euclaise/mathqa_programs huggingface dataset:
Problem: a man rows his boat 90 km downstream and 40 km upstream , taking 2 1 / 2 hours each time . find the speed of the stream ?
Options: a ) 6 , b ) 7 , c ) 5 , d ) 8 , e ) 15
Rationale: "speed downstream = d / t = 90 / ( 2 1 / 2 ) = 36 kmph speed upstream = d / t = 40 / ( 2 1 / 2 ) = 16 kmph the speed of the stream = ( 36 - 16 ) / 2 = 15 kmph answer : e"
Answer: e
Python program:
a = 90 / 2
b = 40 / 2
c = a - b
d = c / 2
Problem: in the youth summer village there are 300 people , 200 of them are not working , 100 of them have families and 125 of them like to sing in the shower . what is the largest possible number of people in the village , which are working , that do n ' t have families and that are singing in the shower ?
Options: a ) 150 , b ) 125 , c ) 175 , d ) 200 , e ) 100
Rationale: "total = 300 not working = 200 having family = 100 like to sing in shower = 125 working = 300 - 200 = 100 not having family = 300 - 100 = 200 like to sing in shower = 125 largest possible number is the lowest possible among the above thus 100 e"
Answer: e
Python program:
a = 200 + 100 
b = a + 125 
c = b - 300
Problem: if x > 0 , x / 5 + x / 25 is what percent of x ?
Options: a ) 6 % , b ) 24 % , c ) 37 1 / 2 % , d ) 60 % , e ) 75 %
Rationale: "just plug and chug . since the question asks for percents , pick 100 . ( but any number will do . ) 100 / 5 + 100 / 25 = 20 + 4 = 24 24 is 24 % of 100 = b"
Answer: b
Python program:
a = 1 / 5
b = 1 / 25
c = a + b 
d = c * 100
Problem: each month , after jill pays for rent , utilities , food , and other necessary expenses , she has one fifth of her net monthly salary left as discretionary income . of this discretionary income , she puts 30 % into a vacation fund , 20 % into savings , and spends 35 % on eating out and socializing . this leaves her with $ 102 dollar , which she typically uses for gifts and charitable causes . what is jill ’ s net monthly salary ?
Options: a ) $ 3400 , b ) $ 3200 , c ) $ 6000 , d ) $ 6400 , e ) $ 9600
Rationale: "let x be the monthly salary 15 % of 1 / 5 * x = 102 x = 3400 answer a"
Answer: a
Python program:
a = 3 + 2 
b = 100 * a
c = 30 + 20 
d = c + 35 
e = 100 - d
f = 102 / e
g = b * f
Problem: if f ( f ( n ) ) + f ( n ) = 2 n + 3 , f ( 0 ) = 1 then f ( 2017 ) = ?
Options: a ) 2018 , b ) 2088 , c ) 270 , d ) 1881 , e ) 1781
Rationale: "f ( f ( 0 ) ) + f ( 0 ) = 2 ( 0 ) + 3 ⇒ ⇒ f ( 1 ) = 3 - 1 = 2 , f ( 1 ) = 2 f ( f ( 1 ) ) + f ( 1 ) = 2 ( 1 ) + 3 ⇒ ⇒ f ( 2 ) = 5 - 2 = 3 , f ( 2 ) = 3 f ( f ( 2 ) ) + f ( 2 ) = 2 ( 2 ) + 3 ⇒ ⇒ f ( 3 ) = 7 - 3 = 4 , f ( 3 ) = 4 . . . . . . . . . . . . . . f ( 2017 ) = 2018 ans : a"
Answer: a
Python program:
a = 1 + 2017
Problem: the h . c . f . of two numbers is 32 and the other two factors of their l . c . m . are 13 and 14 . the larger of the two numbers is :
Options: a ) 448 , b ) 299 , c ) 421 , d ) 460 , e ) 365
Rationale: "clearly , the numbers are ( 32 x 13 ) and ( 32 x 14 ) . larger number = ( 32 x 14 ) = 448 . answer : option a"
Answer: a
Python program:
a = 32 * 14
Problem: a solution is 90 % glycerin . if there are 4 gallons of the solution , how much water , in gallons must be addded to make a 75 % glycerin solution
Options: a ) 1.8 , b ) 1.4 , c ) 1.2 , d ) 1.0 , e ) 0.8
Rationale: in 4 gallons of the solution there are 0.9 ∗ 4 = 3.80 gallons of glycerin . we want to add ww gallons of water to 4 gallons of solution so that these 3.6 gallons of glycerin to be 75 % of new solution : 0.9 ∗ 4 = 0.75 ( 4 + w ) - - > w = 0.8 answer : e .
Answer: e
Python program:
a = 90 / 100
b = a * 4
c = 75 / 100
d = b / c
e = d - 4
Problem: of the 120 passengers on flight 750 , 30 % are female . 10 % of the passengers sit in first class , and the rest of the passengers sit in coach class . if 1 / 3 of the passengers in first class are male , how many females are there in coach class ?
Options: a ) 44 , b ) 28 , c ) 50 , d ) 52 , e ) 56
Rationale: "number of passengers on flight = 120 number of female passengers = . 3 * 120 = 36 number of passengers in first class = ( 10 / 100 ) * 120 = 12 number of passengers in coach class = ( 90 / 100 ) * 120 = 108 number of male passengers in first class = 1 / 3 * 12 = 4 number of female passengers in first class = 12 - 4 = 8 number of female passengers in coach class = 36 - 8 = 28 answer b"
Answer: b
Python program:
a = 30 / 100
b = 120 * a
c = 10 / 100
d = 120 * c
e = 10 / 100
f = 120 * e
g = f / 3
h = d - g
i = b - h
Problem: 1240 men have provisions for 12 days . if 300 more men join them , for how many days will the provisions last now ?
Options: a ) 12.9 , b ) 12.0 , c ) 9.7 , d ) 8.6 , e ) 12.1
Rationale: "1240 * 12 = 1540 * x x = 9.7 answer : c"
Answer: c
Python program:
a = 12 * 1240
b = 1240 + 300 
c = a / b
Problem: on a certain transatlantic crossing , 15 percent of a ship ' s passengers held round - trip tickets and also took their cars abroad the ship . if 60 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 ) 37.5 % , b ) 40 % , c ) 50 % , d ) 60 % , e ) 66.6 %
Rationale: 0.15 p = rt + c 0.6 ( rt ) = no c = > 0.40 ( rt ) had c 0.15 p = 0.40 ( rt ) rt / p = 37.5 % answer - a
Answer: a
Python program:
a = 100 - 60
b = a / 100
c = 15 / b
Problem: in how many seconds will a train 150 meters long pass an oak tree , if the speed of the train is 36 km / hr ?
Options: a ) 11 , b ) 13 , c ) 15 , d ) 17 , e ) 19
Rationale: "speed = 36 * 5 / 18 = 10 m / s time = 150 / 10 = 15 seconds the answer is c ."
Answer: c
Python program:
a = const_0_2778 * 36
b = 150 / a
Problem: two numbers n and 16 have lcm = 48 and gcf = 4 . find n .
Options: a ) 35 , b ) 56 , c ) 76 , d ) 87 , e ) 12
Rationale: "the product of two integers is equal to the product of their lcm and gcf . hence . 16 * n = 48 * 4 n = 48 * 4 / 16 = 12 correct answer e"
Answer: e
Python program:
a = 48 * 4
b = a / 16
Problem: every year an amount increases by 1 / 8 th of itself . how much will it be after two years if its present value is rs . 65000 ?
Options: a ) 81000 , b ) 81007 , c ) 81008 , d ) 81066 , e ) 82265.6
Rationale: "65000 * 9 / 8 * 9 / 8 = 82265.6 answer : e"
Answer: e
Python program:
a = 1 / 8
b = a * 65000
c = 65000 + b 
d = 1 / 8
e = 1 / 8
f = e * 65000
g = 65000 + f 
h = d * g
i = c + h
Problem: a track covers a distance of 550 metres in 1 minute whereas a bus covers a distance of 33 kms in 45 minute . the ratio of their speeds is :
Options: a ) 4 : 3 , b ) 3 : 5 , c ) 3 : 4 , d ) 50 : 3 , e ) none
Rationale: solution : speed of track = 550 per minute . speed of bus = 33 kms / 45 = 33000 / 45 = 733.33 m / minute ratio of their speeds = 550 / 733.33 = 3 : 4 . answer : option c
Answer: c
Python program:
a = 550 / const_60
b = 33 * 1000
c = 45 * const_60
d = b / c
e = a / d
Problem: the length of rectangle is thrice its breadth and its perimeter is 64 m , find the area of the rectangle ?
Options: a ) 432 sq m , b ) 192 sq m , c ) 452 sq m , d ) 428 sq m , e ) 528 sq m
Rationale: "2 ( 3 x + x ) = 64 l = 24 b = 8 lb = 24 * 8 = 192 answer : b"
Answer: b
Python program:
a = 3 * 2
b = 1 * 2
c = a + b 
d = 64 / c
e = d * 3
f = 3 * 2
g = 1 * 2
h = f + g 
i = 64 / h
j = e * i
Problem: the instructions state that cheryl needs 3 / 8 square yards of one type of material and 1 / 3 square yards of another type of material for a project . she buys exactly that amount . after finishing the project , however , she has 15 / 40 square yards left that she did not use . what is the total amount of square yards of material cheryl used ?
Options: a ) 1 / 12 , b ) 1 / 9 , c ) 2 / 3 , d ) 1 / 3 , e ) 2 1 / 9
Rationale: "total bought = 3 / 8 + 1 / 3 left part 15 / 40 - - - > 3 / 8 so used part 3 / 8 + 1 / 3 - 3 / 8 = 1 / 3 ans d"
Answer: d
Python program:
a = 3 / 8
b = 1 / 3
c = a + b 
d = 15 / 40
e = c - d
Problem: what number has a 1 : 20 ratio to the number 10 ?
Options: a ) 10 , b ) 1 / 2 , c ) 2 , d ) 1 / 4 , e ) 20
Rationale: "1 : 20 = x : 10 20 x = 10 ; x = 10 / 20 x = 1 / 2 answer : b"
Answer: b
Python program:
a = 10 * 1
Problem: running at the same rate , 8 identical machines can produce 560 paperclips a minute . at this rate , how many paperclips could 10 machines produce in 6 minutes ?
Options: a ) 1344 , b ) 4200 , c ) 8400 , d ) 50400 , e ) 67200
Rationale: 8 machines produce 560 in 1 min 8 machines produce 560 * 6 in 6 min 10 machine produce 560 * 6 * ( 10 / 8 ) in 6 minutes 560 * 6 * 10 / 8 = 4200 answer is b .
Answer: b
Python program:
a = 10 / 8
b = 560 * a
c = b * 6
Problem: speed of a boat in standing water is 16 kmph and the speed of the stream is 2 kmph . a man rows to a place at a distance of 7020 km and comes back to the starting point . the total time taken by him is :
Options: a ) 914.2 hours , b ) 900 hours , c ) 915 hours , d ) 891.4 hours , e ) 915 hours
Rationale: "explanation : speed downstream = ( 16 + 2 ) = 18 kmph speed upstream = ( 16 - 2 ) = 14 kmph total time taken = 7020 / 18 + 7020 / 14 = 390 + 501.4 = 891.4 hours answer : option d"
Answer: d
Python program:
a = 16 + 2 
b = 7020 / a
c = 16 - 2
d = 7020 / c
e = b + d
Problem: the angle between the minute hand and the hour hand of a clock when the time is 4.20 ° is
Options: a ) 0 ° , b ) 5 ° , c ) 10 ° , d ) 20 ° , e ) none
Rationale: "sol . angle traced by hour hand in 13 / 3 hrs = ( 360 / 12 x 13 / 3 ) ° = 130 ° angle traced by min . hand in 20 min . = ( 360 / 60 x 20 ) ° = 120 ° ∴ required angle = ( 130 - 120 ) ° = 10 ° answer c"
Answer: c
Python program:
a = 3 * 4
b = 3 * 4
c = b - 1
d = a / c
e = 4 + 1 
f = 3 * 4
g = f - 1
h = e * g
i = d * h
j = const_60 / 2
k = i - j
l = 3 * 4
m = l - 1
n = k * m
o = n / 2
Problem: a man invests some money partly in 9 % stock at 96 and partly in 12 % stock at 120 . to obtain equal dividends from both , he must invest the money in the ratio :
Options: a ) 3 : 4 , b ) 3 : 5 , c ) 4 : 5 , d ) 16 : 15 , e ) none
Rationale: "solution for an income of rs . 1 in 9 % stock at 96 , investment = rs . ( 96 / 9 ) = rs . 32 / 3 . for an income of rs . 1 in 12 % stock at 120 , investment = rs . ( 120 / 12 ) = rs . 10 . ∴ ratio of investments = 32 / 3 : 10 = 32 : 30 = 16 : 15 answer d"
Answer: d
Python program:
a = 96 * 2
b = 120 * 3
c = a / b
Problem: at 6 ' o clock clock ticks 6 times . the time between first and last ticks was 30 sec . how much time it takes at 8 ' o clock .
Options: a ) 54 sec , b ) 48 sec , c ) 42 sec , d ) 70 sec , e ) 60 sec
Rationale: at 6 ' 0 clock , clock ticks 6 times . so , there must be 5 intervals between clock ticks . time between first and last ticks = 30 sec so , 1 interval = 30 / 5 = 6 sec so 6 ' o clock 5 * 6 = 30 sec 7 ' o clock 6 * 6 = 36 sec 8 ' o clock 7 * 6 = 42 sec so , 42 sec at 8 ' o clock . answer : c
Answer: c
Python program:
a = 8 - 1
b = 6 - 1
c = 30 / b
d = a * c
Problem: 9 fencers participate in a fencing championship . assuming all competitors have an equal chance of winning , how many possibilities are there with respect to how a first - place and second - place medal can be awarded ?
Options: a ) 72 , b ) 75 , c ) 81 , d ) 84 , e ) 88
Rationale: 9 * 8 = 72 the answer is a .
Answer: a
Python program:
a = math.factorial(9)
b = 9 - 2
c = math.factorial(b)
d = a / c
Problem: what is the units digit of 2222 ^ ( 333 ) * 3333 ^ ( 222 ) ?
Options: a ) 0 , b ) 2 , c ) 4 , d ) 6 , e ) 8
Rationale: "( 2222 ^ 333 ) * ( 3333 ^ 222 ) = 2222 ^ 111 * ( 2222 ^ 222 * 3333 ^ 222 ) here please pay attention to the fact that the unit digit of multiplication of 2222 and 3333 is 6 ( 2222 ^ 222 * 3333 ^ 222 ) . since 6 powered in any number more than 0 results in 6 as a units digit , as a result we have - 6 * 2222 ^ 111 2 has a cycle of 4 . 111 = 27 * 4 + 3 . 2 ^ 3 = 8 6 * 8 = 48 so the units digit is 8 , and the answer is e"
Answer: e
Python program:
a = 4 + 3 
b = a + 2
Problem: in a factory , an average of 70 tv ' s are produced per day for the fist 25 days of the months . a few workers fell ill for the next 5 days reducing the daily avg for the month to 68 sets / day . the average production per day for day last 5 days is ?
Options: a ) 20 , b ) 36 , c ) 48 , d ) 50 , e ) 58
Rationale: "production during these 5 days = total production in a month - production in first 25 days . = 30 x 68 - 25 x 70 = 290 ∴ average for last 5 days = 290 / 5 = 58 e"
Answer: e
Python program:
a = 25 + 5 
b = a * 68
c = 25 * 70
d = b - c
e = d / 5
Problem: alex has 4 pens worth of { 22 , 25 , 30 , 40 } , what is the total mean and median of the worth of pens ?
Options: a ) 3.42 , b ) 6.16 , c ) 8.32 , d ) 2.0 , e ) 1.75
Rationale: this is a good question to understand the difference between mean and median . mean : average of all the numbers . ( sum of all the elements divided by the number of elements ) median : arrange the elements of the set in increasing order . if the number of terms is odd , the middle term is the median . if the number of terms is even , the average of middle two terms is the median coming to this question , mean = ( 22 + 25 + 30 + 40 ) / 4 = 29.25 median = ( 25 + 30 ) / 2 = 27.5 total = 1.75 option e
Answer: e
Python program:
a = 22 + 25 
b = a + 30 
c = b + 40 
d = c / 4
e = 25 + 30 
f = e / 2
g = d - f
Problem: there were 35 students in a hostel . due to the admission of 7 new students , ; he expenses of the mess were increased by rs . 42 per day while the average expenditure per head diminished by rs 1 . what was the original expenditure of the mess ?
Options: a ) 320 , b ) 120 , c ) 400 , d ) 420 , e ) 514
Rationale: "sol . let the original average expenditure be rs . x . then , 42 ( x - 1 ) - 35 x = 42  7 x = 84  x = 12 . original expenditure = rs . ( 35 x 12 ) = rs . 420 . . answer d"
Answer: d
Python program:
a = 42 + 42 
b = 42 - 35
c = a / b
d = c * 35
e = 42 + 42 
f = 42 - 35
g = e / f
h = 42 - g
i = 42 + 42 
j = 42 - 35
k = i / j
l = h - k
m = l + 2 
n = d - m
Problem: 1 , 0.5 , 0.5 , 0.75 , 1.5 , ____
Options: a ) 1.25 , b ) 5.75 , c ) 3.25 , d ) 3.75 , e ) none
Rationale: "1 , 0.5 , 0.5 , 0.75 , 1.5 , . . . . . 1 * 0.5 = 0.5 0.5 * 1 = 0.5 0.5 * 1.5 = 0.75 0.75 * 2 = 1.5 so , 1.5 * 2.5 = 3.75 answer : d"
Answer: d
Python program:
a = negate - (
Problem: what percent of 15 kg is 30 gms ?
Options: a ) 25 , b ) 66 , c ) 20 , d ) 19 , e ) 17
Rationale: "explanation : required percentage = ( 30 / 15000 * 100 ) % = 1 / 5 % = 0.2 % answer : c ) . 20 %"
Answer: c
Python program:
a = 15 / 30
b = a * 100
Problem: if $ 100 invested at a certain rate of simple interest amounts to $ 140 at the end of 3 years , how much will $ 150 amount to at the same rate of interest in 6 years ?
Options: a ) $ 190 , b ) $ 180 , c ) $ 200 , d ) $ 240 , e ) $ 270
Rationale: 100 amounts to 140 in 3 years . i . e ( principal + interest ) on 120 in 3 years = 140 100 + 100 * ( r / 100 ) * ( 3 ) = 140 = > r = 40 / 3 150 in 6 years = principal + interest = 150 + 150 * ( r / 100 ) * ( 6 ) = 270 answer is e .
Answer: e
Python program:
a = 150 * 6
b = 140 - 100
c = b * 100
d = c / 100
e = d / 3
f = a * e
g = f / 100
h = 150 + g
Problem: the owner of a furniture shop charges his customer 100 % more than the cost price . if a customer paid rs . 1000 for a computer table , then what was the cost price of the computer table ?
Options: a ) 800 , b ) 650 , c ) 500 , d ) 600 , e ) 250
Rationale: "cp = sp * ( 100 / ( 100 + profit % ) ) = 1000 ( 100 / 200 ) = rs . 500 . answer : c"
Answer: c
Python program:
a = 100 / 100
b = 1 + a 
c = 1000 / b
Problem: if a father said to his elder son , ` ` i was as old as you are at the present at the time of your birth ' ' . if the father ' s age is 25 years now , what was the son ' s age 4 years back ?
Options: a ) 7.5 , b ) 8.5 , c ) 9 , d ) 9.5 , e ) 10
Rationale: let son ' s present age be a years . then , ( 25 − a ) = a ⇒ 2 a = 25 ⇒ a = 25 / 2 = 12.5 son ' s age 4 years back = 12.5 - 4 = 8.5 answer : b
Answer: b
Python program:
a = 25 / 2
b = a - 4
Problem: a circle graph shows how the megatech corporation allocates its research and development budget : 13 % microphotonics ; 24 % home electronics ; 15 % food additives ; 29 % genetically modified microorganisms ; 8 % industrial lubricants ; and the remainder for basic astrophysics . if the arc of each sector of the graph is proportional to the percentage of the budget it represents , how many degrees of the circle are used to represent basic astrophysics research ?
Options: a ) 8 ° , b ) 40 ° , c ) 18 ° , d ) 36 ° , e ) 52 °
Rationale: "here all percentage when summed we need to get 100 % . as per data 13 + 24 + 15 + 29 + 8 = 89 % . so remaining 11 % is the balance for the astrophysics . since this is a circle all percentage must be equal to 360 degrees . 100 % - - - - 360 degrees then 11 % will be 40 degrees . . imo option b ."
Answer: b
Python program:
a = 13 + 24 
b = a + 15 
c = b + 29 
d = c + 8 
e = 100 - d
f = 3600 / 10
g = e * f
h = g / 100
Problem: 7 , 10.5 , 15.75 , 23.63 , 35.43 , ( . . . )
Options: a ) 52.112 , b ) 53.156 , c ) 54 , d ) 89 , e ) 88
Rationale: "7 ( 7 ã — 3 ) ã · 2 = 10.5 ( 10.5 ã — 3 ) ã · 2 = 15.75 ( 15.75 ã — 3 ) ã · 2 = 23.63 ( 23.63 ã — 3 ) ã · 2 = 35.43 ( 35.43 ã — 3 ) ã · 2 = 53.156 answer is b"
Answer: b
Python program:
a = negate - (
Problem: jim ’ s taxi service charges an initial fee of $ 2.25 at the beginning of a trip and an additional charge of $ 0.25 for each 2 / 5 of a mile traveled . what is the total charge for a trip of 3.6 miles ?
Options: a ) $ 3.15 , b ) $ 4.5 , c ) $ 4.80 , d ) $ 5.05 , e ) $ 5.40
Rationale: "let the fixed charge of jim ’ s taxi service = 2.25 $ and charge per 2 / 5 mile ( . 4 mile ) = . 25 $ total charge for a trip of 3.6 miles = 2.25 + ( 3.6 / . 4 ) * . 25 = 2.25 + 9 * . 25 = 4.5 $ answer b"
Answer: b
Python program:
a = 2 / 5
b = 3 / 6
c = 0 * 25
d = 2 + 25
Problem: payal finished 2 / 3 of a book . she calculated that she finished 20 more pages than she has yet to read . how long is her book ?
Options: a ) a ) 60 , b ) b ) 150 , c ) c ) 130 , d ) d ) 90 , e ) e ) 210
Rationale: let x be the total number of pages in the book , then she finished 2 / 3 * x pages . then she has x − 2 / 3 * x = 1 / 3 * x pages left . 2 / 3 * x − 1 / 3 * x = 20 1 / 3 * x = 20 x = 60 so the book is 270 pages long . answer is a .
Answer: a
Python program:
a = 2 / 3
b = a / 2
c = 20 / b
Problem: the tax on a commodity is diminished by 10 % and its consumption increased by 15 % . the effect on revenue is ?
Options: a ) 2 % decrease , b ) 3.5 % increase , c ) 9 % decrease , d ) 3 % decrease , e ) 2 % increase
Rationale: "100 * 100 = 10000 90 * 115 = 10350 - - - - - - - - - - - 10000 - - - - - - - - - - - 350 100 - - - - - - - - - - - ? = > 3.5 % decrease answer : b"
Answer: b
Python program:
a = 15 / 100
b = 1 + a 
c = 10 / 100
d = 1 - c
e = b * d
f = e * 100
g = 100 - f
Problem: a monkey ascends a greased pole 19 metres high . he ascends 2 metres in first minute and slips down 1 metre in the alternate minute . in which minute , he reaches the top ?
Options: a ) 21 st , b ) 22 nd , c ) 23 rd , d ) 35 th , e ) none of these
Rationale: "in 2 minutes , he ascends = 1 metre â ˆ ´ 17 metres , he ascends in 34 minutes . â ˆ ´ he reaches the top in 35 th minute . answer d"
Answer: d
Python program:
a = 2 * 19
b = a - 1
Problem: the length of a rectangle is twice its breadth . if its length is decreased by 5 cm and breadth is increased by 4 cm , the area of the rectangle is increased by 75 sq . cm . find the length of the rectangle .
Options: a ) 20 cm , b ) 25 cm , c ) 26 cm , d ) 100 / 3 cm , e ) 23 cm
Rationale: explanation : let breadth = x . then , length = 2 x . then , ( 2 x - 5 ) ( x + 4 ) - 2 x * x = 75 = > 3 x - 25 = 75 = > x = 100 / 3 . length of the rectangle = 100 / 3 cm . answer : option d
Answer: d
Python program:
a = 100 / 3
Problem: there is a 1 km long wire placed on some number of poles which are in equal distance . if the number of poles is reduced by 1 then the distance of wire between each poles increases 1 ( 2 / 3 ) . how many poles are there initially .
Options: a ) 24 , b ) 25 , c ) 26 , d ) 27 , e ) 28
Rationale: 26 answer : c
Answer: c
Python program:
a = 2 / 3
b = 1 + 1 
c = a * b
d = c * 3
e = d * 12
f = e / 2
g = f + 2
Problem: by investing rs . 1620 in 8 % stock , michael earns rs . 135 . the stock is then quoted at :
Options: a ) rs . 80 , b ) rs . 96 , c ) rs . 106 , d ) rs . 108 , e ) rs . 118
Rationale: michel earns rs 135 by investing rs 1620 to earn rs 8 how much he have to invest ? = ( 8 * 1620 ) / 135 = rs 96 answer : b
Answer: b
Python program:
a = 1620 / 135
b = 8 / 100
c = a * b
d = c * 100
Problem: the initial price of an article is rs . 2000 which increases 30 % increse in its price in the first year , a 20 % decrease in the second year and a 10 % increase in the next year . what is the final price of the article ?
Options: a ) rs . 1748 , b ) rs . 1948 , c ) rs . 1848 , d ) rs . 2048 , e ) rs . 2148
Rationale: the initial price of the article , four years age is rs . 2000 in the 1 st year , price of the article = 2000 + 600 = rs . 2600 . in the 2 nd year , price = 2600 - 20 % of 2600 = 2200 - 520 = rs . 1680 . in the 3 rd year , price = 1680 + 10 % of 1680 = 1680 + 168 = rs . 1848 . required price = rs . 1848 answer : c
Answer: c
Python program:
a = 2000 * 20
b = a / 100
c = 2000 - b
d = 2000 * 20
e = d / 100
f = 2000 - e
g = f * 10
h = g / 100
i = c + h
Problem: at what rate percent on simple interest will rs . 750 amount to rs . 900 in 16 years ?
Options: a ) 6.25 % , b ) 1.25 % , c ) 4 % , d ) 5 % , e ) 3.25 %
Rationale: "150 = ( 750 * 16 * r ) / 100 r = 1.25 % answer : b"
Answer: b
Python program:
a = 900 - 750
b = a / 750
c = b / 16
d = c * 100
Problem: if there are only 2 wheelers and 4 wheelers parked in a school located at the heart of the city , find the number of 4 wheelers parked there if the total number of wheels is 58 ?
Options: a ) 11 , b ) 12 , c ) 13 , d ) 14 , e ) 15
Rationale: "four wheeler = 14 * 4 = 56 ( max ) 2 wheel = 1 so no of 4 wheeler = 14 answer : d"
Answer: d
Python program:
a = 58 - 2
b = a / 4
Problem: if a coin has an equal probability of landing heads up or tails up each time it is flipped , what is the probability that the coin will land tails up exactly once in 3 consecutive flips ?
Options: a ) 0.125 , b ) 0.375 , c ) 0.325 , d ) 0.5 , e ) 0.666
Rationale: total number of ways in which h or t can appear in 3 tosses of coin is = 2 * 2 * 2 = 8 ways for 2 t and 1 th thus probability is = p ( htt ) + p ( tth ) + p ( tht ) = 1 / 8 + 1 / 8 + 1 / 8 = 3 / 8 = . 375 answer : b
Answer: b
Python program:
a = 1 / 2
b = a ** 3
c = b * 3
Problem: a pipe takes a hours to fill the tank . but because of a leakage it took 2 times of its original time . find the time taken by the leakage to empty the tank
Options: a ) 50 min , b ) 60 min , c ) 90 min , d ) 80 min , e ) 120 min
Rationale: "pipe a can do a work 60 min . lets leakage time is x ; then 1 / 60 - 1 / x = 1 / 120 x = 120 min answer : e"
Answer: e
Python program:
a = 1 * 2
b = 10 * a
Problem: if the ratio of two number is 5 : 7 and lcm of the number is 320 then what is the number .
Options: a ) 15 , b ) 9 , c ) 10 , d ) 11 , e ) 35
Rationale: "product of two no = lcm * hcf 5 x * 7 x = 320 * x x = 9 answer : b"
Answer: b
Python program:
a = 5 * 7
b = 320 / a
Problem: find the principle on a certain sum of money at 5 % per annum for 3 1 / 5 years if the amount being rs . 2030 ?
Options: a ) rs . 2000 , b ) rs . 1750 , c ) rs . 2010 , d ) rs . 2005 , e ) none of these
Rationale: "explanation : 2030 = p [ 1 + ( 5 * 16 / 5 ) / 100 ] p = 1750 answer : option b"
Answer: b
Python program:
a = 3 * 5
b = a + 3 
c = b / 5
d = c * 5
e = d / 100
f = e + 1 
g = 2030 / f