euclaise/mathqa_programs huggingface dataset:
Problem: of the two square fields , the area of the one is 1 hectare , while anothe one is broader by 1 % . there differences in area is :
Options: a ) 201 m ( power ) 2
b ) 220 m ( power ) 2
c ) 211 m ( power ) 2
d ) 219 m ( power ) 2
e ) 205 m ( power ) 2
Rationale: area of one square field = 10000 m ( power ) 2 10000 × 1 = 10000 side of this field = √ 10000 m = 100 m side of another square = 101 m difference of areas = [ 101 ( power ) 2 - 100 ( power ) 2 ] m ( power ) 2 [ 101 + 100 ] [ 101 - 100 ] m ( power ) 2 ( 201 ) ( 1 ) m 2 = 201 m ( power ) 2 answer is a .
Answer: a
Python program:
a = 10 * 1000
b = math.sqrt(a)
c = 1 + b 
d = square_area - (
Problem: if there are 4 peanuts in a box and mary puts 8 more peanuts inside , how many peanuts are in the box ?
Options: a ) 8 , b ) 9 , c ) 10 , d ) 11 , e ) 12
Rationale: "8 + 4 = 12 correct answer is e ) 12"
Answer: e
Python program:
a = 4 + 8
Problem: rs . 6000 is lent out in two parts . one part is lent at 5 % p . a simple interest and the other is lent at 10 % p . a simple interest . the total interest at the end of one year was rs . 450 . find the ratio of the amounts lent at the lower rate and higher rate of interest ?
Options: a ) 5 : 1 , b ) 5 : 5 , c ) 5 : 8 , d ) 5 : 4 , e ) 5 : 2
Rationale: let the amount lent at 5 % be rs . x amount lent at 10 % is rs . ( 6000 - x ) total interest for one year on the two sums lent = 5 / 100 x + 10 / 100 ( 6000 - x ) = 600 - 1 x / 20 = > 600 - 1 / 20 x = 450 = > x = 3000 amount lent at 10 % = 3000 required ratio = 3000 : 3000 = 5 : 5 answer : b
Answer: b
Python program:
a = 450 * 100
b = 6000 * 5
c = a - b
d = 10 - 5
e = c / d
f = 450 * 100
g = 6000 * 5
h = f - g
i = 10 - 5
j = h / i
k = e / j
Problem: if rs . 1440 / - are divided among a , b and c so that a receives 1 / 3 rd as much as b and b receives 1 / 4 th as much as c . the amount b received is ?
Options: a ) 250 , b ) 270 , c ) 310 , d ) 330 , e ) 350
Rationale: a : b : c = 1 : 3 : 12 total parts = 16 b ' s share is = 3 parts 16 - - - - - > 1440 1 - - - - - > 90 3 - - - - - > 270 ( b ' s share is 270 ) b )
Answer: b
Python program:
a = 3 * 4
b = 1 / a
c = 1 / 4
d = b + c 
e = d + 1 
f = 1440 / e
g = f / 4
Problem: 375 metres long yard , 26 trees are palnted at equal distances , one tree being at each end of the yard . what is the distance between 2 consecutive trees
Options: a ) 10 , b ) 12 , c ) 14 , d ) 16 , e ) 15
Rationale: "26 trees have 25 gaps between them , required distance ( 375 / 25 ) = 15 e"
Answer: e
Python program:
a = 26 - 2
b = a + 1 
c = 375 / b
Problem: when toys are grouped into 12 and 18 , always 3 toys remain ungrouped . what is the minimum number of toys to be added so that when they are grouped into 7 , no toys will remain ungrouped ?
Options: a ) 0 , b ) 1 , c ) 2 , d ) 3 , e ) 4
Rationale: t = 12 a + 3 = 18 b + 3 2 a = 3 b - - > min ( a , b ) = ( 3,2 ) so minimum number of toys - - > 12 * 3 + 3 = 39 when toys are grouped into 7 , 4 will remain ungrouped so in order to make another group of 7 toys - - > 7 - 4 = 3 toys at least to be added . answer : d
Answer: d
Python program:
a = 2 + 4 
b = 7 * a
c = math.lcm(12, 18)
d = c + 3 
e = b - d
Problem: in a particular state , 62 % of the counties received some rain on monday , and 54 % of the counties received some rain on tuesday . no rain fell either day in 28 % of the counties in the state . what percent of the counties received some rain on monday and tuesday ?
Options: a ) 25 % , b ) 44 % , c ) 56 % , d ) 62 % , e ) 70 %
Rationale: "62 + 54 + 28 = 144 % the number is 44 % above 100 % because 44 % of the counties were counted twice . the answer is b ."
Answer: b
Python program:
a = 62 + 54 
b = 100 - 28
c = a - b
Problem: the average temperature for monday , tuesday , wednesday and thursday was 48 degrees and for tuesday , wednesday , thursday and friday was 46 degrees . if the temperature on monday was 41 degrees . find the temperature on friday ?
Options: a ) 65 degrees , b ) 73 degrees , c ) 37 degrees , d ) 34 degrees , e ) 33 degrees
Rationale: "m + tu + w + th = 4 * 48 = 192 tu + w + th + f = 4 * 46 = 184 m = 41 tu + w + th = 192 - 41 = 151 f = 184 – 151 = 33 answer : e"
Answer: e
Python program:
a = 48 * 4
b = 46 * 4
c = a - b
d = 41 - c
Problem: a courtyard is 18 meter long and 16 meter board is to be paved with bricks of dimensions 20 cm by 10 cm . the total number of bricks required is ?
Options: a ) 22877 , b ) 27778 , c ) 20000 , d ) 27999 , e ) 14400
Rationale: "number of bricks = courtyard area / 1 brick area = ( 1800 × 1600 / 20 × 10 ) = 14400 answer : e"
Answer: e
Python program:
a = 18 * 100
b = 16 * 100
c = a * b
d = 20 * 10
e = c / d
Problem: a can finish a work in 21 days and b can do the same work in 15 days . b worked for 10 days and left the job . in how many days , a alone can finish the remaining work ?
Options: a ) 6 , b ) 5 , c ) 5.5 , d ) 7 , e ) 8
Rationale: "b ' s 10 day ' s work = ( 1 x 10 ) = 2 . 15 3 remaining work = ( 1 - 2 ) = 1 . 3 3 now , 1 work is done by a in 1 day . 21 therefore 1 work is done by a in ( 21 x 1 ) = 7 days . d"
Answer: d
Python program:
a = 1 / 15
b = a * 10
c = b * 21
d = c / 2
Problem: a boat having a length 3 m and breadth 2 m is floating on a lake . the boat sinks by 1 cm when a man gets on it . the mass of man is :
Options: a ) 12 kg , b ) 60 kg , c ) 72 kg , d ) 96 kg , e ) none of these
Rationale: "solution volume of water displaced = ( 3 × 2 × 0.01 ) m 3 = 0.06 m 3 . ∴ mass of man = volume of water displaced × density of water = ( 0.06 × 100 ) kg = 60 kg . answer b"
Answer: b
Python program:
a = 3 * 2
b = 1 / 100
c = a * b
d = c * 1000
Problem: what profit percent is made by selling an article at a certain price , if by selling at 2 / 3 rd of that price , there would be a loss of 16 % ?
Options: a ) 26 % , b ) 28 % , c ) 27 % , d ) 40 % , e ) 70 %
Rationale: "sp 2 = 2 / 3 sp 1 cp = 100 sp 2 = 84 2 / 3 sp 1 = 84 sp 1 = 126 100 - - - 26 = > 26 % answer : a"
Answer: a
Python program:
a = 100 - 16
b = 2 / 3
c = a / b
d = c - 100
Problem: uba capital recently bought brand new vehicles for office use . uba capital only went for toyota and honda and bought less of toyota than honda at the ratio of 4 : 6 . if 40 % of the toyota bought and 60 % of the honda bought were suv ã ¢ â ‚ ¬ â „ ¢ s . how many suv ã ¢ â ‚ ¬ â „ ¢ s did uba capital buy in the aforementioned purchase ?
Options: a ) 66 % , b ) 64 % , c ) 68 % , d ) 52 % , e ) 72 %
Rationale: "let total no of vehicles bought be 100 , toyota 40 and honda 60 , so total number of suv ' s bought for toyota and honda respectively 40 * 40 / 100 = 16 and 60 * 60 / 100 = 36 so total 52 suv ' s were bought out of 100 vehicles bought . . so required % is 52 % answer : d"
Answer: d
Python program:
a = 4 * 6
b = 6 * 4
c = a + b 
d = 100 - c
Problem: an investor can sell her microtron stock for 36 $ per share and her dynaco stock for 56 $ per share , if she sells 300 shares altogether , some of each stock , at an average price per share of 40 $ , how many shares of dynaco stock has she sold ?
Options: a ) 52 , b ) 75 , c ) 60 , d ) 136 , e ) 184
Rationale: "w 1 / w 2 = ( a 2 - aavg ) / ( aavg - a 1 ) = ( 56 - 40 ) / ( 40 - 36 ) = 16 / 4 = 4 / 1 = number of microtron stocks / number of dynaco stocks so for every 4 microtron stock , she sold 1 dynaco stock . so out of 300 total stocks , ( 1 / 5 ) th i . e . 300 / 5 = 60 must be dynaco stock . answer ( c )"
Answer: c
Python program:
a = 56 - 36
b = 40 / a
c = 300 * b
d = 36 + 56 
e = 56 - 36
f = d / e
g = c / f
Problem: if each edge of cube increased by 20 % , the percentage increase in
Options: a ) 42 , b ) 44 , c ) 48 , d ) 45 , e ) 47
Rationale: "100 × ( 120 ) / 100 × ( 120 ) / 100 = 144 = > 44 % answer is b ."
Answer: b
Python program:
a = 100 + 20 
b = a ** 3
c = 100 ** 3
d = b - c
e = 100 ** 3
f = d / e
g = 100 * f
Problem: if 15 % of 40 is greater than 25 % of a number by 2 , then the number is ?
Options: a ) 12 , b ) 8 , c ) 15 , d ) 20 , e ) 16
Rationale: "let the number be x 50 % of 40 - 25 % of x = 2 25 / 100 x = ( 15 / 100 * 40 ) - 2 x / 4 = 4 x = 16 answer is e"
Answer: e
Python program:
a = 15 / 100
b = a * 40
c = b - 2
d = 25 / 100
e = c / d
Problem: what is the angle between the hands of a clock when time is 8 : 20 ?
Options: a ) 65 deg , b ) 75 deg , c ) 50 deg , d ) 15 deg , e ) 30 deg
Rationale: "angle between two hands = 20 h - 11 / 2 m = 20 * 8 - 20 * 11 / 2 = 160 - 110 = 50 deg answer : c"
Answer: c
Python program:
a = 3 * 2
b = 20 * a
c = b - 8
Problem: month average price per dozen april $ 1.2 may $ 1.20 june $ 3.00 the table above shows the average ( arithmetic mean ) price per dozen of the large grade a eggs sold in a certain store during 3 successive months . if 2 / 3 as many dozen were sold in april as in may , and twice as many were sold in june as in april , what was the average price per dozen of the eggs sold over the 3 - month period ?
Options: a ) 1.8 , b ) 2.2 , c ) 2 , d ) 1.9 , e ) 2.4
Rationale: say x dozen eggs were sold in may . then 2 x / 3 dozen eggs were sold in april and 2 * 2 x / 3 = 4 x / 3 dozen eggs were sold in may . total x + 2 x / 3 + 4 x / 3 = 3 x dozen eggs were sold in three months . total sales : 2 x / 3 * 1.2 + x * 1.2 + 4 x / 3 * 3.00 = $ 6.00 x . the average price per dozen 6.00 x / 3 x = $ 2.00 c
Answer: c
Python program:
a = 2 / 3
b = 3 * a
Problem: walking 7 / 6 of his usual rate , a boy reaches his school 7 min early . find his usual time to reach the school ?
Options: a ) 22 , b ) 28 , c ) 99 , d ) 49 , e ) 66
Rationale: "speed ratio = 1 : 7 / 6 = 6 : 7 time ratio = 7 : 6 1 - - - - - - - - 7 7 - - - - - - - - - ? 49 m answer : d"
Answer: d
Python program:
a = 7 * 7
Problem: a company received $ 2 million in royalties on the first $ 10 million in sales and then $ 8 million in royalties on the next $ 100 million in sales . by what percent did the ratio of royalties to sales decrease from the first $ 10 million in sales to the next $ 100 million in sales ?
Options: a ) 30 % , b ) 40 % , c ) 50 % , d ) 60 % , e ) 70 %
Rationale: first find out ( ratio of royalties to sales ) : 2 : 10 first 0.2 8 : 100 second 0.08 decrease = 0.2 - 0.08 = 0.12 percent = ( 0.12 / 0.20 ) = 60 % . answer : d
Answer: d
Python program:
a = 2 / 10
b = 8 / 100
c = a - b
d = 2 / 10
e = c / d
f = e * 100
Problem: the cost price of a radio is rs . 1500 and it was sold for rs . 1200 , find the loss % ?
Options: a ) 18 , b ) 16 , c ) 26 , d ) 17 , e ) 20
Rationale: "explanation : 1500 - - - - 300 100 - - - - ? = > 20 % answer : e"
Answer: e
Python program:
a = 1500 - 1200
b = a / 1500
c = b * 100
Problem: a trailer carries 3 , 4 and 6 crates on a trip . each crate weighs no less than 100 kg . what is the maximum weight of the crates on a single trip ?
Options: a ) 100 , b ) 625 , c ) 600 , d ) 7500 , e ) 375
Rationale: "max no . of crates = 6 . max weight = 100 kg max . weight carried = 6 * 100 = 100 kg = a ."
Answer: a
Python program:
a = 6 * 100
Problem: the toll for crossing a certain bridge is $ 0.70 each crossing . drivers who frequently use the bridge may instead purchase a sticker each month for $ 13.00 and then pay only $ 0.30 each crossing during that month . if a particular driver will cross the bridge twice on each of x days next month and will not cross the bridge on any other day , what is the least value of x for which this driver can save money by using the sticker ?
Options: a ) 14 , b ) 15 , c ) 16 , d ) 28 , e ) 29
Rationale: "option # 1 : $ 0.75 / crossing . . . . cross twice a day = $ 1.5 / day option # 2 : $ 0.30 / crossing . . . . cross twice a day = $ 0.6 / day + $ 13 one time charge . if we go down the list of possible answers , you can quickly see that 14 days will not be worth purchasing the sticker . 1.5 x 14 ( 21 ) is cheaper than 0.6 x 14 + 13 ( 21.4 ) . . . it ' s pretty close so let ' s see if one more day will make it worth it . . . if we raise the number of days to 15 , the sticker option looks like a better deal . . . 1.5 x 15 ( 22.5 ) vs 0.6 x 15 + 13 ( 22 ) . answer : c"
Answer: c
Python program:
a = 0 - 70
b = a * 2
c = 13 / 0
d = c * 2
e = d / 10
f = e * 2
g = 0 - 70
h = g * 2
i = 13 / 0
j = i * 2
k = f + j
Problem: zinc and copper are melted together in the ratio 9 : 11 . what is the weight of melted mixture , if 35.1 kg of zinc has been consumed in it ?
Options: a ) 78 kg , b ) 60 kg , c ) 64 kg , d ) 70 kg , e ) none
Rationale: "sol . for 9 kg zinc , mixture melted = ( 9 + 11 ) kg . for 35.1 kg zinc , mixture , melted = [ 20 / 9 x 35.1 ] kg = 78 kg . answer a"
Answer: a
Python program:
a = 11 / 9
b = a * 35
c = b + 35
Problem: p and q started a business investing rs . 54,000 and rs . 36,000 respectively . out of a total profit of rs . 18,000 , q ' s share is :
Options: a ) 5980 , b ) 5990 , c ) 6000 , d ) 6010 , e ) 6020
Rationale: "ratio of their shares = 54000 : 27000 = 6 : 3 . q ’ s share = rs . 18000 * 3 / 9 = rs . 6000 answer : c"
Answer: c
Python program:
a = 18 + 0 
b = a + 3 
c = 18 + 0 
d = c * 18
e = b * d
f = 18 + 0 
g = e + f 
h = 18 + 0 
i = h * 18
j = 3 * i
k = 18 + 0 
l = j + k 
m = g / l
Problem: two numbers are respectively 71 % and 80 % more than a third number . the percentage that is first of the second is ?
Options: a ) 4 % , b ) 5 % , c ) 6 % , d ) 7 % , e ) 8 %
Rationale: "i ii iii 171 180 100 180 - - - - - - - - - - 171 100 - - - - - - - - - - - ? = > 5 % answer : b"
Answer: b
Python program:
a = 71 + 100 
b = 80 + 100 
c = a / b
d = c * 100
e = 100 - d
Problem: a machine , working at a constant rate , manufactures 20 candles in 40 minutes . how many candles does it make in 1 hr 20 min ?
Options: a ) 25 , b ) 30 , c ) 40 , d ) 45 , e ) 50
Rationale: "change 1 hr 20 min to 80 min . for this , we need to set up a simple proportion of staplers per time 20 / 40 = s / 80 the absolutely worst thing you could do at this point in the problem is to cross - multiply . that would be a supremely unstrategic move . instead , cancel before you multiply . for what we can and can ’ t cancel in a proportion , seethis post . we can cancel the factor of 10 in the 20 and 40 . 2 / 4 = s / 80 1 / 2 = s / 80 ; 1 / 2 * 2 = s / 80 * 2 1 / 1 = s / 40 now that the fraction is entirely simplified , we can cross - multiply . s = 1 * 40 = 40 the machine would be 40 candles in 1 hr 20 min . answer : c ."
Answer: c
Python program:
a = 1 * const_60
b = a + 20 
c = b / 40
d = c * 20
Problem: a person can swim in still water at 4 km / h . if the speed of water 2 km / h , how many hours will the man take to swim back against the current for 8 km ?
Options: a ) 4 , b ) 7 , c ) 8 , d ) 9 , e ) 6
Rationale: "m = 4 s = 2 us = 4 - 2 = 2 d = 8 t = 8 / 2 = 4 answer : a"
Answer: a
Python program:
a = 4 - 2
b = 8 / a
Problem: if a and b are both odd prime numbers and a < b , then how many different positive integer factors does 2 ab have ?
Options: a ) 3 , b ) 4 , c ) 6 , d ) 8 , e ) 12
Rationale: a and b are both odd prime numbers - it means either a or b is not 2 and since prime numbers have only two factors - 1 and the number itself a and b each will have ( 1 + 1 ) = 2 factors hence 2 ab will have ( 1 + 1 ) ( 1 + 1 ) ( 1 + 1 ) = 8 factors d is the answer
Answer: d
Python program:
a = 2 * 4
Problem: rs . 2500 is divided into two parts such that if one part be put out at 5 % simple interest and the other at 6 % , the yearly annual income may be rs . 130 . how much was lent at 5 % ?
Options: a ) 2000 , b ) 2777 , c ) 2688 , d ) 1000 , e ) 2871
Rationale: "( x * 5 * 1 ) / 100 + [ ( 2500 - x ) * 6 * 1 ] / 100 = 130 x = 2000 answer : a"
Answer: a
Python program:
a = 6 * 2500
b = a / 100
c = 130 - b
d = 5 / 100
e = 6 / 100
f = d - e
g = c / f
Problem: find the lowest common multiple of 15 , 25 and 35 .
Options: a ) 360 , b ) 420 , c ) 510 , d ) 525 , e ) 280
Rationale: "lcm = 3 * 5 * 5 * 7 = 525 . answer is d"
Answer: d
Python program:
a = math.lcm(15, 25)
b = math.lcm(a, 35)
Problem: a person travels equal distances with speeds of 5 km / hr , 10 km / hr , 15 km / hr . and takes a total time of 11 minutes . find the total distance ?
Options: a ) 1 km , b ) 1500 mts , c ) 1600 mts , d ) 2 km , e ) 1250 mts
Rationale: "let the each distance be x km total distance = 3 x then total time , ( x / 5 ) + ( x / 10 ) + ( x / 15 ) = 11 / 60 x = 0.5 total distance = 3 * 0.5 = 1.5 km = 1500 meters correct option is b"
Answer: b
Python program:
a = 11 / const_60
b = 1 / 5
c = 1 / 10
d = b + c 
e = 1 / 15
f = d + e 
g = a / f
h = g * 3
i = h * 1000
Problem: a charitable woman gave one penny more than half pennies in her purse to a farmer . afterwards she came across a beggar whom she gave 2 pennies more than half of what she had in her purse . in the end she gave 3 pennies more than half of what she had in her purse and left with a penny with her to a boy . find what she had in the beginning ?
Options: a ) 41 , b ) 42 , c ) 43 , d ) 44 , e ) 45
Rationale: she gave 1 penny more than the half in the purse i . e ( x / 2 + 1 ) now she is left with : : ( x - ( x / 2 + 1 ) ) = ( x - 2 ) / 2 now to the beggar : : she gave 2 pennies more than the half in the purse i . e ( x - 2 ) / 4 + 2 and she is left with : : ( ( x - 2 ) / 2 ) - ( ( x - 2 ) / 4 + 2 ) = ( x - 10 ) / 4 now at last sh gave 3 pennies more then the half she was left with i . e ( ( x - 10 ) / 8 + 3 ) = a so she is left with ( x - 10 ) / 4 - a = ( x - 34 ) / 8 now acc . to quest ( x - 34 ) / 8 = 1 hence x = 42 answer : b
Answer: b
Python program:
a = 1 + 3 
b = a * 2
c = b + 2 
d = c * 2
e = d + 1 
f = e * 2
Problem: if x , y , and z are positive integers , and 2 x = 5 y = 6 z , then the least possible value of x + y + z is
Options: a ) 15 , b ) 26 , c ) 37 , d ) 42 , e ) 60
Rationale: "take lcm of 2,5 and 6 = 30 now 2 x = 30 = > x = 15 5 y = 30 = > y = 6 6 z = 30 = > z = 5 15 + 6 + 5 = 26 . option b ."
Answer: b
Python program:
a = 2 * 5
b = a * 6
c = b / 2
d = c / 2
e = 2 * 5
f = e * 6
g = f / 2
h = g / 5
i = d + h 
j = 2 * 5
k = j * 6
l = k / 2
m = l / 6
n = i + m
Problem: a rectangular circuit board is designed to have width w inches , perimeter p inches , and area x square inches . which of the following equations must be true ?
Options: a ) w ^ 2 + pw + x = 0
b ) w ^ 2 - pw + 2 x = 0
c ) 2 w ^ 2 + pw + 2 x = 0
d ) 2 w ^ 2 - pw - 2 x = 0
e ) 2 w ^ 2 - pw + 2 x = 0
Rationale: notice that we can discard options a , and c right away . the sum of 3 positive values can not be 0 . now , assume : width = w = 1 inchand length = 1 inch ; perimeter = p = 4 inches ; area = x = 1 square inches . plug the values of w , p , and x into the answer choices : only for e 2 w ^ 2 - pw + 2 x = 2 - 4 + 2 = 0 . answer : e .
Answer: e
Python program:
a = 2 * 1
b = 1 ** 2
c = 2 * b
d = 1 ** 2
e = 2 * d
f = c + e 
g = a - f
h = 1 ** 2
i = 2 * h
j = g + i
Problem: one - third of rahul ' s savings in national savings certificate is equal to one - half of his savings in public provident fund . if he has rs . 1 , 80000 as total savings , how much has he saved in public provident fund ?
Options: a ) 81000 , b ) 85000 , c ) 75000 , d ) 72000 , e ) 77000
Rationale: let savings in national savings certificate = x and savings in public provident fund = ( 180000 - x ) 1 / 3 x = 1 / 2 ( 180000 − x ) ⇒ 2 x = 3 ( 180000 − x ) ⇒ 2 x = 540000 − 3 x ⇒ 5 x = 540000 ⇒ x = 540000 / 5 = 108000 savings in public provident fund = ( 180000 - 108000 ) = 72000 answer is d .
Answer: d
Python program:
a = 10 ** 4
b = a * 10
c = b + 80000 
d = 10 ** 4
e = d * 10
f = e + 80000 
g = f / 2
h = 2 * 3
i = g * h
j = 2 + 3 
k = i / j
l = c - k
Problem: the weight of every type a widget is the same , the weight of every type b widget is the same , and the weight of every type c widget is the same . if the weight of 7 type a widgets is equal to the weight of 2 type b widgets , and the weight of 3 type b widgets is equal to the weight of 7 type c widgets . what is the ratio of the total weight of 1 type a widget and 1 type b widget , to the total weight of 1 type b widget and 1 type c widget ?
Options: a ) 1 : 2 , b ) 3 : 4 , c ) 5 : 6 , d ) 7 : 8 , e ) 9 : 10
Rationale: 3 b = 7 c and so b = 7 c / 3 7 a = 2 b and so a = 2 b / 7 = 2 c / 3 a + b = 2 c / 3 + 7 c / 3 = 9 c / 3 b + c = 7 c / 3 + c = 10 c / 3 the ratio of a + b : b + c = 9 : 10 the answer is e .
Answer: e
Python program:
a = 7 / 2
b = 1 + a 
c = 7 / 2
d = 3 / 2
e = c + d 
f = b / e
Problem: what least number must be added to 1170 , so that the sum is completely divisible by 23 ?
Options: a ) 3 , b ) 5 , c ) 7 , d ) 9 , e ) 11
Rationale: "51 * 23 = 1173 1173 - 1170 = 3 answer : a"
Answer: a
Python program:
a = 4 * 10
b = a + 2 
c = b * 23
d = c - 1170
Problem: in a 500 member association consisting of men and women , exactly 20 % of men and exactly 50 % women are homeowners . what is the least number of members who are homeowners ?
Options: a ) 149 , b ) 147 , c ) 101 , d ) 143 , e ) 141
Rationale: "solution simple out of 500 20 % are male i . e 100 and 50 % are female i . e 250 , so total homeowner is 350 . now min number homeowner is 100 and max is 250 so question ask us to find least and 101 has least value among all option . so ans is 101 . ans : c"
Answer: c
Python program:
a = 50 / 100
b = a * 20
c = 50 / 100
d = c * 20
e = b * d
f = 500 - 20
g = f / 20
h = e + g
Problem: two trains 140 m and 160 m long run at the speed of 60 kmph and 48 kmph in opposite directions in parallel tracks . the time which they take to cross each other is ?
Options: a ) 5.6 sec , b ) 8.9 sec , c ) 10 sec , d ) 12.6 sec , e ) 15 sec
Rationale: "relative speed = 60 + 48 = 108 kmph * 5 / 18 = 30 m / s distance covered in crossing each other = 140 + 160 = 300 m required time = 300 * 1 / 30 = 10 sec answer is c"
Answer: c
Python program:
a = 140 + 160 
b = 60 + 48 
c = b * const_0_2778
d = a / c
Problem: there are 408 boys and 192 girls in a school which are to be divided into equal sections of either boys or girls alone . find the total number of sections thus formed .
Options: a ) 25 , b ) 32 , c ) 35 , d ) 30 , e ) 45
Rationale: "explanation : hcf ( 408 , 192 ) = 24 the number of boys or girls that can be placed in a section = 24 . thus the total number of sections is given by 408 / 24 + 192 / 24 = 17 + 8 = 25 answer : a"
Answer: a
Python program:
a = 408 + 192 
b = 2 * 2
c = b * 2
d = c * 3
e = a / d
Problem: joe needs to paint all the airplane hangars at the airport , so he buys 360 gallons of paint to do the job . during the first week , he uses 1 / 4 of all the paint . during the second week , he uses 1 / 7 of the remaining paint . how many gallons of paint has joe used ?
Options: a ) 18 , b ) 128 , c ) 175 , d ) 216 , e ) 250
Rationale: "total paint initially = 360 gallons paint used in the first week = ( 1 / 4 ) * 360 = 90 gallons . remaning paint = 270 gallons paint used in the second week = ( 1 / 7 ) * 270 = 38 gallons total paint used = 128 gallons . option b"
Answer: b
Python program:
a = 360 / 4
b = a * 1
c = 360 / 4
d = c * 1
e = 360 - d
f = e / 7
g = b + f
Problem: the sale price sarees listed for rs . 540 after successive discount is 5 % and 2 % is ?
Options: a ) 288 , b ) 500 , c ) 502 , d ) 540 , e ) 262
Rationale: "540 * ( 95 / 100 ) * ( 98 / 100 ) = 502 answer : c"
Answer: c
Python program:
a = 540 * 5
b = a / 100
c = 540 - b
d = 540 * 5
e = d / 100
f = 540 - e
g = f * 2
h = g / 100
i = c - h
Problem: a bag contains 3 red , 2 blue and 3 green balls . if 2 ballsare picked at random , what is the probability that both are red ?
Options: a ) 2 / 21 , b ) 3 / 41 , c ) 3 / 28 , d ) 3 / 31 , e ) 5 / 32
Rationale: "p ( both are red ) , = 3 c 2 / 8 c 2 = 6 c 213 c 2 = 3 / 28 c"
Answer: c
Python program:
a = math.comb(3, 2)
b = 3 + 2 
c = b + 3 
d = math.comb(c, 2)
e = a / d
Problem: company p had 15 percent more employees in december than it had in january . if company p had 480 employees in december , how many employees did it have in january ?
Options: a ) 391 , b ) 417 , c ) 410 , d ) 423 , e ) 445
Rationale: "d = number of employees in december j = number of employees in january j x 1.15 = d j x 1.15 = 480 j = 480 / 1.15 j = 48,000 / 115 = 417 thus b is the correct answer ."
Answer: b
Python program:
a = 15 / 100
b = 1 + a 
c = 480 / b