euclaise/mathqa_programs huggingface dataset:
Problem: at milk factory , each employee working the second shift produced 2 / 3 as many widgets as each employee working the first shift . if the first shift has 3 / 4 as many employees , what fraction of the total widgets did the second shift produce ?
Options: a ) 8 / 17 , b ) 1 / 2 , c ) 8 / 9 , d ) 9 / 8 , e ) 17 / 8
Rationale: at milk factory , let the first shift have 3 employee and each produce 3 widgets , so the total number of widgets produced by the first shift is 3 * 3 = 9 ; then the second shift would have 4 employees and each second shift employee would produce 3 * 2 / 3 = 2 widgets , so the total number of widgets produced by the second shift employees would be 4 * 2 = 8 ; the ratio of the second shift production to the total is 8 / ( 9 + 8 ) = 8 / 17 . answer : a .
Answer: a
Python program:
a = 2 / 3
b = a * 3
c = b * 4
d = 3 * 3
e = 2 / 3
f = e * 3
g = f * 4
h = d + g 
i = c / h
Problem: the cost of one photocopy is $ 0.02 . however , a 25 % discount is offered on orders of more than 100 photocopies . if steve and david have to make 80 copies each , how much will each of them save if they submit a single order of 160 copies ?
Options: a ) $ 0.32 , b ) $ 0.40 , c ) $ 0.45 , d ) $ 0.48 , e ) $ 0.54
Rationale: "if steve and david submit separate orders , each would be smaller than 100 photocopies , so no discount . each would pay ( 80 ) * ( $ 0.02 ) = $ 1.60 , or together , a cost of $ 3.20 - - - that ' s the combined ` ` no discount cost ' ' . if they submit things together as one big order , they get a discount off of that $ 3.20 price - - - - 25 % or 1 / 4 of that is $ 0.80 , the discount on the combined sale . they each effective save half that amount , or $ 0.40 . answer = ( b ) ."
Answer: b
Python program:
a = 80 * 0
b = 2 * a
c = 100 - 25
d = c / 100
e = 160 * d
f = e * 0
g = b - f
h = g / 2
Problem: a sum of money is to be distributed among a , b , c , d in the proportion of 5 : 2 : 4 : 3 . if c gets $ 500 more than d , what is a ' s share ?
Options: a ) $ 1200 , b ) $ 1600 , c ) $ 2000 , d ) $ 2500 , e ) $ 3000
Rationale: "let the shares of a , b , c and d be 5 x , 2 x , 4 x and 3 x respectively . then , 4 x - 3 x = 500 x = $ 500 a ' s share = 5 x = 5 * $ 500 = $ 2500 the answer is d ."
Answer: d
Python program:
a = 4 - 3
b = a * 500
c = b * 3
Problem: when a certain tree was first planted , it was 4 feet tall , and the height of the tree increased by a constant amount each year for the next 6 years . at the end of the 6 th year , the tree was 1 / 7 taller than it was at the end of the 4 th year . by how many feet did the height of the tree increase each year ?
Options: a ) 3 / 10 , b ) 2 / 5 , c ) 1 / 2 , d ) 2 / 3 , e ) 6 / 5
Rationale: say , the tree grows by x feet every year . then , 4 + 6 x = ( 1 + 1 / 7 ) ( 4 + 4 x ) or , x = 2 / 5 answer b
Answer: b
Python program:
a = 6 - 4
b = a * 7
c = b - 4
d = 4 / c
Problem: a , b and c have rs . 500 between them , a and c together have rs . 200 and b and c rs . 350 . how much does c have ?
Options: a ) 50 , b ) 88 , c ) 77 , d ) 66 , e ) 51
Rationale: "a + b + c = 500 a + c = 200 b + c = 350 - - - - - - - - - - - - - - a + b + 2 c = 550 a + b + c = 500 - - - - - - - - - - - - - - - - c = 50 answer : a"
Answer: a
Python program:
a = 200 + 350 
b = a - 500
Problem: two trains are moving in the same direction at 72 kmph and 36 kmph . the faster train crosses a man in the slower train in 18 seconds . find the length of the faster train ?
Options: a ) 270 , b ) 277 , c ) 187 , d ) 180 , e ) 271
Rationale: "relative speed = ( 72 - 36 ) * 5 / 18 = 2 * 5 = 10 mps . distance covered in 18 sec = 18 * 10 = 180 m . the length of the faster train = 180 m . answer : d"
Answer: d
Python program:
a = 72 - 36
b = a / const_3_6
c = b * 18
Problem: matt gets a $ 1,000 commission on a big sale . this commission alone raises his average commission by $ 150 . if matt ' s new average commission is $ 550 , how many sales has matt made ?
Options: a ) 3 , b ) 4 , c ) 5 , d ) 6 , e ) 7
Rationale: "let , average commission = x no . of items sold = y total commission = xy new commission = xy + 1000 new average = ( xy + 1000 ) / ( y + 1 ) = 150 + x i . e . ( xy + 1000 ) = ( y + 1 ) * ( 150 + x ) i . e . ( xy + 1000 ) = ( xy + x + 150 y + 150 ) i . e . ( 850 ) = ( x + 150 y ) new commission = 550 = 150 + x i . e . x = 400 i . e . y = 3 new sales = y + 1 = 4 answer : option b"
Answer: b
Python program:
a = 1 - 0
b = 550 - 150
c = 550 - b
d = a / c
Problem: a man invested rs . 14400 in rs . 100 shares of a company at 20 % premium . if his company declares 5 % dividend at the end of the year , then how much does he get ?
Options: a ) 234 , b ) 600 , c ) 388 , d ) 278 , e ) 129
Rationale: explanation : number of shares = = 120 . face value = rs . ( 100 x 120 ) = rs . 12000 . annual income = = rs . 600 answer : b ) rs . 600
Answer: b
Python program:
a = 20 + 100 
b = a / 100
c = 14400 / b
d = 5 / 100
e = c * d
Problem: the distance between two cities a and b is 1140 km . a train starts from a at 8 a . m . and travel towards b at 60 km / hr . another train starts from b at 9 a . m and travels towards a at 75 km / hr . at what time do they meet ?
Options: a ) 09 am , b ) 07 am , c ) 11 am , d ) 05 pm , e ) 03 pm
Rationale: "explanation : suppose they meet x hrs after 8 a . m then , [ distance moved by first in x hrs ] + [ distance moved by second in ( x - 1 ) hrs ] = 1140 . therefore , 60 x + 75 ( x - 1 ) = 1140 . = > x = 9 . so , they meet at ( 8 + 9 ) i . e , 5 pm answer : d"
Answer: d
Python program:
a = 1140 + 75 
b = 60 + 75 
c = a / b
d = c + 8
Problem: the sale price of an article including the sales tax is rs . 616 . the rate of sales tax is 10 % . if the shopkeeper has made a profit of 15 % , then the cost price of the article is :
Options: a ) 500 , b ) 334 , c ) 555 , d ) 536 , e ) 5598
Rationale: "110 % of s . p . = 616 s . p . = ( 616 * 100 ) / 110 = rs . 560 c . p = ( 110 * 560 ) / 115 = rs . 536 answer : option d"
Answer: d
Python program:
a = 616 * 100
b = 100 + 10 
c = a / b
d = 100 + 10 
e = c * d
f = 100 + 15 
g = e / f
Problem: pipe a fills a swimming pool in 4 hours . pipe b empties the pool in 6 hours . if pipe a was opened at 7 : 00 am and pipe b at 8 : 00 am , at what time will the pool be full ?
Options: a ) 16 : 00 , b ) 18 : 00 , c ) 19 : 00 , d ) 20 : 00 , e ) 17 : 00
Rationale: "pipe a fills the pool in 4 hrs . 1 hour ' s work : 1 / 4 pipe b empties the pool in 6 hrs . 1 hour ' s work : 1 / 6 together if they work , 1 hour ' s work = 1 / 4 - 1 / 6 = 1 / 12 given : pipe a started at 7 : 00 a . m and pipe b at 8 : 00 a . m pool filled after 1 hour by pipe a : 1 / 4 or 3 / 12 after 8 : 00 a . m pool filled after 1 hour with both the pipes on : 1 / 12 pool filled after 9 hours with both pipes on : 9 / 12 pool filled in 1 hour + pool filled in 9 hours = 3 / 12 + 9 / 12 = 1 therefore , it takes 10 hrs to fill the pool as pipe a started at 7 : 00 a . m , pool is full at 17 : 00 hrs answer : e"
Answer: e
Python program:
a = 3 / 4
b = 1 / 4
c = 1 / 6
d = b - c
e = 1 / d
f = a * e
Problem: selling an kite for rs . 30 , a shop keeper gains 35 % . during a clearance sale , the shopkeeper allows a discount of 10 % on the marked price . his gain percent during the sale is ?
Options: a ) 8 % , b ) 10 % , c ) 11 % , d ) 15 % , e ) 21.5 %
Rationale: "explanation : marked price = rs . 30 c . p . = 100 / 135 * 30 = rs . 22.22 sale price = 90 % of rs . 30 = rs . 27 required gain % = 4.77 / 22.22 * 100 = 21.5 % . answer : e"
Answer: e
Python program:
a = 30 / 100
b = 100 - 10
c = a * b
d = 30 * 100
e = 35 + 100 
f = d / e
g = c - f
h = 30 * 100
i = 35 + 100 
j = h / i
k = g / j
l = k * 100
Problem: if the simple interest on a sum of money for 2 years at 5 % per annum is rs . 58 , what is the compound interest on the same sum at the rate and for the same time ?
Options: a ) s . 59.45 , b ) s . 56.22 , c ) s . 51.219 , d ) s . 59.18 , e ) s . 51.11
Rationale: "explanation : sum = ( 58 * 100 ) / ( 2 * 5 ) = rs . 580 amount = [ 580 * ( 1 + 5 / 100 ) 2 ] = rs . 639.45 c . i . = ( 639.45 - 580 ) = rs . 59.45 answer : a"
Answer: a
Python program:
a = 5 / 100
b = a * 2
c = 58 / b
d = c * 5
e = d / 100
f = 5 / 100
g = f * 2
h = 58 / g
i = e + h 
j = 5 / 100
k = j * 2
l = 58 / k
m = l * 5
n = m / 100
o = 5 / 100
p = o * 2
q = 58 / p
r = n + q 
s = r * 5
t = s / 100
u = i + t 
v = 5 / 100
w = v * 2
x = 58 / w
y = u - x
Problem: if a = 105 and a ^ 3 = 21 × 25 × 45 × d , what is the value of d ?
Options: a ) 35 , b ) 42 , c ) 45 , d ) 49 , e ) 54
Rationale: "a = 105 = 3 * 5 * 7 a ^ 3 = 21 × 25 × 45 × d = > a ^ 3 = ( 7 * 3 ) x ( 5 * 5 ) x ( 3 ^ 2 * 5 ) x d = > a ^ 3 = 3 ^ 3 * 5 ^ 3 * 7 x d = > ( 3 * 5 * 7 ) ^ 3 = 3 ^ 3 * 5 ^ 3 * 7 x d d = 7 ^ 2 = 49 answer d"
Answer: d
Python program:
a = 105 ** 3
b = 21 * 25
c = b * 45
d = a / c
Problem: a present value of a machine is $ 40000 . its value depletiation rate is 5 % per annum then find the machine value after 2 years ?
Options: a ) $ 36540 , b ) $ 36100 , c ) $ 29580 , d ) $ 31256 , e ) $ 41250
Rationale: "p = $ 40000 r = 5 % t = 2 years machine value after 3 years = p / ( 1 - r / 100 ) ^ t = 40000 * 19 / 20 * 19 / 20 * 19 / 20 = $ 36100 answer is b"
Answer: b
Python program:
a = 5 / 100
b = 1 - a
c = b ** 2
d = 40000 * c
Problem: find the compound ratio of ( 3 : 4 ) , ( 4 : 5 ) and ( 1 : 2 ) is
Options: a ) 1 : 2 , b ) 2 : 3 , c ) 3 : 10 , d ) 4 : 10 , e ) 3 : 2
Rationale: "required ratio = 3 / 4 * 4 / 5 * 1 / 2 = 3 / 10 = 3 : 10 answer is c"
Answer: c
Python program:
a = 3 / 3
b = 3 / 4
c = 4 / 4
d = b * c
e = a * d
Problem: at veridux corporation , there are 218 employees . of these , 90 are female , and the rest are males . there are a total of 40 managers , and the rest of the employees are associates . if there are a total of 135 male associates , how many female managers are there ?
Options: a ) 15 , b ) 20 , c ) 25 , d ) 30 , e ) 47
Rationale: "well , first let â € ™ s take care of the â € œ totals â €  . the numbers in the â € œ totals â €  row must add up . if 90 are females , the other 218 â € “ 90 = 128 must be males . similarly , the numbers in the â € œ totals â €  column must add up . if 40 are managers , then the other 218 â € “ 40 = 178 must be associates . now , in the â € œ associate â €  row , 135 + e = 178 , which means e = 43 â € ” the other 43 associates must be female . now , to find b , which is what the question is asking , we need only look at the sum in the â € œ female â €  column : b + 43 = 90 , which means b = 47 . there are fifteen female managers in this company . thus , the answer = 47 ( e ) ."
Answer: e
Python program:
a = 40 * 1
Problem: find a sum for 1 st 9 prime number ' s ?
Options: a ) 25 , b ) 28 , c ) 30 , d ) 34 , e ) 100
Rationale: required sum = ( 2 + 3 + 5 + 7 + 11 + 13 + 17 + 19 + 23 ) = 100 note : 1 is not a prime number option e
Answer: e
Python program:
a = 2 + 3 
b = 2 + 3 
c = a + b 
d = 2 + 3 
e = d + 2 
f = c + e 
g = 9 + 2 
h = f + g 
i = 9 + 2 
j = i + 2 
k = h + j 
l = 9 + 2 
m = l + 2 
n = m + 4 
o = k + n 
p = 9 + 2 
q = p + 2 
r = q + 4 
s = r + 2 
t = o + s 
u = 9 + 2 
v = u + 2 
w = v + 4 
x = w + 2 
y = x + 4 
z = t + y
Problem: if d = 1 / ( 2 ^ 3 * 5 ^ 11 ) is expressed as a terminating decimal , how many nonzero digits will d have ?
Options: a ) one , b ) two , c ) three , d ) seven , e ) ten
Rationale: "another way to do it is : we know x ^ a * y ^ a = ( x * y ) ^ a given = 1 / ( 2 ^ 3 * 5 ^ 11 ) = multiply and divide by 2 ^ 8 = 2 ^ 8 / ( 2 ^ 3 * 2 ^ 8 * 5 ^ 11 ) = 2 ^ 8 / 10 ^ 11 = > non zero digits are 256 = > ans c"
Answer: c
Python program:
a = 1 + 2
Problem: a man is 25 years older than his son . in two years , his age will be twice the age of his son . the present age of the son is ?
Options: a ) 11 , b ) 23 , c ) 27 , d ) 22 , e ) 91
Rationale: "let the son ' s present age be x years . then , man ' s present age = ( x + 25 ) years . ( x + 25 ) + 2 = 2 ( x + 2 ) x + 27 = 2 x + 4 = > x = 23 . answer : b"
Answer: b
Python program:
a = 2 * 2
b = a - 2
c = 25 - b
d = 2 - 1
e = c / d
Problem: calculate the sum of first 89 natural numbers .
Options: a ) 2017 , b ) 2647 , c ) 2147 , d ) 2045 , e ) 4005
Rationale: "solution we know that ( 1 + 2 + 3 + . . . . . + 89 ) = n ( n + 1 ) / 2 therefore ( 1 + 2 + 3 + . . . . + 89 ) = ( 89 × 90 / 2 ) = 4005 . answer e"
Answer: e
Python program:
a = 89 + 1 
b = 89 / 2
c = a * b
Problem: a jogger running at 10 km / hr along side a railway track is 340 m ahead of the engine of a 120 m long train running at 46 km / hr in the same direction . in how much time will the train pass the jogger ?
Options: a ) 76 sec , b ) 67 sec , c ) 98 sec , d ) 46 sec , e ) 23 sec
Rationale: "speed of train relative to jogger = 46 - 10 = 36 km / hr . = 36 * 5 / 18 = 10 m / sec . distance to be covered = 340 + 120 = 460 m . time taken = 460 / 10 = 46 sec . answer : d"
Answer: d
Python program:
a = 340 + 120 
b = 46 - 10
c = 10 / 2
d = 46 - 10
e = d / 2
f = c / e
g = b * f
h = a / g
Problem: an amount of rs . 10000 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 3 / 4 % , then the amount invested at 11 % was ?
Options: a ) 2377 , b ) 3750 , c ) 2997 , d ) 2677 , e ) 1987
Rationale: let the sum invested at 9 % be rs . x and that invested at 11 % be rs . ( 10000 - x ) . then , ( x * 9 * 1 ) / 100 + [ ( 10000 - x ) * 11 * 1 ] / 100 = ( 10000 * 39 / 4 * 1 / 100 ) ( 9 x + 110000 - 11 x ) / 100 = 3900 / 4 = 975 ( 9 x + 110000 - 11 x ) = 97500 x = 6250 sum invested at 9 % = rs . 6250 sum invested at 11 % = rs . ( 10000 - 6250 ) = rs . 3750 . answer : b
Answer: b
Python program:
a = 3 / 4
b = 9 + a 
c = b / 100
d = 10000 * c
e = 9 / 100
f = 10000 * e
g = d - f
h = 11 / 100
i = 9 / 100
j = h - i
k = g / j
Problem: the present population of a town is 300 . population increase rate is 10 % p . a . find the population of town after 1 years ?
Options: a ) 100 , b ) 120 , c ) 200 , d ) 220 , e ) 330
Rationale: p = 300 r = 10 % required population of town = p * ( 1 + r / 100 ) ^ t = 300 * ( 1 + 10 / 100 ) = 300 * ( 11 / 10 ) = 330 answer is e
Answer: e
Python program:
a = 300 * 10
b = a / 100
c = 300 + b
Problem: in a race of 1000 m , a can beat by 100 m , in a race of 800 m , b can beat c by 100 m . by how many meters will a beat c in a race of 600 m ?
Options: a ) 236 , b ) 127.5 , c ) 267 , d ) 268 , e ) 281
Rationale: "when a runs 1000 m , b runs 900 m and when b runs 800 m , c runs 700 m . when b runs 900 m , distance that c runs = ( 900 * 700 ) / 800 = 6300 / 8 = 787.5 m . in a race of 1000 m , a beats c by ( 1000 - 787.5 ) = 212.5 m to c . in a race of 600 m , the number of meters by which a beats c = ( 600 * 212.5 ) / 1000 = 127.5 m answer : b"
Answer: b
Python program:
a = 1000 - 100
b = 800 - 100
c = a * b
d = c / 800
e = 1000 - d
Problem: a powder tin has a square base with side 8 cm and height 14 cm . another tin has a circular base with diameter 8 cm and height 14 cm . the difference in their capacities is :
Options: a ) 168 cm ³
b ) 192 cm ³
c ) 228 cm ³
d ) 236 cm ³
e ) none
Rationale: sol . difference in capacities = [ 8 * 8 * 14 - 22 / 7 * 4 * 4 * 14 ] cm ³ = 192 cm ³ answer b
Answer: b
Python program:
a = volume_rectangular_prism - (
Problem: today david , who is 40 years old , and his daughter , who is 12 years old , celebrate their birthdays . how many years will pass before david ’ s age is twice his daughter ’ s age ?
Options: a ) 22 , b ) 20 , c ) 16 , d ) 18 , e ) 14
Rationale: forget conventional ways of solving math questions . in ps , ivy approach is the easiest and quickest way to find the answer . after x years passes david ’ s age will be ( 40 + x ) years old , and his daughter ’ s age will be ( 12 + x ) years old . since the david ’ s age is twice his daughter ’ s age ( 40 + x ) = 2 * ( 12 + x ) - - - > 40 + x = 24 + 2 x - - - > x = 16 the answer is ( c ) .
Answer: c
Python program:
a = 40 + 12 
b = a + 2 
c = b / 2
d = c - 12
e = d + 1
Problem: ( 17 ) 3.5 x ( 17 ) ? = 178
Options: a ) 2.29 , b ) 2.75 , c ) 4.25 , d ) 4.5 , e ) none of these
Rationale: "solution let ( 17 ) 3.5 * ( 17 ) x = 178 . then , ( 17 ) 3.5 + x = ( 17 ) 8 . ∴ 3.5 + x = 8 ⇔ x = ( 8 - 3.5 ) ⇔ x = 4.5 answer d"
Answer: d
Python program:
a = 17 * 17
Problem: earl can stuff advertising circulars into envelopes at the rate of 36 envelopes per minutes and ellen requires a minutes and half to stuff the same number of envelops . working together , how long will it take earl and ellen to stuff 120 envelopes
Options: a ) 2 minutes , b ) 5 minutes , c ) 7 minutes , d ) 3 minutes , e ) 4 minutes
Rationale: "earl takes 1 min . for 36 envelopes . ellen takes 3 / 2 mins for the same . so ellen can stuff ( ( 36 ) / ( 3 / 2 ) ) in 1 min . i . e . , 24 envelopes a min . so both of them when work together can stuff 36 + 24 = 60 envelopes in 1 min . for 120 envelopes they will take 120 / 60 mins . i . e . , 2 mins . answer : a"
Answer: a
Python program:
a = 3 / 2
b = 36 / a
c = 36 + b 
d = 120 / c
Problem: if ( 400 ) ( 7000 ) = ( 28000 ) ( 100 ^ x ) , what is the value of x ?
Options: a ) 5 , b ) 4 , c ) 3 , d ) 2 , e ) 1
Rationale: ( 400 ) ( 7,000 ) = ( 2,800 ) ( 100 ^ x ) = > ( 400 ) ( 7,000 ) / 2,800 = 100 ^ x = > 100 = 100 ^ x = > 100 ^ 1 = 100 ^ x since , base is same so powers will be same too . so , x = 1 answer will be e
Answer: e
Python program:
a = 400 * 7000
b = a / 28000
c = b / 100
Problem: having received his weekly allowance , john spent 3 / 5 of his allowance at the arcade . the next day he spent one third of his remaining allowance at the toy store , and then spent his last $ 0.64 at the candy store . what is john ’ s weekly allowance ?
Options: a ) $ 2.40 , b ) $ 3.00 , c ) $ 3.20 , d ) $ 3.60 , e ) $ 4.80
Rationale: "total allowance = x amount spent at the arcade = 3 / 5 x amount remaining = 2 / 5 x amount spent at the toy store = 2 / 5 * 1 / 3 x = 2 / 15 x amount remaining = 2 / 5 x - 2 / 15 x = 4 / 15 x now , 4 / 15 x = $ 0.64 therefore , x = $ 2.40 . answer a"
Answer: a
Python program:
a = 3 / 5
b = 1 / 3
c = 3 / 5
d = 1 - c
e = b * d
f = a + e 
g = 1 - f
h = 0 / 64
Problem: a number of 41 marbles is to be divided and contain with boxes . if each box is to contain 3 , 4 , or 5 marbles , what is the largest possible number of boxes ?
Options: a ) 13 , b ) 12 , c ) 15 , d ) 16 , e ) 17
Rationale: "to maximize # of boxes we should minimize marbles per box : 12 * 3 + 1 * 5 = 41 - - > 12 + 1 = 13 . answer : a ."
Answer: a
Python program:
a = 41 / 3
Problem: the sum of the present age of henry and jill is 41 . what is their present ages if 7 years ago henry was twice the age of jill ?
Options: a ) and 25 , b ) and 24 , c ) and 22 , d ) and 29 , e ) of these
Rationale: let the age of jill 7 years ago be x , age of henry be 2 x x + 7 + 2 x + 7 = 41 x = 9 present ages will be 16 and 25 answer : a
Answer: a
Python program:
a = 41 + 7 
b = a / 3
c = 41 - b
Problem: set x consists of the integers from 0 to 12 , inclusive , while set y consists of the integers from 6 to 10 , inclusive . how many distinct integers do belong to the both sets at the same time ?
Options: a ) 4 , b ) 10 , c ) 5 , d ) 9 , e ) 8
Rationale: "x = { 0 , 1,2 , 3,4 , 5,6 , 7 , 8 , 9 , 10 , 11 , 12 } y = { 6 , 7 , 8 , 9 , 10 } common elements = { 6 , 7 , 8 , 9 , 10 } = 5 elements answer : option c ."
Answer: c
Python program:
a = 12 - 0
b = a + 0
Problem: a watch was sold at a loss of 10 % . if it was sold for rs . 500 more , there would have been a gain of 10 % . what is the cost price ?
Options: a ) 1000 , b ) 2998 , c ) 2500 , d ) 2788 , e ) 2991
Rationale: "90 % 110 % - - - - - - - - 20 % - - - - 500 100 % - - - - ? = > rs . 2500 answer : c"
Answer: c
Python program:
a = 500 * 100
b = 100 + 10 
c = 100 - 10
d = b - c
e = a / d
Problem: what is the area of a square field whose diagonal of length 26 m ?
Options: a ) 287 , b ) 269 , c ) 338 , d ) 200 , e ) 230
Rationale: "d 2 / 2 = ( 26 * 26 ) / 2 = 338 answer : c"
Answer: c
Python program:
a = square_area / (
Problem: a book is bought for $ 600 and sold for $ 624 . what is the profit in percentage ?
Options: a ) 2 , b ) 4 , c ) 6 , d ) 8 , e ) 10
Rationale: "624 / 600 = 1.04 the answer is b ."
Answer: b
Python program:
a = 624 - 600
b = a / 600
c = b * 100
Problem: a store owner estimates that the average price of type a products will increase by 35 % next year and that the price of type b products will increase by 20 % next year . this year , the total amount aid for type a products was $ 3500 and the total price paid for type b products was $ 6300 . 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 ) $ 16,000 , d ) $ 12,285 , e ) $ 17,155
Rationale: "cost of type a products next year = 1.35 * 3500 = 4725 cost of type b products next year = 1.2 * 6300 = 7560 total 4725 + 7560 = 12285 answer : d"
Answer: d
Python program:
a = 3 / 4
b = a * 1000
Problem: a , b and c play a cricket match . the ratio of the runs scored by them in the match is a : b = 2 : 3 and b : c = 2 : 5 . if the total runs scored by all of them are 75 , the runs scored by a are ?
Options: a ) 11 , b ) 18 , c ) 13 , d ) 17 , e ) 12
Rationale: "a : b = 2 : 3 b : c = 2 : 5 a : b : c = 4 : 6 : 15 4 / 25 * 75 = 12 answer : e"
Answer: e
Python program:
a = 2 / 3
b = 5 / 2
c = a + b 
d = c + 2 
e = 75 / d
f = e * 5
Problem: two trains are moving in the same direction at 72 kmph and 36 kmph . the faster train crosses a man in the slower train in 10 seconds . find the length of the faster train ?
Options: a ) 270 , b ) 288 , c ) 100 , d ) 299 , e ) 126
Rationale: "relative speed = ( 72 - 36 ) * 5 / 18 = 2 * 5 = 10 mps . distance covered in 27 sec = 10 * 10 = 100 m . the length of the faster train = 100 m . answer : c"
Answer: c
Python program:
a = 72 - 36
b = a / const_3_6
c = b * 10
Problem: a trader sells 78 meters of cloth for rs . 6788 at the profit of rs . 29 per metre of cloth . what is the cost price of one metre of cloth ?
Options: a ) 22 , b ) 75 , c ) 60 , d ) 58 , e ) 11
Rationale: "sp of 1 m of cloth = 6788 / 78 = rs . 87 cp of 1 m of cloth = sp of 1 m of cloth - profit on 1 m of cloth = rs . 87 - rs . 29 = rs . 58 . answer : d"
Answer: d
Python program:
a = 6788 / 78
b = a - 29
Problem: by selling an article at rs . 800 , a shopkeeper makes a profit of 25 % . at what price should he sell the article so as to make a loss of 50 % ?
Options: a ) s . 429 , b ) s . 480 , c ) s . 320 , d ) s . 128 , e ) s . 419
Rationale: "sp = 800 profit = 25 % cp = ( sp ) * [ 100 / ( 100 + p ) ] = 800 * [ 100 / 125 ] = 640 loss = 50 % = 50 % of 640 = rs . 320 sp = cp - loss = 640 - 320 = rs . 320 answer : c"
Answer: c
Python program:
a = 800 * 100
b = 25 + 100 
c = a / b
d = 800 * 100
e = 25 + 100 
f = d / e
g = f * 50
h = g / 100
i = c - h
Problem: a ( 8 , w ^ 2 ) is the ( x , y ) coordinate of point located on the parabola y = x ^ 2 + 17 . what is the value of w ?
Options: a ) 3 . , b ) 4 . , c ) 5 . , d ) 6 . , e ) 9 .
Rationale: "y = x ^ 2 + 17 w ^ 2 = 8 ^ 2 + 17 w ^ 2 = 81 w = 9 answer e"
Answer: e
Python program:
a = 8 ** 2
b = a - 17
c = 17 / 8
d = b ** c
Problem: on a certain transatlantic crossing , 40 percent of a ship ’ s passengers held round - trip tickets and also took their cars abroad the ship . if 50 percent of the passengers with round - trip tickets did not take their cars abroad the ship , what percent of the ship ’ s passengers held round - trip tickets ?
Options: a ) 40 % , b ) 50 % , c ) 60 % , d ) 80 % , e ) 90 %
Rationale: let t be the total number of passengers . let x be the number of people with round trip tickets . 0.4 t had round trip tickets and took their cars . 0.5 x had round trip tickets and took their cars . 0.5 x = 0.4 t x = 0.8 t the answer is d .
Answer: d
Python program:
a = 50 / 100
b = 1 - a
c = 40 / b
Problem: if log 2 = 0.30103 , the number of digits in 2128 is .
Options: a ) 38 , b ) 39 , c ) 40 , d ) 41 , e ) 56
Rationale: log ( 2128 ) = 128 log ( 2 ) = 128 × 0.30103 ≈ 38.4 ie , its characteristic = 38 hence , number of digits in 2128 = 38 + 1 = 39 answer : option b
Answer: b
Python program:
a = 2 * 1000
b = 2128 - a
c = 0 * 30103