euclaise/mathqa_programs huggingface dataset:
Problem: the present worth of rs . 242 due in 2 years at 10 % per annum compound interest is :
Options: a ) rs . 200 , b ) rs . 250 , c ) rs . 240 , d ) rs . 220 , e ) rs . 230
Rationale: "explanation : present worth of rs . x due t years hence is given by present worth ( pw ) = x / ( 1 + r / 100 ) t present worth ( pw ) = 242 / ( 1 + 10 / 100 ) 2 = 242 / ( 11 / 10 ) 2 = rs . 200 answer : option a"
Answer: a
Python program:
a = 10 / 100
b = a + 1 
c = b ** 2
d = 242 / c
Problem: beginning in town a , biker bob rides his bike 20 miles west , 6 miles north , 10 miles east , and then 18 miles north , to town b . how far apart are town a and town b ? ( ignore the curvature of the earth . )
Options: a ) 28 miles , b ) 30 miles , c ) 26 miles , d ) 18 miles , e ) 22 miles
Rationale: using pythagoras we have one side i , e total distance traveled in north direction = 18 + 6 = 24 m other being the base ie distance traveled west - distance traveled eat = 20 - 10 = 10 m now this third side or the distance between town a and town b = 24 ^ 2 + 10 ^ 2 = sq root 676 = 26 m answer : c
Answer: c
Python program:
a = 6 + 18 
b = a ** 2
c = 10 ** 2
d = b + c 
e = math.sqrt(d)
Problem: a brick measures 20 cm * 10 cm * 7.5 cm how many bricks will be required for a wall 23 m * 2 m * 0.75 m ?
Options: a ) 22377 , b ) 27782 , c ) 27891 , d ) 25000 , e ) 23000
Rationale: "23 * 2 * 0.75 = 20 / 100 * 10 / 100 * 7.5 / 100 * x 23 = 1 / 100 * x = > x = 23000 answer : e"
Answer: e
Python program:
a = 23 * 100
b = 2 * 100
c = a * b
d = 0 * 75
e = c * d
f = e / 20
g = f / 10
h = g / 7
Problem: a certain bus driver is paid a regular rate of $ 16 per hour for any number of hours that does not exceed 40 hours per week . for any overtime hours worked in excess of 40 hours per week , the bus driver is paid a rate that is 75 % higher than his regular rate . if last week the bus driver earned $ 1340 in total compensation , how many total hours did he work that week ?
Options: a ) 76 , b ) 60 , c ) 65 , d ) 48 , e ) 52
Rationale: "for 40 hrs = 40 * 16 = 640 excess = 1340 - 640 = 700 for extra hours = . 75 ( 16 ) = 12 + 16 = 28 number of extra hrs = 700 / 28 = 25 total hrs = 40 + 25 = 65 answer c 65"
Answer: c
Python program:
a = 16 * 40
b = 1340 - a
c = 100 + 75 
d = 16 * c
e = d / 100
f = b / e
g = 40 + f
Problem: find the area of right angled triangle whose hypotenuse is 15 cm and one of the sides is 12 cm .
Options: a ) 34 cm ²
b ) 38 cm ²
c ) 54 cm ²
d ) 56 cm ²
e ) 64 cm ²
Rationale: ab ² = ac ² - bc ² = 15 ² - 12 ² = 225 - 144 = 81 therefore , ab = 9 therefore , area of the triangle = ¹ / ₂ × base × height = ¹ / ₂ × 12 × 9 = 54 cm ² answer : c
Answer: c
Python program:
a = 15 ** 2
b = 12 ** 2
c = a - b
d = math.sqrt(c)
e = d * 12
f = e / 2
Problem: 3 buffaloes eat as much as 4 cows or 2 oxen . at a farm , there are 15 buffaloes , 8 oxen , and 24 cows . the fodder for these cattle is available for 24 days . if 40 more cows and 15 more buffaloes are brought in , how many days will the fodder last ?
Options: a ) 10 , b ) 12 , c ) 15 , d ) 18 , e ) 21
Rationale: "2 oxen = 3 buffaloes = 4 cows also : 15 buffaloes + 8 oxen + 24 cows = 10 oxen + 8 oxen + 12 oxen = 30 oxen there is enough fodder for 1 oxen for 30 * 24 days . 40 cows + 15 buffaloes = 20 oxen + 10 oxen = 30 oxen the new total is equal to 60 oxen instead of 30 oxen . 30 * 24 / 60 oxen = 12 days the answer is b ."
Answer: b
Python program:
a = 24 / 4
b = a * 3
c = 15 + b 
d = 8 / 2
e = d * 3
f = c + e 
g = 24 * f
h = 15 + 15 
i = 24 + 40 
j = i / 4
k = j * 3
l = h + k 
m = 8 / 2
n = m * 3
o = l + n 
p = g / o
Problem: the time it took car p to travel 300 miles was 2 hours less than the time it took car r to travel the same distance . if car p ’ s average speed was 10 miles per hour greater than that of car r , what was car r ’ s average speed , in miles per hour ?
Options: a ) 34 , b ) 50 , c ) 60 , d ) 70 , e ) 80
Rationale: "let speed of car r be = x then speed of car p = x + 10 a / q , ( 300 / x ) - ( 300 / ( x + 10 ) ) = 2 solving for x = 34 miles \ hr . a"
Answer: a
Python program:
a = negate + ( 
b = negate ** (
c = b - 2
d = 300 * 10
e = d / 2
f = 4 * negate
g = math.sqrt(c)
h = a / g
Problem: a boat having a length 7 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 the man is :
Options: a ) 140 kg , b ) 60 kg , c ) 72 kg , d ) 96 kg , e ) none of these
Rationale: "explanation : volume of water displaced = ( 7 x 2 x 0.01 ) m 3 = 0.14 m 3 . ∴ mass of man = volume of water displaced x density of water = ( 0.14 x 1000 ) kg = 140 kg . answer : a"
Answer: a
Python program:
a = 7 * 2
b = 1 / 100
c = a * b
d = c * 1000
Problem: a certain car can travel 64 kilometers on a liter of fuel . if the fuel tank ’ s contents decrease by 3.9 gallons over a period of 5.7 hours as the car moves at a constant speed , how fast is the car moving , in miles per hour ? ( 1 gallon = 3.8 liters ; 1 mile = 1.6 kilometers )
Options: a ) 52 , b ) 65 , c ) 78 , d ) 91 , e ) 104
Rationale: "fuel used 3.9 gallons ; convert to liters - - > 3.9 x 3.8 liters time = 5.7 hours 1 mile = 1.6 kilometers ; convert to miles - - > 1 km = 1 / 1.6 mile speed ( km / hour ) = d / t = 64 ( km * ) x 3.9 x 3.8 / 5.7 replace ( km * ) to miles ; multiply by 1 / 1.6 mile speed ( miles / hour ) = 64 x 3.9 x 3.8 / 5.7 x 1.6 = 78 miles / hour ans : e ps : i felt the factors were easy to cancel out , so did n ' t require much rounding off = 64 x 3.9 x 3.8 / 5.7 x 1.6 = 104 e"
Answer: e
Python program:
a = 64 * 3
b = a / 1
c = b * 3
d = c / 5
Problem: an amount of money is to be distributed among faruk , vasim and ranjith in the ratio 3 : 5 : 9 . if vasims share is rs . 1500 , what is the difference between faruk ' s and ranjith ' s shares ?
Options: a ) s 1800 , b ) s 1500 , c ) s 1600 , d ) s 1900 , e ) s 1700
Rationale: "explanation : let p = faruk , q = vasim , r = ranjith let p = 3 x , q = 5 x and r = 9 x . then , 5 x = 1500 ? x = 300 . p = 900 , q = 1500 and r = 2700 . hence , ( r - p ) = ( 2700 - 900 ) = 1800 answer : a"
Answer: a
Python program:
a = 1500 / 5
b = 9 - 3
c = a * b
Problem: a grocer has a sale of rs . 5420 , rs . 5660 , rs . 6200 , rs . 6350 and rs . 6500 for 5 consecutive months . find the sale he should have in the sixth month , so that he gets an average sale of rs . 6000 ?
Options: a ) rs . 5870 , b ) rs . 5991 , c ) rs . 6020 , d ) rs . 6850 , e ) none of these
Rationale: "explanation : total sale for 5 months = rs . ( 5420 + 5660 + 6200 + 6350 + 6500 ) = rs . 30,130 therefore , required sale = rs . [ ( 6000 * 6 ) – 30,130 ] = rs . ( 36000 – 30,130 ) = rs . 5870 answer a"
Answer: a
Python program:
a = 5 + 1 
b = a * 6000
c = 5420 + 5660 
d = c + 6200 
e = d + 6350 
f = e + 6500 
g = b - f
Problem: of the total amount that jill spent on a shopping trip , excluding taxes , she spent 60 percent on clothing , 10 percent on food , and 30 percent on other items . if jill paid a 4 percent tax on the clothing , no tax on the food , and an 8 percent tax on all other items , then the total tax that she paid was what percent of the total amount that she spent , excluding taxes ?
Options: a ) 2.8 % , b ) 3.6 % , c ) 4.4 % , d ) 5.2 % , e ) 4.8 %
Rationale: "let amount spent by jill = 100 clothing = 50 , food = 20 , others = 30 tax on clothing = 2.4 tax on others = 2.4 percentage = 4.8 / 100 = 4.8 % answer : e"
Answer: e
Python program:
a = 4 / 100
b = 60 * a
c = 8 / 100
d = 30 * c
e = b + d 
f = e / 100
g = f * 100
Problem: x ^ 2 + sx + 72 = 0 has two distinct integer roots ; how many values are possible for s ?
Options: a ) 3 , b ) 6 , c ) 8 , d ) 12 , e ) 24
Rationale: for a quadratic equation ax ^ 2 + sx + c = 0 , we know that - s / a is sum of roots and c / a is product of roots . the quadratic equation here is x ^ 2 + sx + 72 = 0 , where product of roots is 72 . if we find all the factors of 72 , we have the answer . by prime factorization , we get 72 = 2 ^ 3 * 3 ^ 2 . we know that total factors are ( 3 + 1 ) * ( 2 + 1 ) = 12 ( reason : with 2 ^ n , we have n + 1 possibilities . n ^ 0 to n ^ n . so n + 1 ) = d
Answer: d
Python program:
a = 3 + 1 
b = 2 + 1 
c = a * b
Problem: the sides of a square region , measured to the nearest centimeter , are 5 centimeters long . the least possible value of the actual area of the square region is
Options: a ) 25.25 sq cm , b ) 20.25 sq cm , c ) 30.25 sq cm , d ) 36.25 sq cm , e ) 40.25 sq cm
Rationale: "though there might be some technicalities concerning the termnearest ( as 4.5 is equidistant from both 4 and 5 ) the answer still should be : 4.5 ^ 2 = 20.25 . answer : b"
Answer: b
Python program:
a = 5 - const_0_25
b = a - const_0_25
c = b ** 2
Problem: an outlet pipe empties a tank which is full in 10 hours . if the inlet pipe is kept open , which lets water in at the rate of 4 litres / min then outlet pipe would take 6 hours longer . find the capacity of the tank .
Options: a ) 8600 litres , b ) 6400 litres , c ) 12800 litres , d ) 11200 litres , e ) 13200 litres
Rationale: "let the rate of outlet pipe be x liters / hour ; rate of inlet pipe is 4 litres / min , or 4 * 60 = 240 liters / hour ; net outflow rate when both pipes operate would be x - 240 liters / hour . capacity of the tank = x * 10 hours = ( x - 240 ) * ( 10 + 6 ) hours 10 x = ( x - 240 ) * 16 - - > x = 640 - - > capacity = 10 x = 6400 liters . answer : b ."
Answer: b
Python program:
a = 4 * const_60
b = 10 + 6 
c = a * b
d = c / 6
e = d * 10
Problem: a , b and c invest in the ratio of 3 : 4 : 5 . the percentage of return on their investments are in the ratio of 6 : 5 : 4 . find the total earnings , if b earns rs . 350 more than a :
Options: a ) 10150 , b ) 7250 , c ) 2767 , d ) 1998 , e ) 2771
Rationale: "explanation : a b c investment 3 x 4 x 5 x rate of return 6 y % 5 y % 4 y % return \ inline \ frac { 18 xy } { 100 } \ inline \ frac { 20 xy } { 100 } \ inline \ frac { 20 xy } { 100 } total = ( 18 + 20 + 20 ) = \ inline \ frac { 58 xy } { 100 } b ' s earnings - a ' s earnings = \ inline \ frac { 2 xy } { 100 } = 350 total earning = \ inline \ frac { 58 xy } { 100 } = 10150 answer : a ) rs . 10150"
Answer: a
Python program:
a = 3 * 6
b = 4 * 5
c = a + b 
d = 5 * 4
e = c + d 
f = 4 * 5
g = 3 * 6
h = f - g
i = 350 / h
j = e * i
Problem: a train 50 m long is running with a speed of 68 kmph . in what time will it pass a man who is running at 8 kmph in the same direction in which the train is going ?
Options: a ) 3 sec . , b ) 7 sec . , c ) 9 sec . , d ) 11 sec . , e ) none
Rationale: "solution speed of the train relative to man = ( 68 - 8 ) = 60 kmph = 60 x 5 / 18 = 50 / 3 m / sec . time taken by it to cover 50 m at ( 50 / 3 ) m / sec = ( 112 - 50 ) kmph = ( 50 x 3 / 50 ) sec = 3 sec . answer a"
Answer: a
Python program:
a = 68 + 8 
b = a * const_0_2778
c = 50 / b
Problem: indu gave bindu rs . 4375 on compound interest for 2 years at 4 % per annum . how much loss would indu has suffered had she given it to bindu for 2 years at 4 % per annum simple interest ?
Options: a ) s . 10 , b ) s . 7 , c ) s . 5 , d ) s . 3 , e ) s . 4
Rationale: "4375 = d ( 100 / 4 ) 2 d = 7 answer : b"
Answer: b
Python program:
a = 4 / 100
b = 1 + a 
c = b ** 2
d = 4375 * c
e = d - 4375
f = 4 / 100
g = 4375 * f
h = g * 2
i = e - h
Problem: how many books each of volume 100 meter cube can be packed into a crate of volume 3000 meter cube ?
Options: a ) 50 , b ) can not be determined , c ) 150 , d ) 300 , e ) 350
Rationale: "gud question with a simple concept . in geo if we want to insert one shape into another we need to know the dimensions of the two shapes . in above with volume given , we can come up with different shapes , so we cant know the answer for ex : 3000 m 3 can be 300 * 10 or 30 * 100 or just 3000 * 1 we do n ' t know , so we cant calculate answer : b"
Answer: b
Python program:
a = 3000 * 1
Problem: an article is bought for rs . 675 and sold for rs . 700 , find the gain percent ?
Options: a ) 2 % , b ) 3 % , c ) 4 % , d ) 5 % , e ) 6 %
Rationale: "675 - - - - 25 100 - - - - ? = > = 4 % answer : c"
Answer: c
Python program:
a = 700 * 100
b = a / 675
c = 100 - b
Problem: having scored 98 runs in the 19 th inning , a cricketer increases his average score by 4 . what will be his average score after 19 innings ?
Options: a ) 28 , b ) 27 , c ) 26 , d ) 22 , e ) 24
Rationale: "explanation : let the average score of the first 18 innings be n 18 n + 98 = 19 ( n + 4 ) = > n = 22 so , average score after 19 th innings = x + 4 = 26 . answer : c"
Answer: c
Python program:
a = 19 * 4
b = 98 - a
c = b + 4
Problem: p can do a work in the same time in which q and r together can do it . if p and q work together , the work can be completed in 10 days . r alone needs 50 days to complete the same work . then q alone can do it in
Options: a ) 30 days , b ) 25 days , c ) 20 days , d ) 15 days , e ) 24 days
Rationale: "work done by p and q in 1 day = 1 / 10 work done by r in 1 day = 1 / 50 work done by p , q and r in 1 day = 1 / 10 + 1 / 50 = 6 / 50 but work done by p in 1 day = work done by q and r in 1 day . hence the above equation can be written as work done by p in 1 day × 2 = 6 / 50 = > work done by p in 1 day = 3 / 50 = > work done by q and r in 1 day = 3 / 50 hence work done by q in 1 day = 3 / 50 – 1 / 50 = 2 / 50 = 1 / 25 so q alone can do the work in 25 days option b"
Answer: b
Python program:
a = 1 / 10
b = 1 / 50
c = a + b 
d = c / 2
e = 1 / 50
f = d - e
g = 1 / f
Problem: dhoni spent 40 percent of his earning last month on rent and 20 percent less than what he spent on rent to purchase a new dishwasher . what percent of last month ' s earning did dhoni have left over ?
Options: a ) 30 % , b ) 28 % , c ) 32 % , d ) 33 % , e ) 34 %
Rationale: "say dhoni ' s earning last month was $ 100 . dhoni spent 40 percent of his earning last month on rent - - > $ 40 on rent ; 20 percent less than what he spent on rent to purchase a new dishwasher - - > $ 40 * 0.8 = $ 32 on the dishwasher . left over amount 100 - ( 40 + 32 ) = $ 28 answer : b"
Answer: b
Python program:
a = 20 / 100
b = 1 - a
c = 40 * b
d = 40 + c 
e = 100 - d
Problem: a man whose bowling average is 12.4 , takes 7 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 ) 143 , b ) 144 , c ) 145 , d ) 146 , e ) 147
Rationale: 12.4 * x + 26 = ( 7 + x ) 12 solve equation x = 145 answer : c
Answer: c
Python program:
a = math.floor(12, 4)
b = a * 7
c = b - 26
d = math.floor(12, 4)
e = 12 - 4
f = c / e
Problem: a batsman scored 120 runs which included 6 boundaries and 4 sixes . what % of his total score did he make by running between the wickets
Options: a ) 40 % , b ) 60 % , c ) 65 % , d ) 70 % , e ) 75 %
Rationale: number of runs made by running = 110 - ( 6 x 4 + 4 x 6 ) = 120 - ( 48 ) = 72 now , we need to calculate 60 is what percent of 120 . = > 72 / 120 * 100 = 60 % b
Answer: b
Python program:
a = 6 * 4
b = 4 * 6
c = a + b 
d = 120 - c
e = d / 120
f = e * 100
Problem: a bag contains 3 red , 2 blue and 4 green balls . if 2 balls are picked at random , what is the probability that both are red ?
Options: a ) 1 / 12 , b ) 1 / 13 , c ) 1 / 14 , d ) 1 / 15 , e ) 1 / 18
Rationale: "p ( both are red ) , = 3 c 2 / 9 c 2 = 1 / 12 a"
Answer: a
Python program:
a = math.comb(3, 2)
b = 3 + 2 
c = b + 4 
d = math.comb(c, 2)
e = a / d
Problem: two pipes can separately fill a tank in 20 and 30 hours respectively . both the pipes are opened to fill the tank but when the tank is full , a leak develops in the tank through which one - third of water supplied by both the pipes goes out . what is the total time taken to fill the tank ?
Options: a ) 17 hrs , b ) 16 hrs , c ) 15 hrs , d ) 13 hrs , e ) 12 hrs
Rationale: 1 / 20 + 1 / 30 = 1 / 12 1 + 1 / 3 = 4 / 3 1 - - - 12 4 / 3 - - - ? 4 / 3 * 12 = 16 hrs answer : b
Answer: b
Python program:
a = 1/(20)
b = 1/(30)
c = a + b 
d = 1/(c)
e = 1/(20)
f = 1/(30)
g = e + f 
h = 1/(g)
i = h / 3
j = d + i
Problem: the area of playground is 5900 sq . meters . what will be the cost of covering it with grass sheet 1 cm deep , if cost of grass sheet is $ 2.80 per cubic meter .
Options: a ) a ) $ 144
b ) b ) $ 150.50
c ) c ) $ 165
d ) d ) $ 158.60
e ) e ) $ 160.70
Rationale: total volume * unit cost = total cost or , 5900 * 0.01 * 2.8 = total cost = 165 = c
Answer: c
Python program:
a = 1 / 100
b = 5900 * a
c = 2 * 8
Problem: hcf and lcm two numbers are 12 and 396 respectively . if one of the numbers is 48 , then the other number is ?
Options: a ) 99 , b ) 66 , c ) 132 , d ) 264 , e ) 364
Rationale: "12 * 396 = 48 * x x = 99 answer : a"
Answer: a
Python program:
a = 12 * 396
b = a / 48
Problem: the total number of plums that grow during each year on a certain plum tree is equal to the number of plums that grew during the previous year , less the age of the tree in years ( rounded down to the nearest integer ) . during its 4 th year , the plum tree grew 50 plums . if this trend continues , how many plums will it grow during its 6 th year ?
Options: a ) 36 , b ) 41 , c ) 38 , d ) 40 , e ) 42
Rationale: "1 st year : 0 - 1 ( age ) , we take age = 0 ( as the question says that we have to ( rounded down to the nearest integer ) ) 2 ndyear : 1 - 2 ( age ) , we take age = 1 3 rd year : 2 - 3 ( age ) , we take age = 2 4 th year : 3 - 4 ( age ) , we take age = 3 5 th year : 4 - 5 ( age ) , we take age = 4 6 th year : 5 - 6 ( age ) , we take age = 5 thus for the 4 th year = 50 , 5 th year = 50 - 4 = 46 6 th year = 46 - 5 = 41 the correct answer is b ."
Answer: b
Python program:
a = 4 - 1
b = a - 1
c = 4 - 1
d = 50 + c 
e = b + d 
f = e / 3
g = f + 3
Problem: a person buys an article at rs . 500 . at what price should he sell the article so as to make a profit of 20 % ?
Options: a ) 600 , b ) 2877 , c ) 208 , d ) 1882 , e ) 191
Rationale: explanation : cost price = rs . 500 profit = 20 % of 500 = rs . 100 selling price = cost price + profit = 500 + 100 = 600 answer : a
Answer: a
Python program:
a = 20 / 100
b = 500 * a
c = 500 + b
Problem: if x ^ 2 is divisible by 240 what is the least possible value of integer x ?
Options: a ) 120 , b ) 30 , c ) 90 , d ) 60 , e ) 12
Rationale: 240 can be written as ( 2 ^ 4 ) * 3 * 5 . for x ^ 2 to be divisible by 240 it should contain at least 2 ^ 4 and 3 and 5 in its factors . we can leave out option e because 12 doesnt have 5 as one of its factor . now if we check for option b , 30 can be written as 2 * 3 * 5 , hence 30 ^ 2 will have 2 as the maximum power of 2 , so we can leave out this option too . option d is the right answer if we follow the same method as we followed for other two previous options . 60 = ( 2 ^ 2 ) * 3 * 5 ; 60 ^ 2 = ( 2 ^ 4 ) * ( 3 ^ 2 ) * ( 5 ^ 2 ) . so it shows that 60 ^ 2 is divisible by 240 and hence the answer . answer : d
Answer: d
Python program:
a = 240 / 2
b = a / 2
Problem: machine t can produce x units in 3 / 4 of the time it takes machine n to produce x units . machine n can produce x units in 2 / 3 the time it takes machine o to produce x units . if all 3 machines are working simultaneously , what fraction of the total output is produced by machine n ?
Options: a ) 1 / 2 , b ) 1 / 3 , c ) 4 / 13 , d ) 8 / 29 , e ) 6 / 33
Rationale: let the following be true : t makes x in time t then the following follows : n makes x in 4 t / 3 o makes x in 3 / 2 ( 4 t / 3 ) = 2 t m : n : o = 1 : 4 / 3 : 2 = 3 : 4 : 6 so n = 4 / ( 3 + 4 + 6 ) = 4 / 13 = c
Answer: c
Python program:
a = 2 / 3
b = 2 / 3
c = 3 / 4
d = b * c
e = 1 + d 
f = a + e 
g = 1/(f)
h = 2 / 3
i = g * h
Problem: ( ( 1 ^ m ) / ( 5 ^ m ) ) ( ( 1 ^ 16 ) / ( 4 ^ 16 ) ) = 1 / ( 2 ( 10 ) ^ 31 ) what is m ?
Options: a ) 17 , b ) 18 , c ) 34 , d ) 31 , e ) 36
Rationale: ( ( 1 ^ m ) / ( 5 ^ m ) ) ( ( 1 ^ 16 ) / ( 4 ^ 16 ) ) = 1 / ( 2 ( 10 ) ^ 31 ) ( ( 1 / 5 ) ^ m ) * ( ( 1 / 2 ) ^ 32 ) = 1 / ( 2 * ( 2 * 5 ) ^ 31 ) ) 2 ^ 36 will cancel out , since 1 can be written as 1 ^ 35 , so ( 1 / 5 ) ^ m = ( 1 / 5 ) ^ 31 ( ( 1 / 5 ) ^ m ) * ( ( 1 / 2 ) ^ 32 ) = 1 / [ ( 2 ^ 32 ) * ( 5 ^ 31 ) ] so , m = 31 answer d
Answer: d
Python program:
a = 1/(31)
b = 1 / 16
c = 4 / 16
d = b / c
e = 2 * 10
f = 1 / e
g = d / f
h = g / 5
i = a * h
j = 1/(i)
Problem: in a recent head - to - head run - off election , 12000 absentee ballets were cast . 1 / 6 of the absentee ballets were thrown out and 3 / 5 of the remaining absentee ballets were cast for candidate a . how many absentee votes did candidate b receive ?
Options: a ) 2,000 , b ) 3,000 , c ) 4,000 , d ) 8,000 , e ) 9,000
Rationale: 5 / 6 * 2 / 5 ( total absentee votes ) = 1 / 3 ( total votes ) = 1 / 3 * 12000 = 4000 answer is c
Answer: c
Python program:
a = 12000 / 6
b = a * 5
c = b / 5
d = c * 3
e = 12000 / 6
f = e * 5
g = f / 5
h = d - g
i = h / 1000
j = i - 1
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 , 00,000 as total savings , how much has he saved in public provident fund ?
Options: a ) 80000 , b ) 40000 , c ) 50000 , d ) 75000 , e ) 90000
Rationale: "let savings in n . s . c and p . p . f . be rs . x and rs . ( 100000 - x ) respectively . then , = 1 / 3 x = 1 / 2 ( 100000 - x ) = x / 3 + x / 2 = 50000 = 5 x / 6 = 50000 = x = 50000 x 6 / 5 = 60000 savings in public provident fund = rs . ( 100000 - 60000 ) = rs . 40000 answer is b ."
Answer: b
Python program:
a = 100 * 10
b = a * 100
c = 100 * 10
d = c * 100
e = 2 * 100
f = e * 100
g = d - f
h = b + g 
i = 3 / 2
j = i + 1 
k = 1 / j
l = h * k
Problem: what is the probability that company g ' s advertisement will be one of the first two be shown during the first commercial break ?
Options: a ) 1 / 225 , b ) 1 / 30 , c ) 1 / 15 , d ) 2 / 15 , e ) 4 / 15
Rationale: g 1 / 15 + ( 14 / 15 ) * 1 / 14 = 2 / 15 d
Answer: d
Python program:
a = 3 * 5
b = 2 / a
Problem: at what rate percent on simple interest will rs . 750 amount to rs . 900 in 10 years ?
Options: a ) 6 % , b ) 2 % , c ) 4 % , d ) 5 % , e ) 3 %
Rationale: "150 = ( 750 * 10 * r ) / 100 r = 2 % answer : b"
Answer: b
Python program:
a = 900 - 750
b = a / 750
c = b / 10
d = c * 100
Problem: one drier dries certain quantity of material in 24 minutes . another drier does the same work in 2 minutes how much time will it take to do the same job when both driers are put to work ?
Options: a ) 1.00 minutes , b ) 1.20 minutes , c ) 1.50 min , d ) 1.85 min , e ) 2.00 minutes
Rationale: by guess it is clear that the time taken will be less than 2 minutes and more than 1.5 mintes therefore , answer 1.85 minutes will be correct . answer - d
Answer: d
Python program:
a = 1 / 24
b = 1 / 2
c = a + b 
d = 1 / c
Problem: if the lcm and hcf of 8 and another number is 24 and 4 respectively . find the other number ?
Options: a ) 11 , b ) 12 , c ) 14 , d ) 15 , e ) 16
Rationale: "hcf x lcm = product of numbers 4 x 24 = 8 x the other number other number = ( 4 x 24 ) / 8 other number = 12 answer : b"
Answer: b
Python program:
a = 24 * 4
b = a / 8
Problem: the average age of an adult class is 40 years . 18 new students with an avg age of 32 years join the class . therefore decreasing the average by 4 year . find what was theoriginal strength of class ?
Options: a ) 8 , b ) 12 , c ) 15 , d ) 17 , e ) 18
Rationale: "let original strength = y then , 40 y + 18 x 32 = ( y + 18 ) x 36 â ‡ ’ 40 y + 576 = 36 y + 648 â ‡ ’ 4 y = 72 â ˆ ´ y = 18 e"
Answer: e
Python program:
a = 40 - 4
b = 18 * a
c = 18 * 32
d = b - c
e = d / 4
Problem: a number whose fifth part increased by 7 is equal to its fourth part diminished by 7 is ?
Options: a ) 160 , b ) 180 , c ) 200 , d ) 280 , e ) none
Rationale: "answer let the number be n . then , ( n / 5 ) + 7 = ( n / 4 ) - 7 â ‡ ’ ( n / 4 ) - ( n / 5 ) = 14 â ‡ ’ ( 5 n - 4 n ) / 20 = 14 â ˆ ´ n = 280 option : d"
Answer: d
Python program:
a = 7 + 7 
b = 1 / 4
c = 1 + 4 
d = 1 / c
e = b - d
f = a / e
Problem: a tradesman sold an article at a loss of 25 % . if the selling price had been increased by $ 500 , there would have been a gain of 15 % . what was the cost price of the article ?
Options: a ) $ 1000 , b ) $ 1200 , c ) $ 1120 , d ) $ 1350 , e ) $ 1250
Rationale: let c . p . be $ x then 125 % of x - 85 % of x = 500 40 % of x = 500 2 x / 5 = 500 x = $ 1250 answer is e
Answer: e
Python program:
a = 25 + 15 
b = a / 100
c = 500 / b