1 / 2 ( 10 + 4 ) = 7 km / hr rate of current = 1 / 2 ( 10 - 4 ) = 3 km / hr answer : option b"
Answer: b
Python program:
a = 10 - 4
b = a / 2
Problem: worker a takes 8 hours to do a job . worker b takes 12 hours to do the same job . how long it take both a & b , working together but independently , to do the same job ?
Options: a ) 40 days , b ) 24 / 5 days , c ) 39 / 9 days , d ) 30 / 9 days , e ) 60 / 9 days
Rationale: "a ' s one hour work = 1 / 8 . b ' s one hour work = 1 / 12 . ( a + b ) ' s one hour work = 1 / 8 + 1 / 12 = 5 / 24 . both a & b can finish the work in 24 / 5 days b"
Answer: b
Python program:
a = 1 / 8
b = 1 / 12
c = a + b 
d = 1 / c
Problem: denominator of a number is 4 less than the numerator . if 6 is added to the numerator , it becomes 3 times the denominator . find the denominator .
Options: a ) 1 , b ) 3 , c ) 5 , d ) 7 , e ) 9
Rationale: let the numerator be x and denominator be y . then = > x = y + 4 and 6 + x = 3 * y = > 6 + y + 4 = 3 * y = > 2 y = 10 = > y = 5 option c
Answer: c
Python program:
a = 4 + 6 
b = 3 - 1
c = a / b
Problem: if m is an integer such that ( - 2 ) ^ 2 m = 2 ^ ( 3 - m ) then m = ?
Options: a ) 1 , b ) 2 , c ) 3 , d ) 5 , e ) 6
Rationale: "( - 2 ) ^ ( 2 m ) = 4 ^ m and 2 ^ ( 3 - m ) = 4 ^ ( ( 3 - m ) / 2 ) therefore , m = ( 3 - m ) / 2 2 m = 3 - m m = 1 answer a"
Answer: a
Python program:
a = 2 + 1 
b = 3 / a
Problem: a rectangular paper when folded into two congruent parts had a perimeter of 34 cm foer each part folded along one set of sides and the same is 38 cm . when folded along the other set of sides . what is the area of the paper ?
Options: a ) 140
b ) 388
c ) 238
d ) 119
e ) 112
Rationale: when folded along the breadth we have 2 ( l / 2 + b ) = 34 or l + 2 b = 34 . . . . . . . . . . . ( 1 ) when folded along the length , we have 2 ( l + b / 2 ) = 38 or 2 l + b = 38 . . . . . ( 2 ) from 1 & 2 we get l = 14 and b = 10 area of the paper = 14 * 10 = 140 sq cmv answer : a
Answer: a
Python program:
a = 10 * 2
b = 34 - a
c = b * 10
Problem: given a certain number ( x ) , find x given that 5.76 is 12 % of 40 % of x ?
Options: a ) 130 , b ) 120 , c ) 140 , d ) 100 , e ) 300
Rationale: using elimination method to pick the correct option it will be discovered that option b i . e 120 is the correct option because 40 % of 120 is 48 and 12 % of 48 is 5.76 . answer : b
Answer: b
Python program:
a = 100 - 12
b = 5 * 76
c = b / 12
d = c + 5 
e = 100 - 40
f = d * e
g = f / 40
h = 100 - 12
i = 5 * 76
j = i / 12
k = j + 5 
l = g + k
Problem: a man sells an article at a profit of 25 % . if he had bought it at 20 % less and sold it for rs . 12.60 less , he would have gained 30 % . find the cost of the article .
Options: a ) 30 , b ) 40 , c ) 50 , d ) 60 , e ) 70
Rationale: "let c . p = 100 gain = 25 % s . p = 125 supposed c . p = 80 gain = 30 % s . p = ( 130 * 80 ) / 100 = 104 diff = ( 125 - 104 ) = 21 diff 21 when c . p = 100 then diff 12.60 when c . p = ( 100 * 12.60 ) / 21 = 60 answer : d"
Answer: d
Python program:
a = 12 * 60
b = 25 + 100 
c = 30 + 100 
d = 100 - 20
e = c * d
f = e / 100
g = b - f
h = a / g
Problem: a 270 m long train running at the speed of 120 km / hr crosses another train running in opposite direction at the speed of 80 km / hr in 9 sec . what is the length of the other train ?
Options: a ) 230 , b ) 200 , c ) 250 , d ) 300 , e ) 500
Rationale: "answer : option a explanation : relative speed = 120 + 80 = 200 km / hr . = 200 * 5 / 18 = 500 / 9 m / sec . let the length of the other train be x m . then , ( x + 270 ) / 9 = 500 / 9 = > x = 230 . answer a"
Answer: a
Python program:
a = 120 + 80 
b = a * const_0_2778
c = b * 9
d = c - 270
Problem: two numbers are in respectively 20 % and 50 % more than a third number . the ratio of the two numbers is ?
Options: a ) 2 : 5 , b ) 1 : 2 , c ) 4 : 5 , d ) 3 : 7 , e ) 5 : 6
Rationale: "let the 3 rd number be x then , first number = 120 % of x = 120 x / 100 = 6 x / 5 second number = 150 % of x = 150 x / 100 = 3 x / 2 ratio of first two numbers = 6 x / 5 : 3 x / 2 = 12 x : 15 x = 4 : 5 answer is c"
Answer: c
Python program:
a = 100 + 20 
b = 100 + 50 
c = a / b
Problem: a gardener wants to plant trees in his garden in such a way that the number of trees in each row should be the same . if there are 4 rows or 5 rows or 6 rows , then no tree will be left . find the least number of trees required
Options: a ) 22 , b ) 60 , c ) 28 , d ) 76 , e ) 21
Rationale: explanation : the least number of trees that are required = lcm ( 4 , 5 , 6 ) = 60 . answer : b
Answer: b
Python program:
a = 6 * 5
b = a * 4
c = b / 2
Problem: a batsman ' s avg in 12 innings is 24.00 . if his avg is to be double of the no of innings ( 15 innings ) , what should he score in the remaining 3 innings ( avg ) ?
Options: a ) 143 , b ) 144 , c ) 145 , d ) 146 , e ) 147
Rationale: let total runs done by a batsman in 12 innings be x therefore , x / 12 = 24 that means x = 12 * 24 = 288 runs for 15 innings , avg was doubled i . e . . 48.00 therefore , ( x + y ) / 15 = 48 where y is the no of runs done in last 3 innings y = 432 therefore average is 432 / 3 = 144 answer : b
Answer: b
Python program:
a = 24 * 2
b = 15 * a
c = 12 * 24
d = b - c
e = d / 3
Problem: in what time will a railway train 80 m long moving at the rate of 40 kmph pass a telegraph post on its way ?
Options: a ) 3 , b ) 5 , c ) 4 , d ) 6.4 , e ) 7.2
Rationale: "t = 80 / 40 * 18 / 5 = 7.2 sec answer : e"
Answer: e
Python program:
a = 40 * const_0_2778
b = 80 / a
Problem: the number of people who purchased book a is twice the number of people who purchased book b . the number of people who purchased both books a and b is 500 , which is twice the number of people who purchased only book b . what is the number of people z who purchased only book a ?
Options: a ) 250 , b ) 500 , c ) 750 , d ) 1000 , e ) 1500
Rationale: "this is best solved using overlapping sets or a venn diagram . we know that a = 2 b , and that 500 people purchased both a and b . further , those purchasing both was double those purchasing b only . this gives us 250 people purchasing b only . with the 500 that pruchased both , we have a total of 750 that purchased b and this is 1 / 2 of those that purchased a . so , 1500 purchased a . less the 500 that purchased both , z = 1000 purchased a only . ( this is much simpler to solve using the venn diagram ) . correct answer is d . 1000"
Answer: d
Python program:
a = 500 / 2
b = 500 + a 
c = b * 2
d = c - 500
Problem: if the sum of two numbers is 20 and the sum of their squares is 200 , then the product of the numbers is
Options: a ) 40 , b ) 44 , c ) 100 , d ) 88 , e ) 48
Rationale: "according to the given conditions x + y = 20 and x ^ 2 + y ^ 2 = 200 now ( x + y ) ^ 2 = x ^ 2 + y ^ 2 + 2 xy so 20 ^ 2 = 200 + 2 xy so xy = 200 / 2 = 100 answer : c"
Answer: c
Python program:
a = 20 ** 2
b = a - 200
c = b / 2
Problem: ratio of two numbers x and y is 3 : 7 . if x is increased by 50 % and y is increased by 2 then the new ratio becomes 1 : 2 . what is the ratio 2 y : ( 2 x + 6 )
Options: a ) 16 : 15 , b ) 4 : 5 , c ) 7 : 12 , d ) 4 : 9 , e ) 6 : 5
Rationale: "let : x = 3 n y = 7 n 4.5 n / ( 7 n + 5 ) = 1 / 2 9 n = 7 n + 2 n = 1 so , x = 3 ; y = 7 2 y / ( 2 x + 6 ) = 14 / 12 = 7 : 6 answer = c"
Answer: c
Python program:
a = 100 + 50 
b = a / 100
c = b * 2
d = 7 / 3
e = c - d
f = 2 / e
g = 7 / 3
h = f * g
i = 2 * h
j = 100 + 50 
k = j / 100
l = k * 2
m = 7 / 3
n = l - m
o = 2 / n
p = o + 2 
q = i / p