euclaise/mathqa_programs huggingface dataset:
Problem: a jar of 220 marbles is divided equally among a group of marble - players today . if 2 people joined the group in the future , each person would receive 1 marble less . how many people are there in the group today ?
Options: a ) 20 , b ) 21 , c ) 22 , d ) 23 , e ) 24
Rationale: 220 = 20 * 11 = 22 * 10 there are 20 people in the group today . the answer is a .
Answer: a
Python program:
a = 220 * 2
b = a * 4
c = 2 ** 2
d = b + c 
e = math.sqrt(d)
f = e - 2
g = f / 2
Problem: a train running at the speed of 60 km / hr crosses a pole in 6 seconds . find the length of the train ?
Options: a ) 100 meter , b ) 170 meter , c ) 156 meter , d ) 168 meter , e ) 154 meter
Rationale: "speed = 60 * ( 5 / 18 ) m / sec = 50 / 3 m / sec length of train ( distance ) = speed * time ( 50 / 3 ) * 6 = 100 meter answer : a"
Answer: a
Python program:
a = 60 * 1000
b = a / 3600
c = b * 6
Problem: a chemist mixes one liter of pure water with x liters of a 60 % salt solution , and the resulting mixture is a 20 % salt solution . what is the value of x ?
Options: a ) 1 / 4 , b ) 1 / 3 , c ) 1 / 2 , d ) 1 , e ) 3
Rationale: "concentration of salt in pure solution = 0 concentration of salt in salt solution = 60 % concentration of salt in the mixed solution = 20 % the pure solution and the salt solution is mixed in the ratio of - - > ( 60 - 20 ) / ( 20 - 0 ) = 2 / 1 1 / x = 2 / 1 x = 1 / 2 answer : c"
Answer: c
Python program:
a = 60 - 20
b = 20 / a
Problem: if a and b are the roots of the equation x 2 - 4 x + 4 = 0 , then the value of a 2 + b 2 is :
Options: a ) 36 , b ) 24 , c ) 17 , d ) 8 , e ) 5
Rationale: "sol . ( b ) the sum of roots = a + b = 4 product of roots = ab = 4 now , a 2 + b 2 = ( a + b ) 2 - 2 ab = 16 - 8 = 8 answer d"
Answer: d
Python program:
a = 4 ** 2
b = 4 * 4
c = a - b
d = math.sqrt(c)
e = 4 - d
f = e / 2
g = f ** 2
h = 4 ** 2
i = 4 * 4
j = h - i
k = math.sqrt(j)
l = 4 + k 
m = l / 2
n = m ** 2
o = g + n
Problem: if a town of 75,000 people is growing at a rate of approx . 1 % per year , the population of the town in 5 years will be closest to ?
Options: a ) a . 76000 , b ) b . 77000 , c ) c . 78000 , d ) d . 79000 , e ) e . 80000
Rationale: 1 % is quite small and hence the answer is a )
Answer: a
Python program:
a = 3 + 4 
b = 5 * a
c = b * 100
d = 3 + 4 
e = d + 3 
f = c * e
Problem: the total cost of 100 paper plates and 200 paper cups is $ 4.00 at the same rates what is the total cost of 20 of the plates and 40 of the cups ?
Options: a ) $ . 80 , b ) $ 1.00 , c ) $ 1.20 , d ) $ 1.50 , e ) $ 1.60
Rationale: "u dont need to go through all this what u have with u is 100 p + 200 c = $ 4.00 just divide the equation by 5 and you will get what u are looking for 20 p + 40 c = $ 0.80 therefore oa is a"
Answer: a
Python program:
a = 20 / 100
b = a * 4
Problem: which greatest possible length can be used to measure exactly 15 meter 75 cm , 11 meter 25 cm and 7 meter 65 cm
Options: a ) 45 cm , b ) 255 cm , c ) 244 cm , d ) 55 cm , e ) 280 cm
Rationale: "explanation : convert first all terms into cm . i . e . 1575 cm , 1125 cm , 765 cm . now whenever we need to calculate this type of question , we need to find the hcf . hcf of above terms is 255 . option b"
Answer: b
Python program:
a = 15 * 100
b = a + 75 
c = 11 * 100
d = c + 25 
e = b / d
f = math.floor(e)
Problem: if ( m - 8 ) is a factor of m ^ 2 - sm - 24 , then s =
Options: a ) 3 , b ) 5 , c ) 6 , d ) 11 , e ) 16
Rationale: "( m - 8 ) ( m - a ) = m ^ 2 - sm - 24 a = - 3 s = 8 + a = 5 = d = b"
Answer: b
Python program:
a = 24 / 8
b = 8 - a
Problem: a dice has one of the first 4 prime number on each its 6 sides , with no two sides having the same number . the dice is rolled 10 times and the results added . the addition is most likely to be closet to
Options: a ) 41 , b ) 43 , c ) 60 , d ) 68 , e ) 70
Rationale: if die is rolled then avg score = ( 2 + 3 + 5 + 7 ) / 4 = 41 / 4 so , most likely sum for 10 times = 41 / 4 * 10 = 43 answer : b
Answer: b
Python program:
a = 6 / 2
b = 2 + a 
c = 2 + 3 
d = b + c 
e = 3 + 4 
f = d + e 
g = 3 + 4 
h = g + 4 
i = f + h 
j = 3 + 4 
k = j + 4 
l = 2 + k 
m = i + l
Problem: each of the products produced yesterday was checked by worker x or worker y . 0.5 % of the products checked by worker x are defective and 0.8 % of the products checked by worker y are defective . if the total defective rate of all the products checked by worker x and worker y is 0.7 % , what fraction of the products was checked by worker y ?
Options: a ) 2 / 3 , b ) 5 / 6 , c ) 7 / 8 , d ) 4 / 5 , e ) 5 / 8
Rationale: x : 0.5 % is 0.2 % - points from 0.7 % . y : 0.8 % is 0.1 % - points from 0.7 % . therefore the ratio of products checked by y : x is 2 : 1 . thus , worker y checked 2 / 3 of the products . the answer is a .
Answer: a
Python program:
a = 0 - 7
b = 0 - 8
c = a / b
Problem: 40 men took a dip in a water tank 40 m long and 20 m broad on a religious day . if the average displacement of water by a man is 4 m 3 , then the rise in the water level in the tank will be :
Options: a ) 25 cm , b ) 20 cm , c ) 35 cm , d ) 50 cm , e ) none of these
Rationale: "explanation : total volume of water displaced = ( 4 x 40 ) m 3 = 160 m 3 rise in water level = 160 / 40 ã — 20 = 0.2 m = 20 cm answer : b"
Answer: b
Python program:
a = 4 * 40
b = 40 * 20
c = a / b
Problem: if a is thrice as fast as b and together can do a work in 18 days . in how many days a alone can do the work ?
Options: a ) 36 , b ) 42 , c ) 24 , d ) 54 , e ) 45
Rationale: "a ’ s one day ’ s work = 1 / x b ’ s one day ’ s work = 1 / 3 x a + b ’ s one day ’ s work = 1 / x + 1 / 3 x = 1 / 18 = 3 + 1 / 3 x = 4 / 3 x = 1 / 18 x = 18 * 4 / 3 = 24 answer : c"
Answer: c
Python program:
a = 18 * 4
b = 3 / a
c = 1/(b)
Problem: what is the average of first 21 multiples of 4 ?
Options: a ) a ) 44 , b ) b ) 77 , c ) c ) 79 , d ) d ) 81 , e ) e ) 82
Rationale: "required average = 7 ( 1 + 2 + . . . . + 21 ) / 21 ( 4 / 21 ) x ( ( 21 x 22 ) / 2 ) ( because sum of first 21 natural numbers ) = 44 a"
Answer: a
Python program:
a = 21 + 1 
b = 21 * a
c = b / 2
d = c / 21
e = d * 4
Problem: a factory produces 3400 toys per week . if the workers at this factory work 5 days a week and if these workers make the same number of toys everyday , how many toys are produced each day ?
Options: a ) 575 toys , b ) 375 toys , c ) 680 toys , d ) 475 toys , e ) 675 toys
Rationale: "to find the number of toys produced every day , we divide the total number of toys produced in one week ( of 5 days ) by 5 . 3400 / 5 = 680 toys correct answer c"
Answer: c
Python program:
a = 3400 / 5
Problem: if the cost price is 99 % of selling price then what is the profit percentage .
Options: a ) 1 , b ) 1.11 , c ) 1.01 , d ) 1.1 , e ) 1.21
Rationale: "selling price = rs 100 : then cost price = rs 99 : profit = rs 1 . profit = { ( 1 / 99 ) * 100 } % = 1.01 % answer is c ."
Answer: c
Python program:
a = 100 - 99
b = a / 99
c = b * 100
Problem: g ( a ) is defined as the product of all even integers k such that 0 < k ≤ x . for example , g ( 14 ) = 2 × 4 × 6 × 8 × 10 × 12 × 14 . if g ( y ) is divisible by 4 ^ 11 , what is the smallest possible value for a ?
Options: a ) 22 , b ) 24 , c ) 28 , d ) 32 , e ) 44
Rationale: g ( a ) = 4 ^ 11 = 2 ^ 22 . so we have to find a product with atleast 22 2 ' s in it . in option 1 22 the total no of 2 ' s = [ 22 / 2 ] + [ 22 / 4 ] + [ 22 / 8 ] + [ 22 / 16 ] = 11 + 5 + 2 + 1 = 19 in option 2 24 the total no of 2 ' s = [ 24 / 2 ] + [ 24 / 4 ] + [ 24 / 8 ] + [ 24 / 16 ] = 12 + 6 + 3 + 1 = 22 . hence b
Answer: b
Python program:
a = 4 / 2
b = a * 11
c = b + 2
Problem: j is 25 % less than p and 20 % less than t . t is w % less than p . what is the value of w ?
Options: a ) 93.5 , b ) 90 , c ) 6.75 , d ) 6.25 , e ) 2
Rationale: "usually we can solve every question of this type by choosing appropriate value of the variable and deriving the value of other related variables . let , p = 400 then j = ( 75 / 100 ) * 400 = 300 also j = ( 80 / 100 ) * t i . e . t = 300 * 100 / 80 = 375 and t = [ 1 - ( w / 100 ) ] * p i . e . 100 - w = 100 * t / p = 100 * 375 / 400 = 93.75 i . e . w = 6.25 answer : option d"
Answer: d
Python program:
a = 25 * 25
b = a / 100
Problem: how many litres of pure acid are there in 4 litres of a 35 % solution
Options: a ) 1.5 , b ) 1.6 , c ) 1.7 , d ) 1.8 , e ) 1.4
Rationale: explanation : question of this type looks a bit typical , but it is too simple , as below . . . it will be 8 * 20 / 100 = 1.4 answer : option e
Answer: e
Python program:
a = 35 / 100
b = a * 4
Problem: last year department store x had a sales total for december that was 7 times the average ( arithmetic mean ) of the monthly sales totals for january through november . the sales total for december was what fraction of the sales total for the year ?
Options: a ) 1 / 4 , b ) 4 / 15 , c ) 1 / 3 , d ) 7 / 18 , e ) 4 / 5
Rationale: "let avg for 11 mos . = 10 therefore , dec = 70 year total = 11 * 10 + 70 = 180 answer = 70 / 180 = 7 / 18 = d"
Answer: d
Python program:
a = 12 - 1
b = a + 7 
c = 7 / b
Problem: a man takes twice as long to row a distance against the stream as to row the same distance in favour of the stream . the ratio of the speed of the boat ( in still water ) and the stream is :
Options: a ) 1 : 2 , b ) 2 : 5 , c ) 6 ' ' 2 , d ) 3 : 1 , e ) 4 : 7
Rationale: explanation : let speed upstream = x hen , speed downstream = 2 x speed in still water = 2 x + x / 2 speed of the stream = 2 x - x / 2 speed in still water : speed of the stream = 3 x / 2 : x / 2 = 3 : 1 answer : d
Answer: d
Python program:
a = 1 + 2 
b = 2 - 1
c = a / b
Problem: the average age of 15 students of a class is 15 years . out of these , the average age of 5 students is 14 years and that of the other 9 students is 16 years . the age of the 15 th student is ?
Options: a ) 9 , b ) 11 , c ) 15 , d ) 12 , e ) 20
Rationale: "age of the 15 th student = 15 * 15 - ( 14 * 5 + 16 * 9 ) = 225 - 214 = 11 years answer is b"
Answer: b
Python program:
a = 15 * 15
b = 5 * 14
c = 9 * 16
d = b + c 
e = a - d
Problem: a shopkeeper sold an article at $ 100 with 10 % profit . then find its cost price ?
Options: a ) $ 120 , b ) $ 100 , c ) $ 91 , d ) $ 72 , e ) $ 69
Rationale: "cost price = selling price * 100 / ( 100 + profit ) c . p . = 100 * 100 / 110 = $ 91 ( approximately ) answer is c"
Answer: c
Python program:
a = 100 + 10 
b = 100 / a
c = 100 * b
Problem: how many factors does 25 ^ 2 have ?
Options: a ) 2 , b ) 8 , c ) 24 , d ) 25 , e ) 26
Rationale: "36 ^ 2 = 6 * 6 * 6 * 6 = 2 ^ 4 * 3 ^ 4 total factors = ( 4 + 1 ) * ( 4 + 1 ) = 4 * 2 = 8 answer b ."
Answer: b
Python program:
a = 10 * 2
b = 25 / a
Problem: a glass was filled with 12 ounces of water , and 0.03 ounce of the water evaporated each day during a 22 - day period . what percent of the original amount of water evaporated during this period ?
Options: a ) 5.002 % , b ) 5.5 % , c ) 0.5 % , d ) 5 % , e ) 20 %
Rationale: "in 22 days 22 * 0.03 = 0.66 ounces of water evaporated , which is 0.66 / 12 â ˆ — 100 = 5.5 of the original amount of water . answer : b ."
Answer: b
Python program:
a = 0 * 3
b = a / 12
c = b * 100
Problem: dan ’ s car gets 32 miles per gallon . if gas costs $ 4 / gallon , then how many miles can dan ’ s car go on $ 38 of gas ?
Options: a ) 212 , b ) 256 , c ) 304 , d ) 372 , e ) 460
Rationale: "38 / 4 = 9.5 gallons 9.5 * 32 = 304 miles the answer is c ."
Answer: c
Python program:
a = 38 * 32
b = a / 4
Problem: if x + y = 20 , x - y = 10 , for integers of x and y , x = ?
Options: a ) 15 , b ) 20 , c ) 25 , d ) 13 , e ) 42
Rationale: "x + y = 20 x - y = 10 2 x = 30 x = 15 answer is a"
Answer: a
Python program:
a = 20 + 10 
b = a / 2
Problem: molly ' s age in 18 years will be 5 times her age 6 years ago . what is molly ' s present age ?
Options: a ) 8 , b ) 9 , c ) 10 , d ) 12 , e ) 14
Rationale: let x be molly ' s present age . x + 18 = 5 ( x - 6 ) x = 12 the answer is d .
Answer: d
Python program:
a = 18 - 6
Problem: in a circuit board factory , all circuit boards that pass a verification process are certified . every board that fails the verification process is indeed faulty , but 1 / 8 of those that pass are also faulty . approximately how many faulty circuit boards exist in a group of 3200 circuit boards where 64 fail inspection ?
Options: a ) 72 , b ) 192 , c ) 456 , d ) 256 , e ) 264
Rationale: total of 3,200 boards . all that fail verification are indeed faulty . so the 64 are indeed faulty . 1 / 8 those that pass are also faulty . from the 3,200 we know 64 fail . so 3,136 must pass . of these 1 / 8 are faulty . 3,136 divided by 8 gives you 392 . what one must do now is to add to the 392 which were not detected the actually detected faulty ones , namely the 64 . total faulty : 456 . answer : c
Answer: c
Python program:
a = 3200 - 64
b = 1 / 8
c = a * b
d = c + 64
Problem: the prices of tea and coffee per kg were the same in june . in july the price of coffee shot up by 20 % and that of tea dropped by 20 % . if in july , a mixture containing equal quantities of tea and coffee costs 90 / kg . how much did a kg of coffee cost in june ?
Options: a ) 50 , b ) 60 , c ) 80 , d ) 90 , e ) 120
Rationale: "let the price of tea and coffee be x per kg in june . price of tea in july = 1.2 x price of coffee in july = 0.8 x . in july the price of 1 / 2 kg ( 900 gm ) of tea and 1 / 2 kg ( 900 gm ) of coffee ( equal quantities ) = 90 1.2 x ( 1 / 2 ) + 0.8 x ( 1 / 2 ) = 90 = > x = 90 thus proved . . . option d ."
Answer: d
Python program:
a = 20 / 100
b = 1 - a
c = 20 / 100
d = c + 1 
e = b * d
f = 90 / e
Problem: a dealer purchased an article at 3 / 4 of its list price and sold 50 % more than the list price . find his gain percent ?
Options: a ) 108 % , b ) 300 % , c ) 100 % , d ) 180 % , e ) 200 %
Rationale: mp = 100 cp = 75 sp = 150 - - - - - - 75 - - - - 75 100 - - - - ? = > 100 % answer : c
Answer: c
Python program:
a = 3 / 4
b = 50 / 100
c = a / b
d = c * 100
e = d - 50
Problem: 4 / 15 of 5 / 7 of a number is greater than 4 / 9 of 2 / 5 of the same number by 24 . what is half of that number ?
Options: a ) 670 , b ) 750 , c ) 945 , d ) 375 , e ) 315
Rationale: "let no . be x 4 / 15 * 5 / 7 * x - 4 / 9 * 2 / 5 * x = 8 by further solving 20 x / 105 - 8 x / 45 = 8 4 x / 315 = 24 x = 1890 we have to find x / 2 = 1890 / 2 = 945 answer : c"
Answer: c
Python program:
a = 4 / 15
b = 5 / 7
c = a * b
d = 2 / 5
e = 4 / 9
f = d * e
g = c - f
h = 24 / g
i = h / 2
Problem: a driver just filled the car ' s gas tank with 54 liters of gasohol , a mixture consisting of 5 % ethanol and 95 % gasoline . if the car runs best on a mixture consisting of 10 % ethanol and 90 % gasoline , how many liters of ethanol must be added into the gas tank for the car to achieve optimum performance ?
Options: a ) 1.5 , b ) 2 , c ) 2.4 , d ) 2.7 , e ) 3
Rationale: "let x be the number of liters of ethanol added to the gas tank . 0.05 ( 54 ) + x = 0.1 ( 54 + x ) 0.9 x = 5.4 - 2.7 = 2.7 x = 3 liters the answer is e ."
Answer: e
Python program:
a = 54 * 5
b = 100 - 10
c = a / b
Problem: a store owner estimates that the average price of type a products will increase by 30 % next year and that the price of type b products will increase by 20 % next year . this year , the total amount paid for type a products was $ 3200 and the total price paid for type b products was $ 5800 . according to the store owner ' s estimate , and assuming the number of products purchased next year remains the same as that of this year , how much will be spent for both products next year ?
Options: a ) $ 14,755 , b ) $ 15,325 , c ) $ 11,129 , d ) $ 16,225 , e ) $ 17,155
Rationale: "cost of type a products next year = 1.3 * 3200 = 4160 cost of type b products next year = 1.2 * 5800 = 6960 total 4169 + 6960 = 11129 answer : c"
Answer: c
Python program:
a = 3 / 4
b = a * 1000
Problem: 20 % of employees are women with fair hair . 40 % of fair - haired employees are women . what percent of employees have fair hair ?
Options: a ) 25 , b ) 30 , c ) 50 , d ) 55 , e ) 60
Rationale: 20 % of employees are women with fair hair . 40 % of fair - haired employees are women . so , 20 % * employees = 40 % * fair haired employees ( because both are equal to the number of fair haired women employees ) ( 1 / 2 ) * employees = fair haired employees answer ( c )
Answer: c
Python program:
a = 20 / 40
b = a * 100
Problem: the cost of a one - family home was $ 120,000 in 1980 . in 1988 , the price had increased to $ 168,000 . what was the percent increase in the cost of the home ?
Options: a ) 60 % , b ) 50 % , c ) 55 % , d ) 40 % , e ) 33.3 %
Rationale: "increase = 168000 - 120000 = 48000 % increase = 48000 * 100 / 120000 = 40 % answer : option d"
Answer: d
Python program:
a = 4 * 4
b = 12 * a
c = b * 1000
d = 12 * 1000
e = d * 10
f = c - e
g = 12 * 1000
h = g * 10
i = f / h
j = i * 100
Problem: marginal cost is the cost of increasing the quantity produced ( or purchased ) by one unit . if the fixed cost for n products is $ 10,000 and the marginal cost is $ 250 , and the total cost is $ 16,000 , what is the value of n ?
Options: a ) 10 , b ) 24 , c ) 60 , d ) 70 , e ) 85
Rationale: "total cost for n products = fixed cost for n products + n * marginal cost - - > $ 16,000 = $ 10,000 + n * $ 250 - - > n = 24 . answer : b ."
Answer: b
Python program:
a = 250 / 10
Problem: in a sports club with 30 members , 17 play badminton and 19 play tennis and 2 do not play either . how many members play both badminton and tennis ?
Options: a ) 3 , b ) 5 , c ) 6 , d ) 7 , e ) 8
Rationale: "17 + 19 = 36 but where as total number is 30 - 2 = 28 therefore answer is 36 - 28 = 8 hence answer is e"
Answer: e
Python program:
a = 17 + 19 
b = a + 2 
c = b - 30
Problem: a boy want to make a cuboid of dimension 5 m , 6 m , 7 m from small cubes of . 04 m 3 . later he realized he can make same cuboid by making it hollow . then it takes some cubes less . what is the no . of these cubes ?
Options: a ) 2150
b ) 2250
c ) 2350
d ) 2850
e ) 3250
Rationale: volume of cuboid = 5 * 6 * 7 = 210 m 3 volume of inner cuboid = ( 5 - 1 ) * ( 6 - 1 ) * ( 7 - 1 ) = 120 m 3 therefore , volume of hollow cuboid = 210 - 120 = 90 m 3 no of cubes required = 90 / . 04 = 2250 cubes answer : b
Answer: b
Python program:
a = 5 * 6
b = a * 7
c = 4 / 100
d = b / c
e = 5 - 1
f = 6 - 1
g = e * f
h = 7 - 1
i = g * h
j = 4 / 100
k = i / j
l = d - k
Problem: a fill pipe can fill 1 / 2 of cistern in 10 minutes . in how many minutes , it can fill 1 / 2 of the cistern ?
Options: a ) 1 min , b ) 4 min , c ) 6 min , d ) 10 min , e ) 25 min
Rationale: "required time = 10 * 2 * 1 / 2 = 10 minutes answer is d"
Answer: d
Python program:
a = 10 / 1
Problem: wink , inc . follows a certain procedure that requires two tasks to be finished independently in order for a job to be done . on any given day , there is a 3 / 8 probability that task 1 will be completed on time , and a 3 / 5 probability that task 2 will be completed on time . on a certain day , what is the probability that task 1 will be completed on time , but task 2 will not ?
Options: a ) 1 / 20 , b ) 3 / 40 , c ) 13 / 40 , d ) 3 / 20 , e ) 13 / 22
Rationale: "p ( 1 and not 2 ) = 3 / 8 * ( 1 - 3 / 5 ) = 14 / 40 = 3 / 20 . answer : d ."
Answer: d
Python program:
a = 3 / 8
b = 3 / 3
c = 1 - b
d = a * c
Problem: the average weight of 10 person ' s increases by 3.5 kg when a new person comes in place of one of them weighing 65 kg . what might be the weight of the new person ?
Options: a ) 100 kg , b ) 102.5 kg , c ) 85 kg , d ) data inadequate , e ) none of these
Rationale: "explanation : total weight increased = ( 10 x 3.5 ) kg = 35 kg . weight of new person = ( 65 + 35 ) kg = 100 kg . answer : a"
Answer: a
Python program:
a = 10 * 3
b = a + 65
Problem: the average marks of 10 students in a class is 100 . but a student mark is wrongly noted as 90 instead of 10 then find the correct average marks ?
Options: a ) a ) 78 , b ) b ) 82 , c ) c ) 92 , d ) d ) 91 , e ) e ) 85
Rationale: "correct avg marks = 100 + ( 10 - 90 ) / 10 avg = 100 - 8 = 92 answer is c"
Answer: c
Python program:
a = 100 * 10
b = a - 90
c = b + 10 
d = c / 10
Problem: what will be remainder when ( 67 ^ 67 + 67 ) is divided by 68 ?
Options: a ) 65 , b ) 66 , c ) 67 , d ) 71 , e ) 72
Rationale: ( xn + 1 ) will be divisible by ( x + 1 ) only when n is odd . ( 67 ^ 67 + 1 ) will be divisible by ( 67 + 1 ) ( 67 ^ 67 + 1 ) + 66 , when divided by 68 will give 66 as remainder . b )
Answer: b
Python program:
a = 67 - 68
b = a ** 67
c = 67 + b
Problem: a reduction of 25 % in the price of oil enables a house wife to obtain 5 kgs more for rs . 1000 , what is the reduced price for kg ?
Options: a ) s . 50 , b ) s . 46 , c ) s . 49 , d ) s . 41 , e ) s . 42
Rationale: "1000 * ( 25 / 100 ) = 250 - - - - 5 ? - - - - 1 = > rs . 50 answer : a"
Answer: a
Python program:
a = 1000 * 25
b = a / 100
c = b / 5
Problem: a specialized type of sand consists of 40 % mineral x by volume and 60 % mineral y by volume . if mineral x weighs 4 grams per cubic centimeter and mineral y weighs 3 grams per cubic centimeter , how many grams does a cubic meter of specialized sand combination weigh ? ( 1 meter = 100 centimeters )
Options: a ) 5 , 500,000
b ) 2 , 400,000
c ) 55,000
d ) 28,000
e ) 280
Rationale: let the volume be 1 m ^ 3 = 1 m * 1 m * 1 m = 100 cm * 100 cm * 100 cm = 1 , 000,000 cm ^ 3 by volume 40 % is x = 400,000 cm ^ 3 60 % is y = 600,000 cm ^ 3 by weight , in 1 cm ^ 3 , x is 4 gms in 400,000 cm ^ 3 , x = 4 * 400,000 = 1 , 600,000 grams in 1 cm ^ 3 , y is 3 gms in 600,000 cm ^ 3 , y = 3 * 600,000 = 1 , 800,000 gms total gms in 1 m ^ 3 = 1 , 600,000 + 1 , 800,000 = 2 , 400,000 answer : b
Answer: b
Python program:
a = volume_cube / (
b = a * 10
c = b * 4
d = c + 4 
e = volume_cube / (
f = e * 10
g = 2 * 3
h = f * g
i = d - h
Problem: two cars a and b start from boston and new york respectively simultaneously and travel towards each other at constant speeds along the same route . after meeting at a point between boston and new york the two cars a and b proceed to their respective destinations of new york and boston . car a reaches new york 20 minutes after the two cars have met and car b reaches boston 90 minutes after they have met . how long did car a take to cover the distance between boston and new york ?
Options: a ) 1 hour , b ) 1 hour 10 minutes , c ) 2 hours 30 minutes , d ) 1 hour 20 minutes , e ) 2 hours 10 minutes
Rationale: "both cars leave at the same time both cars travel at constant speed stealing a useful piece of information from paragkan : if two objects a and b start from opposite points and , after having met en route , reach their respective destinations in a and b mins ( or any other measure of time ) respectively , then the ratio of their speeds ratio of speed : ( a / b ) = sq . rt ( b / a ) sq . rt ( b / a ) sq . rt ( 90 / 20 ) sq . rt ( 3 / 2 ) so , for every three units of distance a travels , b travels two . because we know the ratio of speed and the time it took b to travel the distance a has n ' t yet covered , we can find the time it took a to cover the distance b did in 90 minutes . 90 * ( 2 / 3 ) where 2 / 3 represents the lesser amount of time it took a to travel the distance b did in 90 minutes . = 60 minutes . therefore , a took 20 minutes to travel the first portion then 60 minutes to travel the distance b did in 90 minutes . a spent ( 20 + 60 ) = 80 minutes on the road . d . 1 hour 20 minutes"
Answer: d
Python program:
a = 20 / 90
b = math.sqrt(a)
c = b * 90
d = c + 20
Problem: the price of a coat in a certain store is $ 500 . if the price of the coat is to be reduced by $ 300 , by what percent is the price to be reduced ?
Options: a ) 10 % , b ) 15 % , c ) 20 % , d ) 60 % , e ) 30 %
Rationale: price of a coat in a certain store = $ 500 the price of the coat is to be reduced by $ 300 % change = ( final value - initial value ) * 100 / initial value % reduction = ( reduction in price ) * 100 / initial value i . e . % reduction = ( 300 ) * 100 / 500 = 60 % answer : option d
Answer: d
Python program:
a = 300 / 500
b = a * 100
Problem: what is the 10 th digit to the right of the decimal point in the decimal equivalent of 124 / 22 ?
Options: a ) 2 , b ) 3 , c ) 4 , d ) 7 , e ) 6
Rationale: "124 / 22 = 5.6363 . . . . 63 is non - terminating repeating decimal . the 10 th digit to the right of decimal point will be 3 . answer b"
Answer: b
Python program:
a = 124 / 22