euclaise/mathqa_programs huggingface dataset:
Problem: a alone can complete a work in 16 days and b alone can do in 12 days . star ɵ ng with a , they work on alternate days . the total work will be completed in
Options: a ) 1314 , b ) 1312 , c ) 1334 , d ) 1344 , e ) none of these
Rationale: explana ɵ on : a ' s 1 day work = 1 / 16 b ' s 1 day work = 1 / 12 as they are working on alternate day ' s so their 2 days work = ( 1 / 16 ) + ( 1 / 12 ) = 7 / 48 [ here is a small technique , total work done will be 1 , right , then mul ɵ ply numerator ɵ ll denominator , as 7 * 6 = 42 , 7 * 7 = 49 , as 7 * 7 is more than 48 , so we will consider 7 * 6 , means 6 pairs ] work done in 6 pairs = 6 * ( 7 / 48 ) = 7 / 8 remaining work = 1 - 7 / 8 = 1 / 8 on 13 th day it will a turn , then remaining work = ( 1 / 8 ) - ( 1 / 16 ) = 1 / 16 on 14 th day it is b turn , 1 / 12 work done by b in 1 day 1 / 16 work will be done in ( 12 * 1 / 16 ) = 3 / 4 day so total days = 1334 answer : c
Answer: c
Python program:
a = 1/(12)
b = 1/(16)
c = a + b 
d = 1/(c)
e = d * 2
f = 100 * e
Problem: a cistern which could be filled in 6 hours takes one hour more to be filled owing to a leak in its bottom . if the cistern is full in what time will the leak empty it ?
Options: a ) 76 hrs , b ) 99 hrs , c ) 15 hrs , d ) 90 hrs , e ) 11 hrs
Rationale: "1 / 6 - 1 / x = 1 / 10 = > 15 hrs answer : c"
Answer: c
Python program:
a = 1 / 6
b = 1 / 10
c = a - b
d = 1/(c)
Problem: george is 8 years more than christopher and ford is 2 years younger than christopher . the sum of their ages is 60 . find the ages of ford .
Options: a ) 14 , b ) 15 , c ) 16 , d ) 17 , e ) 18
Rationale: "christopher age = x george age , y = x + 8 - - - - - - - - - - > ( 1 ) ford age , z = x - 2 - - - - - - - - - - - - > ( 2 ) sum of their ages , x + y + z = 60 - - - - > ( 3 ) substitute z and y values in equation ( 3 ) therefore , x + ( x + 8 ) + ( x - 2 ) = 60 = > 3 x + 8 - 2 = 60 = > 3 x = 60 - 6 = > 3 x = 54 = > x = 54 / 3 x = 18 ( christopher ' s age ) substitute x value in equation 1 & 2 y = x + 8 y = 18 + 8 y = 26 ( george ' s age ) z = x - 2 z = 18 - 2 z = 16 ( ford ' s age ) answer : c"
Answer: c
Python program:
a = 8 - 2
b = 60 - a
c = b / 3
Problem: on sunday , bill ran 4 more miles than he ran on saturday . julia did not run on saturday , but she ran twice the number of miles on sunday that bill ran on sunday . if bill and julia ran a total of 28 miles on saturday and sunday , how many miles did bill run on sunday ?
Options: a ) 5 , b ) 6 , c ) 7 , d ) 8 , e ) 9
Rationale: "let bill run x on saturday , so he will run x + 4 on sunday . . julia will run 2 * ( x + 4 ) on sunday . . totai = x + x + 4 + 2 x + 8 = 28 . . 4 x + 12 = 28 . . x = 4 . . ans = x + 4 = 4 + 4 = 8 aswer d"
Answer: d
Python program:
a = 2 * 4
b = 4 + a 
c = 28 - b
d = c / 4
e = d + 4
Problem: bhanu spends 30 % of his income on petrol on scooter 14 % of the remaining on house rent and the balance on food . if he spends rs . 300 on petrol then what is the expenditure on house rent ?
Options: a ) 98 , b ) 140 , c ) 62 , d ) 797 , e ) 123
Rationale: "given 30 % ( income ) = 300 ⇒ ⇒ income = 1000 after having spent rs . 300 on petrol , he left with rs . 700 . his spending on house rent = 14 % ( 700 ) = rs . 98 answer : a"
Answer: a
Python program:
a = 30 / 100
b = 300 / a
c = b - 300
d = 14 / 100
e = c * d
Problem: a man covered a certain distance at some speed . if he had moved 3 kmph faster , he would have taken 40 minutes less . if he had moved 2 kmph slower , he would have taken 40 minutes more . what is the distance in km ?
Options: a ) 36 , b ) 38 , c ) 40 , d ) 42 , e ) 45
Rationale: explanation : speed = 2 v 1 v 2 / v 1 − v 2 = 2 × 3 × 23 − 2 = 12 km / h = hr distance = vt 1 ( 1 + v / v 1 ) = 12 × 40 / 60 ( 1 + 12 / 3 ) = 40 km answer is c
Answer: c
Python program:
a = 40 / const_60
b = 2 * a
c = 40 / const_60
d = 3 * c
e = b + d 
f = 3 - 2
g = e / f
h = 2 * g
i = 40 / const_60
j = 2 * i
k = h + j 
l = 40 / const_60
m = k / l
n = 40 / const_60
o = 2 * n
p = 40 / const_60
q = 3 * p
r = o + q 
s = 3 - 2
t = r / s
u = m * t
Problem: if x * y = xy – 2 ( x + y ) for all integers x and y , then 2 * ( – 3 ) =
Options: a ) – 16 , b ) – 11 , c ) – 4 , d ) 4 , e ) 16
Rationale: "the quickest ( rather only ) way is to apply the given formula : 2 * ( - 3 ) = 2 * ( - 3 ) - 2 ( 2 + ( - 3 ) ) = - 6 + 2 = - 4 option ( c )"
Answer: c
Python program:
a = negate + ( 
b = a * 2
c = negate + (
Problem: a man is 18 years older than his son . in eight years , his age will be twice the age of his son . the present age of this son is
Options: a ) 5 years , b ) 10 years , c ) 15 years , d ) 20 years , e ) 25 years
Rationale: "explanation : let ' s son age is x , then father age is x + 18 . = > 2 ( x + 8 ) = ( x + 18 + 8 ) = > 2 x + 16 = x + 26 = > x = 10 years answer : option b"
Answer: b
Python program:
a = 2 * 2
b = a - 2
c = 18 - b
d = 2 - 1
e = c / d
Problem: operation # is defined as : a # b = 4 a ^ 2 + 4 b ^ 2 + 8 ab for all non - negative integers . what is the value of ( a + b ) + 5 , when a # b = 100 ?
Options: a ) 5 , b ) 8 , c ) 10 , d ) 13 , e ) 17
Rationale: "official solution : ( b ) we know that a # b = 100 and a # b = 4 a ² + 4 b ² + 8 ab . so 4 a ² + 4 b ² + 8 ab = 100 we can see that 4 a ² + 4 b ² + 8 ab is a well - known formula for ( 2 a + 2 b ) ² . therefore ( 2 a + 2 b ) ² = 100 . ( 2 a + 2 b ) is non - negative number , since both a and b are non - negative numbers . so we can conclude that 2 ( a + b ) = 10 . ( a + b ) + 5 = 10 / 2 + 5 = 10 . the correct answer is c ."
Answer: c
Python program:
a = 100 / 4
b = math.sqrt(a)
c = b + 4
Problem: a student got 72 % in math and 84 % in history . to get an overall average of 75 % , how much should the student get in the third subject ?
Options: a ) 65 % , b ) 67 % , c ) 69 % , d ) 71 % , e ) 73 %
Rationale: "72 + 84 + x = 3 * 75 x = 69 the answer is c ."
Answer: c
Python program:
a = 3 * 75
b = 72 + 84 
c = a - b
Problem: if f ( x ) = ax ^ 2 – 6 x + ax + 1 , then f ( b ) – f ( - b ) will equal :
Options: a ) 0 , b ) - 12 b + 2 ab , c ) 2 ab ^ 4 – 8 b ^ 2 – 6 , d ) - 2 ab ^ 4 + 8 b ^ 2 + 6 , e ) 2 ab ^ 4 – 8 b ^ 2 + 2 ab – 6
Rationale: f ( x ) = ax ^ 2 – 6 x + ax + 1 f ( b ) = ab ^ 2 – 6 b + ab + 1 f ( - b ) = ab ^ 2 + 6 b - ab + 1 f ( b ) - f ( - b ) = ab ^ 2 – 6 b + ab + 1 - ab ^ 2 - 6 b + ab - 1 = - 12 b + 2 ab answer b
Answer: b
Python program:
a = 1 * 10
Problem: a 100 meter long train crosses a man standing on the platform in 5 sec . what is the speed of the train ?
Options: a ) 72 kmph , b ) 108 kmph , c ) 176 kmph , d ) 134 kmph , e ) 161 kmph
Rationale: "s = 100 / 5 * 18 / 5 = 72 kmph answer : a"
Answer: a
Python program:
a = 100 / 5
b = a * const_3_6
Problem: what is the sum r of all 3 digit numbers that leave a remainder of ' 2 ' when divided by 3 ?
Options: a ) 897 , b ) 164850 , c ) 164749 , d ) 149700 , e ) 156720
Rationale: the series is = > 101 + . . . 998 number of terms = > 300 sum = > 300 / 2 * [ 101 + 998 ] hence sum r = > 164850 i . e . option b
Answer: b
Python program:
a = 10 ** 3
b = a / 10
c = b - 2
d = c / 3
e = math.floor(d)
f = e + 1 
g = f * 3
h = g + 2 
i = 10 ** 3
j = 10 ** 3
k = j / 10
l = k - 2
m = l / 3
n = math.floor(m)
o = n + 1 
p = o * 3
q = p + 2 
r = i - q
s = r / 3
t = math.floor(s)
u = t * 3
v = 10 ** 3
w = v / 10
x = w - 2
y = x / 3
z = math.floor(y)
A = z + 1 
B = A * 3
C = B + 2 
D = u + C 
E = h + D 
F = 10 ** 3
G = 10 ** 3
H = G / 10
I = H - 2
J = I / 3
K = math.floor(J)
L = K + 1 
M = L * 3
N = M + 2 
O = F - N
P = O / 3
Q = math.floor(P)
R = E * Q
S = R / 2
Problem: find the cost of carpeting a room 13 m long and 9 m broad with a carpet 75 cm wide at the rate of rs . 12 per square metre .
Options: a ) 1824 , b ) 1854 , c ) 1872 , d ) 1888 , e ) 1999
Rationale: explanation : area of the carpet = area of the room = ( 13 × 9 ) m 2 = 117 m 2 . length of the carpet = ( area / width ) = 117 × ( 4 / 3 ) m = 156 m . therefore cost of carpeting = ( 156 × 12 ) = rs . 1872 answer : option c
Answer: c
Python program:
a = 13 * 12
b = a * 12
Problem: each week a restaurant serving mexican food uses the same volume of chili paste , which comes in either 25 - ounce cans or 15 - ounce cans of chili paste . if the restaurant must order 30 more of the smaller cans than the larger cans to fulfill its weekly needs , then how many larger cans are required to fulfill its weekly needs ?
Options: a ) 60 , b ) 70 , c ) 80 , d ) 100 , e ) 45
Rationale: let x be the number of 25 ounce cans . therefore ( x + 30 ) is the number of 15 ounce cans . total volume is same , therefore 25 x = 15 ( x + 30 ) 10 x = 450 x = 45 ans - e
Answer: e
Python program:
a = 15 + 30
Problem: a boat running downstream covers a distance of 22 km in 4 hours while for covering the same distance upstream , it takes 5 hours . what is the speed of the boat in still water ?
Options: a ) 2.75 , b ) 5.95 , c ) 7.95 , d ) 3.25 , e ) 4.95
Rationale: "speed downstream = 22 / 4 = 5.5 kmph speed upstream = 22 / 5 = 4.4 kmph speed of the boat in still water = ( 5.5 + 4.4 ) / 2 = 4.95 kmph answer : e"
Answer: e
Python program:
a = 22 / 4
b = 22 / 5
c = a + b 
d = c / 4
Problem: express a speed of 54 kmph in meters per second ?
Options: a ) 10 mps , b ) 76 mps , c ) 15 mps , d ) 97 mps , e ) 16 mps
Rationale: "54 * 5 / 18 = 15 mps answer : c"
Answer: c
Python program:
a = const_0_2778 * 54
Problem: the cash difference between the selling prices of an article at a profit of 8 % and 6 % is rs 3 . the ratio of two selling prices is
Options: a ) 51 : 52 , b ) 52 : 53 , c ) 53 : 54 , d ) 54 : 53 , e ) none of these
Rationale: "explanation : let the cost price of article is rs . x required ratio = ( 108 % of x ) / ( 106 % of x ) = 108 / 106 = 54 / 53 = 54 : 53 . answer : d"
Answer: d
Python program:
a = 100 + 8 
b = 100 + 6 
c = a / b
Problem: the tax on a commodity is diminished by 16 % and its consumption increased by 15 % . the effect on revenue is ?
Options: a ) 2 % , b ) 3.8 % , c ) 3.4 % , d ) 3.6 % , e ) 1 %
Rationale: 100 * 100 = 10000 84 * 115 = 9660 - - - - - - - - - - - 10000 - - - - - - - - - - - 340 100 - - - - - - - - - - - ? = > 3.4 % decrease answer : c
Answer: c
Python program:
a = 15 / 100
b = 1 + a 
c = 16 / 100
d = 1 - c
e = b * d
f = e * 100
g = 100 - f
Problem: the maximum number of student amoung them 2010 pens and 1050 pencils can be distributed in such a way that each student gets the same number of pens and same number of pencils is :
Options: a ) 90 , b ) 60 , c ) 30 , d ) 1911 , e ) none of these
Rationale: "solution required number of student = h . c . f of 2010 and 1050 = 30 . answer c"
Answer: c
Python program:
a = math.gcd(2010, 1050)
Problem: two quarts containing 2 ⁄ 3 water and 1 ⁄ 3 formula are mixed with 3 quarts containing 3 ⁄ 8 water and 5 ⁄ 8 formula . approximately what percent of the combined 5 - quart mixture is water ?
Options: a ) 40 % , b ) 45 % , c ) 50 % , d ) 55 % , e ) 60 %
Rationale: since we are asking of water in the end , lets concentrate on water only . . a solution has 2 quarts with fraction of water = 2 / 3 , almost 67 % . . b solution has 3 quarts with fraction of water = 3 / 8 almost 37 % . . so the ratio a : b = 2 : 3 . . . the average will therefore be closer to b % and will be 2 / ( 2 + 3 ) of { 67 - 37 } away from b . . 2 / ( 2 + 3 ) of { 67 - 37 } = 2 / 5 * 30 = 12 . . so 37 + 12 = 49 nearly 50 % answer : c
Answer: c
Python program:
a = 2 / 3
b = a * 2
c = 3 / 8
d = c * 3
e = b + d 
f = e / 5
g = f * 100
Problem: two numbers are in the ratio 3 : 4 . if their l . c . m . is 48 . what is sum of the numbers ?
Options: a ) 28 , b ) 56 , c ) 76 , d ) 84 , e ) 85
Rationale: "explanation : let the numbers be 3 x and 4 x lcm of 3 x and 4 x = 12 x ( since lcm of 3 and 4 is 12 . hence lcm of 3 x and 4 x is 12 x ) given that lcm of 3 x and 4 x is 48 = > 12 x = 48 = > x = 48 / 12 = 4 sum of the numbers = 3 x + 4 x = 7 x = 7 x 4 = 28 answer : option a"
Answer: a
Python program:
a = 3 * 4
b = a * 100
c = 4 * 48
d = b + c
Problem: a cricketer scored 134 runs which included 12 boundaries and 2 sixes . what percent of his total score did he make by running between the wickets .
Options: a ) 55.22 % , b ) 54.54 % , c ) 63 % , d ) 70 % , e ) none of these
Rationale: "explanation : number of runs made by running = 134 - ( 12 x 4 + 2 x 6 ) = 134 - ( 60 ) = 74 now , we need to calculate 72 is what percent of 134 . = > 74 / 134 * 100 = 55.22 % answer : a"
Answer: a
Python program:
a = 12 * 4
b = 2 * 3
c = 2 * b
d = a + c 
e = 134 - d
f = e / 134
g = f * 100
Problem: a worker makes a toy in every 2 h . if he works for 80 h , then how many toys will he make ?
Options: a ) 40 , b ) 54 , c ) 45 , d ) 39 , e ) none
Rationale: "answer let number of toys be n . more hours , more toys ( direct proportion ) 2 : 80 : : 1 : n ⇒ n = 80 / 2 = 40 toys correct option : a"
Answer: a
Python program:
a = 80 / 2
Problem: bhavan travelled for 20 hours . he covered the first half of the distance at 50 kmph and remaining half of the distance at 40 kmph . find the distance travelled by bhavan ?
Options: a ) 888.89 , b ) 788.89 , c ) 899.89 , d ) 688.89 , e ) 899.99
Rationale: let the distance travelled be x km . total time = ( x / 2 ) / 50 + ( x / 2 ) / 40 = 20 = > x / 100 + x / 80 = 20 = > ( 4 x + 5 x ) / 400 = 20 = > x = 888.89 km answer : a
Answer: a
Python program:
a = 20 / 2
b = a * 50
c = 20 / 2
d = c * 40
e = b + d
Problem: what is the tens digit of 7 ^ 957 ?
Options: a ) 0 , b ) 1 , c ) 2 , d ) 3 , e ) 4
Rationale: "7 ^ 1 = 7 7 ^ 2 = 49 7 ^ 3 = 343 7 ^ 4 = 2401 7 ^ 5 = 16807 7 ^ 6 = 117649 we should see this as pattern recognition . we have a cycle of 4 . ( we can multiply the last 2 digits only as we care about ten ' s digit ) 0 , 4 , 4 , 0 . 957 = 4 * 239 + 1 the ten ' s digit will be 0 . answer d"
Answer: d
Python program:
a = 4 + 1 
b = 7 ** reminder
c = reminder / (
d = math.floor(c, 100)
Problem: ? x 40 = 173 x 240
Options: a ) 545 , b ) 685 , c ) 1038 , d ) 495 , e ) 534
Rationale: "let y x 40 = 173 x 240 then y = ( 173 x 240 ) / 40 = 1038 answer : c"
Answer: c
Python program:
a = 173 * 240
b = a / 40
Problem: rose made a part payment of $ 300 toward buying a brand new car , which represents 5 % of the total cost of the car , how much remains to be paid ?
Options: a ) $ 5700 , b ) $ 5500 , c ) $ 5800 , d ) $ 5200 , e ) $ 5880
Rationale: explanation : let ' s start with what the total price of the car would be . if 5 % is equal to $ 300 then 100 % equals $ x . we just have to multiply $ 300 by 20 to get total amount = $ 6000 . out of this amount we then need to deduct the amount already paid which was $ 300 so we have $ 6000 - $ 300 = $ 5700 answer : option a
Answer: a
Python program:
a = 300 * 100
b = a / 5
c = b - 300
Problem: a pump can fill a tank with water in 2 hours . because of a leak , it took 2 x 1 / 3 hours to fill the tank . the leak can drain all the water of the tank in
Options: a ) 5 hours , b ) 7 hours , c ) 8 hours , d ) 14 hours , e ) 18 hours
Rationale: "work done by the leak in 1 hour = 1 / 2 - 3 / 7 = 1 / 14 . leak will empty the tank in 14 hrs . answer : d"
Answer: d
Python program:
a = 1 / 2
b = 2 * 3
c = b + 1 
d = c / 3
e = 1/(d)
f = a - e
g = 1/(f)
Problem: rs . 6000 is lent out in two parts . one part is lent at 7 % 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 . 480 . find the ratio of the amounts lent at the lower rate and higher rate of interest ?
Options: a ) 2 : 1 , b ) 5 : 6 , c ) 5 : 2 , d ) 5 : 8 , e ) 5 : 2
Rationale: "let the amount lent at 7 % be rs . x amount lent at 10 % is rs . ( 6000 - x ) total interest for one year on the two sums lent = 7 / 100 x + 10 / 100 ( 6000 - x ) = 600 - 3 x / 100 = > 600 - 3 / 100 x = 480 = > x = 5000 amount lent at 10 % = 2000 required ratio = 2000 : 1000 = 2 : 1 answer : a"
Answer: a
Python program:
a = 480 * 100
b = 6000 * 7
c = a - b
d = 10 - 7
e = c / d
f = 480 * 100
g = 6000 * 7
h = f - g
i = 10 - 7
j = h / i
k = e / j
Problem: the banker ' s gain on a bill due due 1 year hence at 12 % per annum is rs . 7.2 . the true discount is
Options: a ) rs . 72 , b ) rs . 36 , c ) rs . 54 , d ) rs . 60 , e ) none
Rationale: "solution t . d = [ b . g x 100 / r x t ] = rs . ( 7.2 x 100 / 12 x 1 ) = rs . 60 . answer d"
Answer: d
Python program:
a = 12 / 100
b = 7 / 2
Problem: john purchased a grinder and a mobile for rs . 15000 & rs . 8000 respectively . he sold the grinder at a loss of 2 % and the mobile phone at a profit of 10 % . overall how much he make a profit .
Options: a ) s . 90 , b ) s . 120 , c ) s . 200 , d ) s . 250 , e ) s . 500
Rationale: "let the sp of the refrigerator and the mobile phone be rs . r and rs . m respectively . r = 15000 ( 1 - 2 / 100 ) = 15000 - 300 m = 8000 ( 1 + 10 / 100 ) = 8000 + 800 total sp - total cp = r + m - ( 15000 + 8000 ) = - 300 + 800 = rs . 500 as this is positive , an overall profit of rs . 200 was made . e"
Answer: e
Python program:
a = 8000 / 100
b = 10 * a
c = 15000 / 100
d = 2 * c
e = b - d
Problem: mid intended to type a 7 - digit number , but the two 3 ' s he meant to type did not appear . what appeared instead was the 5 - digit number 52115 . how many different 7 - digit numbers could mid have meant to type ?
Options: a ) 10 , b ) 16 , c ) 21 , d ) 24 , e ) 27
Rationale: should be 21 . mid intended to type a seven - digit number there are two possibilities for placing 2 3 s . case 1 : two 3 s were missed consecutively . i . e . he typed 33 and it came blank on screen . - 5 - 2 - 1 - 1 - 5 - in this arrangement we can fit 33 in 6 ways . ( six dashes , each dash represent one possible place for placing 33 ) case 2 : two 3 s are not together , i . e . they have one or more digits between them . - 5 - 2 - 1 - 1 - 5 - , in this arrangement if we place first 3 at first dash i . e . 35 - 2 - 1 - 1 - 5 - then the other 3 can fit into 5 places . if we place first 3 at second dash i . e . - 532 - 1 - 1 - 5 - then the other 3 can fit into 4 places . if we place first 3 at third dash i . e . - 5 - 231 - 1 - 5 - then the other 3 can fit into 3 places . if we place first 3 at fourth dash i . e . - 5 - 2 - 131 - 5 - then the other 3 can fit into 2 places . if we place first 3 at fifth dash i . e . - 5 - 2 - 1 - 135 - then the other 3 can fit into 1 place . so total 15 ways . case 2 + case 1 = 6 + 15 = 21 ways answer c
Answer: c
Python program:
a = math.factorial(7)
b = math.factorial(5)
c = 7 - 5
d = math.factorial(c)
e = b * d
f = a / e
Problem: in a clothing store , there are 6 different colored neckties ( red , orange , yellow , green , blue , and indigo ) and 4 different colored shirts ( red , orange , yellow , green , blue , and indigo ) that must be packed into boxes for gifts . if each box can only fit one necktie and one shirt , what is the probability that all of the boxes will contain a necktie and a shirt of the same color ?
Options: a ) 719 / 720 , b ) 1 / 24 , c ) 2 / 233 , d ) 3 / 543 , e ) 1 / 720
Rationale: 4 ties and 4 shirts . . . red tie can take any of 4 shirts . . orange can take any of the remaining 3 shirts yellow any of remaining 2 . . and so on till last indigo chooses the 1 remaining . . total ways = 4 * 3 * 2 * 1 = 24 out of this 720 , only 1 way will have same colour tie and shirt . . prob = 1 / 720 b
Answer: b
Python program:
a = math.factorial(4)
b = 1 / a
Problem: a , b , c subscribe rs . 50000 for a business , a subscribes rs . 4000 more than b and b rs . 5000 more than c . out of a total profit of rs . 70000 , a receives :
Options: a ) 14700 , b ) 24703 , c ) 29400 , d ) 33777 , e ) 34778
Rationale: explanation : let c = x . then , b = x + 5000 and a = x + 5000 + 4000 = x + 9000 . so , x + x + 5000 + x + 9000 = 50000 < = > 3 x = 36000 < = > x = 12000 . a : b : c = 21000 : 17000 : 12000 = 21 : 17 : 12 . a ' s share = rs . ( 70000 * 21 / 50 ) = rs . 29,400 . answer : c )
Answer: c
Python program:
a = 4000 + 5000 
b = 5000 + a 
c = 50000 - b
d = c / 3
e = 4000 + 5000 
f = d + e 
g = f * 70000
h = g / 50000
Problem: a canoe has two oars , left and right . each oar either works or breaks . the failure or non - failure of each oar is independent of the failure or non - failure of the other . you can still row the canoe with one oar . the probability that the left oar works is 3 / 5 . the probability that the right oar works is also 3 / 5 . what is the probability q that you can still row the canoe ?
Options: a ) 9 / 25 , b ) 10 / 25 , c ) 6 / 10 , d ) 2 / 3 , e ) 21 / 25
Rationale: "simply look at the question from the other side . what is the probability that you can ’ t row the canoe ? this would be 2 / 5 x 2 / 5 = 4 / 25 . using the idea that the probability q of something happening is 1 – the probability that it doesn ’ t happen , you can use the following equation to reach the right answer : 1 – 4 / 25 = 21 / 25 . answer choice e ."
Answer: e
Python program:
a = 3 / 5
b = 3 / 5
c = a * b
d = 3 / 5
e = 2 / 5
f = d * e
g = 3 / 5
h = 2 / 5
i = g * h
j = f + i 
k = c + j
Problem: john purchased a grinder and a mobile for rs . 15000 & rs . 8000 respectively . he sold the grinder at a loss of 4 % and the mobile phone at a profit of 10 % . overall how much he make aprofit .
Options: a ) rs . 90 , b ) rs . 120 , c ) rs . 200 , d ) rs . 250 , e ) rs . 290
Rationale: "let the sp of the refrigerator and the mobile phone be rs . r and rs . m respectively . r = 15000 ( 1 - 4 / 100 ) = 15000 - 600 m = 8000 ( 1 + 10 / 100 ) = 8000 + 800 total sp - total cp = r + m - ( 15000 + 8000 ) = - 600 + 800 = rs . 200 as this is positive , an overall profit of rs . 200 was made . c"
Answer: c
Python program:
a = 8000 / 100
b = 10 * a
c = 15000 / 100
d = 4 * c
e = b - d
Problem: 0.03 x 0.5 = ?
Options: a ) 0.0001 , b ) 0.001 , c ) 0.015 , d ) 0.1 , e ) none of these
Rationale: "explanation : 3 x 5 = 15 . sum of decimal places = 3 0.02 x 0.5 = 0.015 answer - c"
Answer: c
Python program:
a = 0 / 3
b = a * 100
Problem: how much interest can a person get on rs . 7200 at 17.5 % p . a . simple interest for a period of two years and 6 months ?
Options: a ) rs . 4150 , b ) rs . 3850 , c ) rs . 3770 , d ) rs . 3150 , e ) none of these
Rationale: i = ( 7200 * 2.5 * 17.5 ) / 100 = ( 7200 * 5 * 35 ) / ( 100 * 2 * 2 ) = rs . 3150 answer : d
Answer: d
Python program:
a = 6 / 12
b = 2 + a 
c = b * 17
d = c / 100
e = 7200 * d
Problem: what is the units digit of 13 ^ 4 * 17 ^ 2 * 29 ^ 3 ?
Options: a ) 9 , b ) 7 , c ) 5 , d ) 3 , e ) 1
Rationale: "3 ^ 1 = 3 3 ^ 2 = 9 3 ^ 3 = 7 3 ^ 4 = 1 , it is first digit 7 ^ 2 = 9 , it is second digit 9 ^ 3 = 9 , it is third digit 1 * 9 * 9 = 1 answer : e"
Answer: e
Python program:
a = math.factorial(13)
b = math.factorial(4)
c = a * b
d = math.factorial(13)
e = math.factorial(2)
f = d * e
g = c + f 
h = g / 13
Problem: donovan took a math test and got 35 correct and 13 incorrect answers . what was the percentage of correct answers ? ( round to the nearest hundredth )
Options: a ) 57.78 % , b ) 67.78 % , c ) 72.92 % , d ) 47.78 % , e ) 97.78 %
Rationale: 35 correct our of 48 total ( 35 + 13 ) 35 / 48 correct answer c
Answer: c
Python program:
a = 35 + 13 
b = 35 / a
c = b * 100
Problem: the slant height of a cone is 14 cm and radius of the base is 12 cm , find the curved surface of the cone .
Options: a ) 150 , b ) 170 , c ) 48 , d ) 528 , e ) 600
Rationale: "π * 12 * 14 = 528 answer : d"
Answer: d
Python program:
a = math.pi * 12
b = a * 14
Problem: triangle xyz is an isosceles right triangle . if side xy is longer than side yz , and the area of the triangle is 49 , what is the measure of side xy ?
Options: a ) 4
b ) 4 √ 2
c ) 14
d ) 8 √ 2
e ) can not be determined from the information provided
Rationale: ans c . . 14 . . xy being larger means it is the hyp . . area = ( 1 / 2 ) * ( yz ) ^ 2 = 4 or yz = 7 * \ sqrt { 2 } . . therefore hyp = xy = 14
Answer: c
Python program:
a = math.sqrt(49)
b = math.sqrt(2)
c = a * b
d = c ** 2
e = math.sqrt(49)
f = math.sqrt(2)
g = e * f
h = g ** 2
i = d + h 
j = math.sqrt(i)
Problem: if the price of sugar rises from rs . 6 per kg to rs . 7.50 per kg , a person , to have no increase in his expenditure on sugar , will have to reduce his consumption of sugar by
Options: a ) 10 % , b ) 20 % , c ) 25 % , d ) 30 % , e ) none
Rationale: "solution let the original consumption = 100 kg and new consumption = x kg . so , 100 x 6 = x × 7.50 x = 80 kg . reduction in consumption = 20 % . answer b"
Answer: b
Python program:
a = 1 * 6
b = a / 7
c = 1 - b
d = c * 100