euclaise/mathqa_programs huggingface dataset:
Problem: the distance from steve ' s house to work is 28 km . on the way back steve drives twice as fast as he did on the way to work . altogether , steve is spending 6 hours a day on the roads . what is steve ' s speed on the way back from work ?
Options: a ) 5 . , b ) 10 . , c ) 14 . , d ) 15 . , e ) 20 .
Rationale: "time is in the ratio 2 : 1 : : to : fro office therefore , 2 x + 1 x = 6 hrs time take to come back - 2 hrs , distance travelled - 28 km = > speed = 14 kmph c"
Answer: c
Python program:
a = 28 / 2
b = 28 + a 
c = b / 6
d = c * 2
Problem: at a certain company , each employee has a salary grade s that is at least 1 and at most 5 . each employee receives an hourly wage p , in dollars , determined by the formula p = 9.50 + 0.25 ( s – 2 ) . an employee with a salary grade of 5 receives how many more dollars per hour than an employee with a salary grade of 1 ?
Options: a ) $ 0.50 , b ) $ 1.00 , c ) $ 1.25 , d ) $ 1.50 , e ) $ 1.75
Rationale: oa is definitely wrong . the answer should be e .
Answer: e
Python program:
a = 5 - 1
b = 0 * 25
c = b + 0
Problem: there are 20 players in a chess group , and each player plays each of the others once . given that each game is played by two players , how many total games will be played ?
Options: a ) 10 , b ) 30 , c ) 190 , d ) 60 , e ) 90
Rationale: "20 players are there . two players play one game with one another . so 20 c 2 = 20 * 19 / 2 = 190 so option c is correct"
Answer: c
Python program:
a = 20 - 1
b = 20 * a
c = b / 2
Problem: the sum of four consecutive even numbers is 36 . find the sum of the squares of these numbers ?
Options: a ) 296
b ) 252
c ) 344
d ) 388
e ) none of these
Rationale: let the four numbers be x , x + 2 , x + 4 and x + 6 . = > x + x + 2 + x + 4 + x + 6 = 36 = > 4 x + 12 = 36 = > x = 6 the numbers are 6 , 8 , 10 and 12 . sum of their squares = 62 + 82 + 102 + 122 = 36 + 64 + 100 + 144 = 344 . answer : c
Answer: c
Python program:
a = 36 - 10
b = a - 2
c = b / 4
d = c + 2 
e = d + 2 
f = e ** 2
g = 36 - 10
h = g - 2
i = h / 4
j = i + 2 
k = j + 2 
l = k + 2 
m = l ** 2
n = f + m 
o = 36 - 10
p = o - 2
q = p / 4
r = q ** 2
s = 36 - 10
t = s - 2
u = t / 4
v = u + 2 
w = v ** 2
x = r + w 
y = n + x
Problem: p is 40 % more efficient than q . p can complete a work in 24 days . if p and q work together , how many days will it take to complete the same work ?
Options: a ) 8 , b ) 9 , c ) 11 , d ) 14 , e ) 15
Rationale: "the work done by p in 1 day = 1 / 24 let work done by q in 1 day = q q × ( 140 / 100 ) = 1 / 24 q = 100 / ( 24 × 140 ) = 10 / ( 24 × 14 ) the work done by p and q in 1 day = 1 / 24 + 10 / ( 24 × 14 ) = 24 / ( 24 × 14 ) = 1 / 14 p and q together can do the work in 14 days . the answer is d ."
Answer: d
Python program:
a = 40 / 100
b = a + 1 
c = b * 24
d = 40 / 100
e = d + 1 
f = e + 1 
g = c / f
Problem: if a person walks at 14 km / hr instead of 10 km / hr , he would have walked 20 km more . the actual distance travelled by him is :
Options: a ) 50 km , b ) 56 km , c ) 70 km , d ) 80 km , e ) 46 km
Rationale: "let the actual distance travelled be x km . then , x / 10 = ( x + 20 ) / 14 14 x = 10 x + 200 4 x = 200 x = 50 km . answer : a"
Answer: a
Python program:
a = 14 - 10
b = 20 / a
c = 10 * b
Problem: ( 422 + 404 ) 2 − ( 4 × 422 × 404 ) = ?
Options: a ) none of these , b ) 342 , c ) 324 , d ) 312 , e ) can not be determined
Rationale: "explanation : given equation is in the form ( a + b ) 2 − 4 ab where a = 422 and b = 404 hence answer = ( a + b ) 2 − 4 ab = ( a − b ) 2 = ( 422 − 404 ) 2 = 182 = 324 , answer : option c"
Answer: c
Python program:
a = 422 + 404 
b = a / 2
Problem: the length of the rectangular field is double its width . inside the field there is square shaped pond 8 m long . if the area of the pond is 1 / 98 of the area of the field . what is the length of the field ?
Options: a ) 73 , b ) 32 , c ) 34 , d ) 43 , e ) 112
Rationale: "explanation : a / 98 = 8 * 8 = > a = 8 * 8 * 98 x * 2 x = 8 * 8 * 98 x = 56 = > 2 x = 112 answer : option e"
Answer: e
Python program:
a = square_area * (
b = a / 98
c = 1/(2)
d = math.sqrt(b)
Problem: there are 50 players in a chess group , and each player plays each of the others once . given that each game is played by two players , how many total games will be played ?
Options: a ) 1000 , b ) 3000 , c ) 1225 , d ) 6000 , e ) 9000
Rationale: "50 players are there . two players play one game with one another . so 50 c 2 = 50 * 49 / 2 = 1225 so option c is correct"
Answer: c
Python program:
a = 50 - 1
b = 50 * a
c = b / 2
Problem: an amount of rs . 100000 is invested in two types of shares . the first yields an interest of 9 % p . a and the second , 11 % p . a . if the total interest at the end of one year is 9 1 / 4 % , then the amount invested at 11 % was ?
Options: a ) 12500 , b ) 37500 , c ) 29977 , d ) 26777 , e ) 19871
Rationale: "let the sum invested at 9 % be rs . x and that invested at 11 % be rs . ( 100000 - x ) . then , ( x * 9 * 1 ) / 100 + [ ( 100000 - x ) * 11 * 1 ] / 100 = ( 100000 * 37 / 4 * 1 / 100 ) ( 9 x + 1100000 - 11 x ) = 37000 / 4 = 925000 x = 87500 sum invested at 9 % = rs . 87500 sum invested at 11 % = rs . ( 100000 - 87500 ) = rs . 12500 . answer : a"
Answer: a
Python program:
a = 1 / 4
b = 9 + a 
c = b / 100
d = 100000 * c
e = 9 / 100
f = 100000 * e
g = d - f
h = 11 / 100
i = 9 / 100
j = h - i
k = g / j
Problem: a train after traveling for 50 km meets with an accident and then proceeds at 3 / 4 of its former speed and arrives at its destination 35 minutes late . had the accident occurred 24 km farther , it would have reached the destination only 25 minutes late . what is the speed y of the train .
Options: a ) a ) 45 , b ) b ) 33 , c ) c ) 48 , d ) d ) 55 , e ) e ) 61
Rationale: "let y be the balance distance to be covered and x be the former speed . a train after traveling for 50 km meets with an accident and then proceeds at 3 / 4 of its former speed and arrives at its destination 35 minutes late so , y / ( 3 x / 4 ) - y / x = 35 / 60 4 y / 3 x - y / x = 7 / 12 y / x ( 4 / 3 - 1 ) = 7 / 12 y / x * 1 / 3 = 7 / 12 y / x = 7 / 4 4 y - 7 x = 0 . . . . . . . . 1 had the accident occurred 24 km farther , it would have reached the destination only 25 minutes late so , ( y - 24 ) / ( 3 x / 4 ) - ( y - 24 ) / x = 25 / 60 4 ( y - 24 ) / 3 x - ( y - 24 ) / x = 5 / 12 ( y - 24 ) / x ( 4 / 3 - 1 ) = 5 / 12 ( y - 24 ) / x * 1 / 3 = 5 / 12 ( y - 24 ) * 12 = 3 x * 5 ( y - 24 ) * 4 = 5 x 4 y - 5 x = 96 . . . . . . . 2 eq 2 - eq 1 2 x = 96 x = 48 = y ans = c"
Answer: c
Python program:
a = 24 * 4
b = a / 3
c = b - 24
d = 35 - 25
e = d + 50 
f = 35 - 25
g = e / f
h = c * g
Problem: a and b can do a piece of work in 10 days , b and c in 5 days , c and a in 15 days . how long will c take to do it ?
Options: a ) 77 days , b ) 55 days , c ) 12 days , d ) 33 days , e ) 11 days
Rationale: 2 c = 1 / 5 + 1 / 15 – 1 / 10 = 1 / 6 c = 1 / 12 = > 12 days answer : c
Answer: c
Python program:
a = 10 * 3
b = 10 * 3
c = b / 15
d = 10 * 3
e = d / 10
f = 10 * 3
g = f / 5
h = e + g 
i = c + h 
j = i / 2
k = 10 * 3
l = k / 10
m = j - l
n = a / m
Problem: when 1 / 10 percent of 1,000 is subtracted from 1 / 10 of 1,000 , the difference is
Options: a ) 10 , b ) 100 , c ) 999 , d ) 99 , e ) 9
Rationale: "( 1 / 10 ) * 1000 - ( 1 / 10 ) % * 1000 = 100 - ( 1 / 1000 ) * 1000 = 100 - 1 = 99 the answer is d ."
Answer: d
Python program:
a = 3 + 4 
b = a * 1000
c = 1 / 10
d = b * c
e = 1 / 10
f = e / 100
g = 3 + 4 
h = g * 1000
i = f * h
j = d - i
Problem: a rectangular courtyard 3.78 meters long 5.25 meters wide is to be paved exactly with square tiles , all of the same size . what is the largest size of the tile which could be used for the purpose ?
Options: a ) 14 cms
b ) 21 cms
c ) 42 cms
d ) none of these
e ) 56 cms
Rationale: explanation : 3.78 meters = 378 cm = 2 × 3 × 3 × 3 × 7 5.25 meters = 525 cm = 5 × 5 × 3 × 7 hence common factors are 3 and 7 hence lcm = 3 × 7 = 21 hence largest size of square tiles that can be paved exactly with square tiles is 21 cm . answer : b
Answer: b
Python program:
a = 3 * 78
b = a / 2
c = b / 3
d = c / 3
e = 3 * 78
f = e / 2
g = f / 3
h = g / 3
i = h / 3
j = d / i
k = 3 * 78
l = k / 2
m = l / 3
n = m / 3
o = n / 3
p = j * o
Problem: if a , b , c , d , e and f are integers and ( ab + cdef ) < 0 , then what is the maximum number e of integers that can be negative ?
Options: a ) 2 , b ) 3 , c ) 4 , d ) 5 , e ) 6
Rationale: "minimuum should be 1 maximum should be 4 : 1 out of a or b to make the multiplication negative 3 out of c , d , e or f to make the multiplication negative . negative + negative < 0 answer : c maximum will be 5 . . you dont require both the multiplicatin to be negative for entire equation to be negative . . . any one a or b can be negative to make ab negative and it can still be more ( away from 0 ) than the multiplication of 4 other - ve numbers . . . actually by writing minimum required as 1 out of 6 , you are actually meaning 5 out of 6 also possible as you will see e = 5 or 1 will give you same equation . . ans d"
Answer: d
Python program:
a = 10 / 2
b = a + 0
Problem: convert 1.3 hectares in ares
Options: a ) 130 ares . , b ) 160 ares . , c ) 180 ares . , d ) 230 ares . , e ) 250 ares .
Rationale: "1.3 hectares in ares 1 hectare = 100 ares therefore , 1.3 hectares = 1.3 × 100 ares = 130 ares . answer - a"
Answer: a
Python program:
a = 3 + 2 
b = a * 2
c = 3 + 2 
d = c * 2
e = b * d
f = e * 1
g = 3 + 2 
h = g * 2
i = 3 + 2 
j = i * 2
k = h * j
l = f / k
Problem: on a certain road , 10 % of the motorists exceed the posted speed limit and receive speeding tickets , but 40 % of the motorists who exceed the posted speed limit do not receive speeding tickets . what percent of the motorists on that road exceed the posted speed limit ?
Options: a ) 10.5 % , b ) 12.5 % , c ) 16.7 % , d ) 25 % , e ) 30 %
Rationale: "suppose there are x motorists . 10 % of them exceeded the speed limit and received the ticket , i . e . x / 10 . again , suppose total no . of motorists who exceeded the speed limit are y . 40 % of y exceeded the speed limit but did n ' t received the ticket , i . e . 2 y / 5 . it means 3 y / 5 received the ticket . hence , 3 y / 5 = x / 10 or y / x = 1 / 6 or y / x * 100 = 1 / 6 * 100 = 16.7 % c"
Answer: c
Python program:
a = 100 - 40
b = 10 / a
c = b * 100
Problem: there is 60 lit of milk and water in which milk forms 84 % . howmuch water must be added to this solution to make it solution in which milk forms 54 %
Options: a ) 18.75 , b ) 19.75 , c ) 20.75 , d ) 33 , e ) 22.75
Rationale: 60 * 84 / 100 = 50.40 lit milk that is 9.60 lit water let x lit water will be added then ( 60 + x ) * 54 / 100 = 50.40 so x = 33.33 answer : d
Answer: d
Python program:
a = 100 / 54
b = 60 * 84
c = b / 100
d = a * c
e = d - 60
Problem: a certain bus driver is paid a regular rate of $ 14 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 $ 998 in total compensation , how many total hours did he work that week ?
Options: a ) 54 , b ) 51 , c ) 58 , d ) 55 , e ) 52
Rationale: "for 40 hrs = 40 * 14 = 560 excess = 998 - 560 = 438 for extra hours = . 75 ( 14 ) = 10.5 + 14 = 24.5 number of extra hrs = 438 / 24.5 = 17.8 = 18 approx . total hrs = 40 + 18 = 58 answer c"
Answer: c
Python program:
a = 14 * 40
b = 998 - a
c = 100 + 75 
d = 14 * c
e = d / 100
f = b / e
g = 40 + f
Problem: when n is divided by 24 , the remainder is 6 . what is the remainder when 3 n is divided by 8 ?
Options: a ) 3 , b ) 4 , c ) 5 , d ) 6 , e ) 2
Rationale: "let n = 6 ( leaves a remainder of 6 when divided by 24 ) 3 n = 3 ( 6 ) = 18 , which leaves a remainder of 2 when divided by 8 . answer e"
Answer: e
Python program:
a = 6 - reminder
Problem: a certain debt will be paid in 40 installments from january 1 to december 31 of a certain year . each of the first 20 payments is to be $ 410 ; each of the remaining payments is to be $ 65 more than each of the first 20 payments . what is the average ( arithmetic mean ) payment that will be made on the debt for the year ?
Options: a ) 442.5 , b ) 450 , c ) 465 , d ) 468 , e ) 475
Rationale: "total number of installments = 40 payment per installment for the first 20 installments = 410 payment per installment for the remaining 20 installments = 410 + 65 = 475 average = ( 20 * 410 + 20 * 475 ) / 40 = 442.50 answer a"
Answer: a
Python program:
a = 20 * 410
b = 410 + 65 
c = 40 - 20
d = b * c
e = a + d 
f = e / 40
Problem: a shopkeeper buys two articles for rs . 1000 each and then sells them , making 20 % profit on the first article and 20 % loss on second article . find the net profit or loss percent ?
Options: a ) 200 , b ) 177 , c ) 188 , d ) 166 , e ) 129
Rationale: "profit on first article = 20 % of 1000 = 200 . answer : a"
Answer: a
Python program:
a = 100 - 20
b = 100 / a
c = b * 1000
d = 100 + 20 
e = 100 / d
f = e * 1000
g = c + f 
h = 1000 + 1000 
i = g - h
j = i * 100
k = 100 - 20
l = 100 / k
m = l * 1000
n = 100 + 20 
o = 100 / n
p = o * 1000
q = m + p 
r = j / q
s = r * 100
Problem: 20 men do a work in 20 days . how many men are needed to finish the work in 4 days ?
Options: a ) 50 , b ) 20 , c ) 30 , d ) 100 , e ) 15
Rationale: "men required to finish the work in 4 days = 20 * 20 / 4 = 100 answer is d"
Answer: d
Python program:
a = 20 * 20
b = a / 4
Problem: the cost of 20 articles is equal to selling price of 10 . find the gain or loss percent ?
Options: a ) 50 % , b ) 100 % , c ) 25 % , d ) 15 % , e ) 60 %
Rationale: c . p . of each article be $ 1 c . p . of 10 articles = 10 gain % = 10 / 10 * 100 = 100 % answer is b
Answer: b
Python program:
a = 10 / 10
b = a * 100
Problem: a man owns 2 / 3 of market reserch beauro buzness , and sells 3 / 4 of his shares for 6500 rs , what is the value of buzness ?
Options: a ) 150000 , b ) 16000 , c ) 15000 , d ) 190000 , e ) 13000
Rationale: "if value of business = x total sell ( 2 x / 3 ) ( 3 / 4 ) = 6500 - > x = 13000 answer : e"
Answer: e
Python program:
a = 2 / 3
b = 3 / 4
c = a * b
d = 6500 / c
Problem: johnny makes $ 7.35 per hour at his work . if he works 6 hours , how much money will he earn ?
Options: a ) $ 30 , b ) $ 54 , c ) $ 48.32 , d ) $ 44.10 , e ) $ 9.60
Rationale: 4.75 * 6 = 28.50 . answer is c .
Answer: c
Python program:
a = 7 * 35
Problem: find the 25 % of rs . 200 .
Options: a ) rs . 50 , b ) rs . 70 , c ) rs . 100 , d ) rs . 80 , e ) rs . 60
Rationale: explanation : 25 % of 200 = > 25 / 100 * 200 = rs . 50 answer : a
Answer: a
Python program:
a = 25 / 100
b = 200 * a
Problem: what is the least common multiple of 15 , 16 , and 24 ?
Options: a ) 60 , b ) 120 , c ) 240 , d ) 360 , e ) 720
Rationale: "let us first write the numbers in the form of prime factors : 15 = 3 * 5 16 = 2 ^ 4 24 = 2 * 17 ^ 1 the lcm would be the largest powers of the prime numbers from all these three numbers . hence lcm = 240 option c"
Answer: c
Python program:
a = 10 + 2 
b = 3 * 10
c = b - 3
d = math.lcm(a, c)
e = math.lcm(d, 16)
Problem: how many integers from 101 to 800 , inclusive , remains the value unchanged when the digits were reversed ?
Options: a ) 50 , b ) 60 , c ) 70 , d ) 80 , e ) 90
Rationale: "first digit possibilities - 1 through 7 = 7 8 is not possible here because it would result in a number greater than 8 ( i . e 808 , 818 . . ) second digit possibilities - 0 though 9 = 10 third digit is same as first digit = > total possible number meeting the given conditions = 7 * 10 = 70 answer is c ."
Answer: c
Python program:
a = 800 / 10
Problem: a bowl of fruit contains 14 apples and 25 oranges . how many oranges must be removed so that 70 % of the pieces of fruit in the bowl will be apples ?
Options: a ) 3 , b ) 6 , c ) 14 , d ) 17 , e ) 19
Rationale: "number of apples = 14 number of oranges = 25 let number of oranges that must be removed so that 70 % of pieces of fruit in bowl will be apples = x total number of fruits after x oranges are removed = 14 + ( 25 - x ) = 39 - x 14 / ( 39 - x ) = 7 / 10 = > 20 = 39 - x = > x = 19 answer e"
Answer: e
Python program:
a = 14 + 25 
b = 70 / 100
c = a * b
d = c - 14
e = 70 / 100
f = d / e
Problem: on july 1 of last year , total employees at company e was decreased by 10 percent . without any change in the salaries of the remaining employees , the average ( arithmetic mean ) employee salary was 10 percent more after the decrease in the number of employees than before the decrease . the total of the combined salaries of all the employees at company e after july 1 last year was what percent r of thatbeforejuly 1 last year ?
Options: a ) 90 % , b ) 99 % , c ) 100 % , d ) 101 % , e ) 110 %
Rationale: the total number of employees = n the average salary = x total salary to all emplyoees = xn after the total number of employees = n - 0.1 n = 0.9 n the average salary = x + 10 % of x = 1.1 x total salary to all emplyoees = 0.9 n ( 1.1 x ) total salary after as a % of total salary before r = [ 0.9 n ( 1.1 x ) ] / xn = 0.99 or 99 % . b
Answer: b
Python program:
a = 10 * 10
Problem: 3 friends a , b , c went for week end party to mcdonald ’ s restaurant and there they measure there weights in some order in 7 rounds . a , b , c , ab , bc , ac , abc . final round measure is 140 kg then find the average weight of all the 7 rounds ?
Options: a ) 98.5 kgs , b ) 80 kgs , c ) 76.5 kgs , d ) 67.5 kgs , e ) 58.2 kgs
Rationale: "average weight = [ ( a + b + c + ( a + b ) + ( b + c ) + ( c + a ) + ( a + b + c ) ] / 7 = 4 ( a + b + c ) / 7 = 4 x 140 / 7 = 80 kgs answer : b"
Answer: b
Python program:
a = 1 + 3 
b = a * 140
c = b / 7
Problem: the ratio of the volumes of two cubes is 8 : 27 what is the ratio of their total surface areas ?
Options: a ) 2 : 4 , b ) 3 : 6 , c ) 4 : 12 , d ) 4 : 9 , e ) 1 : 3
Rationale: "ratio of the sides = â ³ â ˆ š 8 : â ³ â ˆ š 27 = 2 : 3 ratio of surface areas = 4 : 9 answer : d"
Answer: d
Python program:
a = 8 / 27
b = 1 / 3
c = a ** b
Problem: what is the greatest of 3 consecutive integers whose sum is 21 ?
Options: a ) 6 , b ) 7 , c ) 8 , d ) 9 , e ) 5
Rationale: "the sum of three consecutive integers can be written as n + ( n + 1 ) + ( n + 2 ) = 3 n + 3 if the sum is 24 , we need to solve the equation 3 n + 3 = 21 ; = > 3 n = 18 ; = > n = 6 the greatest of the three numbers is therefore 6 + 2 = 8 answer : c"
Answer: c
Python program:
a = 21 - 3
b = a / 3
c = b + 2
Problem: x starts a business with rs . 45000 . y joins in the business after 3 months with rs . 24000 . what will be the ratio in which they should share the profit at the end of the year ?
Options: a ) 1 : 2 , b ) 2 : 1 , c ) 3 : 2 , d ) 2 : 3 , e ) 5 : 2
Rationale: "ratio in which they should share the profit = ratio of the investments multiplied by the time period = 45000 × 12 : 24000 × 9 = 45 × 12 : 24 × 9 = 15 × 12 : 8 × 9 = 5 : 2 answer is e ."
Answer: e
Python program:
a = 45000 * 12
b = 4 + 3 
c = 24000 * b
d = a / c
Problem: if a and b get profits of rs . 4,000 and rs . 2,000 respectively at the end of year then ratio of their investments are
Options: a ) 4 : 1 , b ) 1 : 4 , c ) 3 : 2 , d ) 2 : 3 , e ) 2 : 1
Rationale: "ratio = 4000 / 2000 = 2 : 1 answer : e"
Answer: e
Python program:
a = 3 * 2
b = a * 100
c = b * 100
d = 3 * 2
e = d * 100
f = e * 100
g = 2 + 3 
h = g * 2
i = f / h
j = c / i
Problem: a certain social security recipient will receive an annual benefit of $ 12,000 provided he has annual earnings of $ 9,360 or less , but the benefit will be reduced by $ 1 for every $ 3 of annual earnings over $ 9,360 . what amount of total annual earnings would result in a 45 percent reduction in the recipient ' s annual social security benefit ? ( assume social security benefits are not counted as part of annual earnings . )
Options: a ) $ 15,360 , b ) $ 17,360 , c ) $ 18,000 , d ) $ 21,360 , e ) $ 29,160
Rationale: "for every $ 3 earn above $ 9360 , the recipient loses $ 1 of benefit . or for every $ 1 loss in the benefit , the recipient earns $ 3 above $ 9360 if earning is ; 9360 + 3 x benefit = 12000 - x or the vice versa if benefit is 12000 - x , the earning becomes 9360 + 3 x he lost 50 % of the benefit ; benefit received = 12000 - 0.45 * 12000 = 12000 - 5400 x = 6600 earning becomes 9360 + 3 x = 9360 + 3 * 6600 = 29160 ans : e"
Answer: e
Python program:
a = 100 * 3
b = a + const_60
Problem: speed of a boat in standing water is 8 kmph and the speed of the stream is 2 kmph . a man rows to place at a distance of 210 km and comes back to the starting point . the total time taken by him is :
Options: a ) 48 hours , b ) 51 hours , c ) 36 hours , d ) 56 hours , e ) none
Rationale: "sol . speed upstream = 6 kmph ; speed downstream = 10 kmph . ∴ total time taken = [ 210 / 6 + 210 / 10 ] hours = 56 hours . answer d"
Answer: d
Python program:
a = 8 + 2 
b = 210 / a
c = 8 - 2
d = 210 / c
e = b + d
Problem: find the annual income derived by investing $ 6800 in 20 % stock at 136 .
Options: a ) 550 , b ) 1000 , c ) 2500 , d ) 300 , e ) 4000
Rationale: "by investing $ 136 , income obtained = $ 20 . by investing $ 6800 , income obtained = $ [ ( 20 / 136 ) * 6800 ] = $ 1000 . answer b ."
Answer: b
Python program:
a = 6800 * 20
b = a / 136
Problem: if x = - 12 / 5 and y = - 6 / 7 , what is the value of the expression - 2 x – y ^ 2 ?
Options: a ) 741 / 357 , b ) 456 / 789 , c ) 636 / 735 , d ) 564 / 263 , e ) - 636 / 735
Rationale: "x = - 12 / 15 and y = - 6 / 7 = = > - 2 ( - 12 / 15 ) - ( - 6 / 7 ) ^ 2 = 24 / 15 - 36 / 49 = 636 / 735 ans : c"
Answer: c
Python program:
a = 12 / 5
b = 7 * a
c = 6 / 7
d = c ** 7
e = b - d
Problem: a man can row his boat with the stream at 16 km / h and against the stream in 6 km / h . the man ' s rate is ?
Options: a ) 5 kmph , b ) 6 kmph , c ) 7 kmph , d ) 4 kmph , e ) 9 kmph
Rationale: "explanation : ds = 16 us = 6 s = ? s = ( 16 - 6 ) / 2 = 5 kmph answer : a"
Answer: a
Python program:
a = 16 - 6
b = a / 2
Problem: if the compound interest on a certain sum of money for 4 years at 10 % per annum be rs . 993 , what would be the simple interest ?
Options: a ) rs . 880 , b ) rs . 890 , c ) rs . 1200 , d ) rs . 900 , e ) none
Rationale: "let p = principal a - amount we have a = p ( 1 + r / 100 ) 3 and ci = a - p atq 993 = p ( 1 + r / 100 ) 3 - p ? p = 3000 / - now si @ 10 % on 3000 / - for 4 yrs = ( 3000 x 10 x 4 ) / 100 = 1200 / - answer : c ."
Answer: c
Python program:
a = 3 * 0
b = a * 10
c = b * 10
d = c * 4
e = d / 100
Problem: when n is divided by 27 , the remainder is 4 . what is the remainder when n + 16 is divided by 7 ?
Options: a ) 2 , b ) 3 , c ) 4 , d ) 5 , e ) 6
Rationale: "assume n = 23 remainder ( n / 27 ) = 4 n + 16 = 39 remainder ( 39 / 7 ) = 4 option c"
Answer: c
Python program:
a = 4 - reminder
Problem: jar a has 16 % more marbles than jar b . what percent of marbles from jar a need to be moved into jar b so that both jars have equal marbles ?
Options: a ) 5 % , b ) 7 % , c ) 9 % , d ) 11 % , e ) 13 %
Rationale: an easy way to solve this question is by number plugging . assume there are 100 marbles in jar b then in jar a there will be 116 marbles . now , for both jars to have equal marbles we should move 8 marbles from a to b , which is 8 / 116 = ~ 7 % of a . answer : b .
Answer: b
Python program:
a = 16 / 2
b = 16 + 100 
c = a / b
d = c * 100
Problem: a and b started a business investing rs . 21,000 and rs . 28,000 respectively . out of a total profit of rs . 14,000 , b ’ s share is :
Options: a ) 7600 , b ) 7700 , c ) 7800 , d ) 7900 , e ) 8000
Rationale: "ratio of their shares = 21000 : 28000 = 3 : 4 . b ’ s share = rs . 14000 * 4 / 7 = rs . 8000 answer : e"
Answer: e
Python program:
a = 3 * 3
b = 3 * 3
c = b + 1 
d = a * c
e = d + 14 
f = 3 * 3
g = f + 1 
h = 14 * 0
i = e / h
Problem: a merchant marks goods up by 75 % and then offers a discount on the marked price . the profit that the merchant makes after offering the discount is 5 % . what % discount did the merchant offer ?
Options: a ) 20 % , b ) 25 % , c ) 35 % , d ) 40 % , e ) 45 %
Rationale: "let p be the original price of the goods and let x be the rate after the markup . ( 1.75 p ) * x = 1.05 p x = 1.05 / 1.75 = 0.6 which is a discount of 40 % . the answer is d ."
Answer: d
Python program:
a = 75 / 100
b = 1 + a 
c = b - 1
d = 5 / 100
e = c - d
f = 75 / 100
g = 1 + f 
h = e / g
i = h * 100