euclaise/mathqa_programs huggingface dataset:
Problem: if i walk at 5 km / h , i miss the bus by 9 minutes . if i walk at 3 km / h , i reach 6 minutes before the arrival of the bus . how far i walk to reach the bus stand ?
Options: a ) 1.99 km , b ) 1.55 km , c ) 1.82 km , d ) 2.87 km , e ) 1.87 km
Rationale: "d = product of speed difference of time / difference of speed d = 5 x 3 / 60 [ 9 â ˆ ’ ( â ˆ ’ 6 ) / 5 - 3 ] [ here , â € “ ve sign indicates before the schedule time ] â ‡ ’ d = 1.87 km answer e"
Answer: e
Python program:
a = 5 * 3
b = 3 - 5
c = a / b
d = 9 + 6 
e = d / const_60
f = c * e
Problem: tom opened a shop investing rs . 30000 . jose joined him 2 months later , investing rs . 45000 . they earned a profit of rs . 27000 after completion of one year . what will be jose ' s share of profit ?
Options: a ) 20000 , b ) 15000 , c ) 25000 , d ) 34000 , e ) 30000
Rationale: "sol = ~ s - so anju ’ s share = [ 5 / 9 ] x 27000 = 15000 b"
Answer: b
Python program:
a = 2 * 3
b = 2 * a
c = 30000 * b
d = 2 * 3
e = 2 * d
f = e - 2
g = 45000 * f
h = 2 * 3
i = 2 * h
j = 30000 * i
k = g + j 
l = c / k
m = 1 - l
n = 27000 * m
Problem: how many numbers from 10 to 50 are exactly divisible by 9 ?
Options: a ) 9 , b ) 10 , c ) 11 , d ) 12 , e ) 14
Rationale: "10 / 9 = 1 and 50 / 9 = 5 = = > 5 - 1 = 4 . therefore 4 answer : e"
Answer: e
Python program:
a = 50 / 9
b = math.floor(a)
c = b * 9
d = 10 / 9
e = math.floor(d)
f = e + 1 
g = f * 9
h = c - g
i = h / 9
j = i + 1
Problem: a certain family has 3 sons : richard is 6 years older than david , and david is 8 years older than scott . if in 8 years , richard will be twice as old as scott , then how old was david 7 years ago ?
Options: a ) 8 , b ) 10 , c ) 12 , d ) 14 , e ) 7
Rationale: "let ' s say age of richard is ` ` r ' ' age of david is ` ` d ' ' age of scott is ` ` s ' ' now richard is 6 years older than david , i . e . r = d + 6 david is 8 years older than scott i . e . d = s + 8 if in 8 years , richard will be twice as old as scott i . e . r + 8 = 2 x ( s + 8 ) i . e . r + 8 = 2 s + 16 i . e . r = 2 s + 8 but r = d + 6 = ( s + 8 ) + 6 = s + 14 therefore , 2 s + 8 = s + 14 i . e . s = 6 i . e . r = 20 i . e . d = 14 now , how old was david 7 years ago ? i . e . d - 7 = 14 - 7 = 7 years answer : e"
Answer: e
Python program:
a = 6 + 8 
b = a - 7
Problem: in a competitive examination in state a , 6 % candidates got selected from the total appeared candidates . state b had an equal number of candidates appeared and 7 % candidates got selected with 84 more candidates got selected than a . what was the number of candidates appeared from each state ?
Options: a ) 7000 , b ) 8400 , c ) 6000 , d ) 5000 , e ) 4000
Rationale: "state a and state b had an equal number of candidates appeared . in state a , 6 % candidates got selected from the total appeared candidates in state b , 7 % candidates got selected from the total appeared candidates but in state b , 84 more candidates got selected than state a from these , it is clear that 1 % of the total appeared candidates in state b = 84 = > total appeared candidates in state b = 84 x 100 = 8400 = > total appeared candidates in state a = total appeared candidates in state b = 8400"
Answer: b
Python program:
a = 7 - 6
b = a / 100
c = 84 / b
Problem: find the area of a parallelogram with base 34 cm and height 18 cm ?
Options: a ) 198 cm 2 , b ) 384 cm 2 , c ) 510 cm 2 , d ) 612 cm 2 , e ) 680 cm 2
Rationale: "area of a parallelogram = base * height = 34 * 18 = 612 cm 2 answer : d"
Answer: d
Python program:
a = 34 * 18
Problem: a car started running at a speed of 30 km / hr and the speed of the car was increased by 2 km / hr at the end of every hour . find the total distance covered by the car in the first 10 hours of the journey ?
Options: a ) 288 , b ) 390 , c ) 287 , d ) 266 , e ) 161
Rationale: "the total distance covered by the car in the first 10 hours = 30 + 32 + 34 + 36 + 38 + 40 + 42 + 44 + 46 + 48 = sum of 10 terms in ap whose first term is 30 and last term is 48 = 10 / 2 [ 30 + 48 ] = 390 km . answer : b"
Answer: b
Python program:
a = 2 * 10
b = 30 + a 
c = b + 30 
d = c / 2
Problem: in a sports club with 35 members , 15 play badminton and 18 play tennis and 5 do not play either . how many members play both badminton and tennis ?
Options: a ) 3 , b ) 5 , c ) 6 , d ) 7 , e ) 8
Rationale: "15 + 18 = 33 but where as total number is 35 - 5 = 30 therefore answer is 33 - 30 = 3 hence answer is a"
Answer: a
Python program:
a = 15 + 18 
b = a + 5 
c = b - 35
Problem: on day one , a store sold 96 pens . on each of the next d days , the company sold 44 pens . if the average daily sales of pens over this time period ( including day one ) is 48 pens , what is the value of d ?
Options: a ) 9 , b ) 10 , c ) 11 , d ) 12 , e ) 13
Rationale: 96 + 44 d = 48 ( d + 1 ) . 4 d = 48 . d = 12 . the answer is d .
Answer: d
Python program:
a = 96 - 48
b = 48 - 44
c = a / b
Problem: walking 7 / 6 of his usual rate , a boy reaches his school 5 min early . find his usual time to reach the school ?
Options: a ) 22 , b ) 28 , c ) 99 , d ) 35 , e ) 66
Rationale: "speed ratio = 1 : 7 / 6 = 6 : 7 time ratio = 7 : 6 1 - - - - - - - - 7 5 - - - - - - - - - ? = 35 m answer : d"
Answer: d
Python program:
a = 5 * 7
Problem: carrie likes to buy t - shirts at the local clothing store . they cost $ 9.15 each . one day , she bought 22 t - shirts . how much money did she spend ?
Options: a ) $ 150 , b ) $ 248.75 , c ) $ 200 , d ) $ 201.3 , e ) $ 190
Rationale: $ 9.15 * 22 = $ 201.3 . answer is d .
Answer: d
Python program:
a = 22 * 9
b = math.floor(a)
Problem: there were two candidates in an election . winner candidate received 56 % of votes and won the election by 288 votes . find the number of votes casted to the winning candidate ?
Options: a ) 776 , b ) 1344 , c ) 299 , d ) 257 , e ) 125
Rationale: "w = 56 % l = 44 % 56 % - 44 % = 12 % 12 % - - - - - - - - 288 56 % - - - - - - - - ? = > 1344 answer : b"
Answer: b
Python program:
a = 100 - 56
b = 56 - a
c = b / 100
d = 288 / c
e = d * 56
f = e / 100
Problem: 243 has been divided into 3 parts such that half of the first part , one - third of the second part and one - fourth of the third part are equal . the largest part is ?
Options: a ) 12628 , b ) 23488 , c ) 26688 , d ) 26667 , e ) 12672
Rationale: explanation : ratio of their shares = ( 35000 * 8 ) : ( 42000 * 10 ) = 2 : 3 . reena ' s share rs . 31570 * ( 2 / 5 ) = rs . 12628 . answer : a ) 12628
Answer: a
Python program:
a = 243 * 3
b = a * 3
c = b * 3
d = c * 2
Problem: in the rectangular coordinate system , points ( 8 , 0 ) and ( – 8 , 0 ) both lie on circle c . what is the maximum possible value of the radius of c ?
Options: a ) 2
b ) 4
c ) 8
d ) 16
e ) none of the above
Rationale: the answer is c it takes 3 distinct points to define a circle . only 2 are given here . the two points essentially identify a single chord of the circle c . since no other information is provided , however , the radius of the circle can essentially be anything . all this information tell us is that the radius isgreater 8 c
Answer: c
Python program:
a = 8 ** 2
b = math.sqrt(a)
Problem: a polling company surveyed a certain country , and it found that 35 % of that country ’ s registered voters had an unfavorable impression of both of that state ’ s major political parties and that 20 % had a favorable impression only of party e . if one registered voter has a favorable impression of both parties for every two registered voters who have a favorable impression only of party b , then what percentage of the country ’ s registered voters have a favorable impression of both parties ( assuming that respondents to the poll were given a choice between favorable and unfavorable impressions only ) ?
Options: a ) 15 , b ) 20 , c ) 30 , d ) 35 , e ) 45
Rationale: "s = 100 not ( e and b ) = 35 only e = 20 ( e and b ) / b = 1 / 2 let ( e and b ) = x only b = 2 x so now , 20 + 35 + x + 2 x = 100 x = 15 a ans"
Answer: a
Python program:
a = 35 + 20 
b = 100 - a
c = b / 3
Problem: if y ¤ w = y ^ ( 2 w ) for all positive integers , then ( 3 ¤ 4 ) ¤ 2 =
Options: a ) 3 ^ 8 , b ) 3 ^ 12 , c ) 3 ^ 16 , d ) 3 ^ 24 , e ) 3 ^ 32
Rationale: y ¤ w = y ^ ( 2 w ) 3 ¤ 4 = 3 ^ ( 8 ) ( 3 ¤ 4 ) ¤ 2 = ( 3 ^ 8 ) ¤ 2 = ( 3 ^ 8 ) ^ 4 = 3 ^ 32 correct option : e
Answer: e
Python program:
a = 2 * 4
b = 3 ** a
c = 2 * 2
d = b ** c
Problem: a circular rim a having a diameter of 45 inches is rotating at the rate of x inches / min . another circular rim b with a diameter of 30 inches is rotating at the rate of y inches / min . what is the value of y in terms of x , if both the rims reach their starting positions at the same time after every rotation .
Options: a ) 3 x / 2
b ) 4 x / 5
c ) 7 x / 5
d ) 5 x / 7
e ) 3 x / 4
Rationale: t = s 1 / v 1 = s 2 / v 2 or , 45 / x = 30 / y or , y = 45 x / 30 = 3 x / 2 ( answer a )
Answer: a
Python program:
a = 3 * 45
b = a / 2
Problem: a typist uses a sheet measuring 20 cm by 30 cm lengthwise . if a margin of 2 cm is left on each side and a 3 cm margin on top and bottom , then percent of the page used for typing is
Options: a ) 40 , b ) 60 , c ) 64 , d ) 72 , e ) none
Rationale: solution area of the sheet = ( 20 x 30 ) cm ² = 600 cm ² area used for typing = [ ( 20 - 4 ) x ( 30 - 6 ) ] cm ² = 384 cm ² required percentage = ( 384 / 600 x 100 ) % = 64 % . answer c
Answer: c
Python program:
a = 3 + 3 
b = 30 - a
c = 20 - 4
d = b * c
e = 20 * 30
f = d / e
g = f * 100
Problem: the h . c . f . of two numbers is 12 and their difference is 12 . the numbers are :
Options: a ) 66 , 78 , b ) 70 , 82 , c ) 94 , 106 , d ) 84 , 96 , e ) none of these
Rationale: explanation : out of the given numbers , the two with h . c . f . 12 and difference 12 are 84 and 96 . answer is d
Answer: d
Python program:
a = 3 + 4 
b = 12 * a
Problem: john , james and jim ' investment ratio in a business is 4 : 7 : 9 . if total total investment is 80000 . find jim ' s investment ?
Options: a ) 35000 , b ) 40000 , c ) 16000 , d ) 36000 , e ) 60000
Rationale: let the investment of john james and jim is 4 x 7 x and 9 x 4 x + 7 x + 9 x = 80000 20 x = 80000 x = 4000 jim ' investment = 9 * 4000 = 36000 answer : d
Answer: d
Python program:
a = 4 + 7 
b = a + 9 
c = 80000 / b
d = c * 9
Problem: two persons a and b can complete a piece of work in 30 days and 45 days respectively . if they work together , what part of the work will be completed in 3 days ?
Options: a ) 1 / 5 , b ) 1 / 1 , c ) 1 / 6 , d ) 1 / 3 , e ) 1 / 7
Rationale: "a ' s one day ' s work = 1 / 30 b ' s one day ' s work = 1 / 45 ( a + b ) ' s one day ' s work = 1 / 30 + 1 / 45 = 1 / 18 the part of the work completed in 3 days = 3 ( 1 / 18 ) = 1 / 6 . answer : c"
Answer: c
Python program:
a = 1 / 30
b = 1 / 45
c = a + b 
d = 3 * c
Problem: calculate how long it will take a swimmer to swim a distance of 8 km against the current of a river which flows at 1.4 km / hr , given that he can swim in still water at 3 km / h
Options: a ) 20 seconds , b ) 3 , c ) 4 , d ) 1 , e ) 5
Rationale: swim in still water at = 3 speed of river = 1.4 us = 3 - 1.4 = 1.6 distance = 8 t = 8 / 1.6 = 5 answer : e
Answer: e
Python program:
a = 3 - 1
b = 8 / a
Problem: a satellite is composed of 24 modular units , each of which is equipped with a set of sensors , some of which have been upgraded . each unit contains the same number of non - upgraded sensors . if the number of non - upgraded sensors on one unit is 1 / 8 the total number of upgraded sensors on the entire satellite , what fraction of the sensors on the satellite have been upgraded ?
Options: a ) 1 / 4 , b ) 1 / 5 , c ) 1 / 6 , d ) 1 / 8 , e ) 1 / 24
Rationale: "let x be the number of upgraded sensors on the satellite . the number of non - upgraded sensors per unit is x / 8 . the number of non - upgraded sensors on the whole satellite is 24 ( x / 8 ) = 3 x . the fraction of sensors which have been upgraded is x / ( x + 3 x ) = x / 4 x = 1 / 4 the answer is a ."
Answer: a
Python program:
a = 1 / 8
b = a * 24
c = 24 * b
d = 24 + c 
e = 24 / d
Problem: if the operation ø is defined for all positive integers x and w by x ø w = ( 2 ^ x ) / ( 2 ^ w ) then ( 4 ø 2 ) ø 1 = ?
Options: a ) 2 , b ) 4 , c ) 8 , d ) 16 , e ) 32
Rationale: "4 ø 2 = 2 ^ 4 / 2 ^ 2 = 4 4 ø 1 = 2 ^ 4 / 2 = 8 the answer is c ."
Answer: c
Python program:
a = 2 ** 4
b = 2 ** 2
c = a / b
d = 2 ** c
e = 2 ** 1
f = d / e
Problem: if 3 ^ x * 4 ^ y = 531,441 and x – y = 12 , then x = ?
Options: a ) 10 , b ) 11 , c ) 12 , d ) 13 , e ) 14
Rationale: "since 531,441 is an odd number , it is not a multiple of 4 . this means that y must equal zero . since x - y = 12 and y = 0 , then x = 12 . the answer is c ."
Answer: c
Python program:
a = 12 * 1
Problem: a man buys a cycle for rs . 2300 and sells it at a loss of 30 % . what is the selling price of the cycle ?
Options: a ) s . 1690 , b ) s . 1610 , c ) s . 1890 , d ) s . 1602 , e ) s . 1092
Rationale: "s . p . = 70 % of rs . 2300 = rs . 70 x 2300 / 100 = rs . 1610 answer : option b"
Answer: b
Python program:
a = 100 - 30
b = a * 2300
c = b / 100
Problem: how many hours are there in 660 minutes ?
Options: a ) 60 hours , b ) 6 hours , c ) 30 hours , d ) 11 hours , e ) 10 hours
Rationale: "solution : number of minutes in 1 hour = 60 minutes so just divide 660 by 60 660 ã · 60 = 11 , so there are 11 hours in 660 minutes option d"
Answer: d
Python program:
a = 660 / const_60
Problem: a is twice as good a workman as b and they took 9 days together to do the work b alone can do it in ?
Options: a ) 25 days , b ) 88 days , c ) 21 days , d ) 27 days , e ) 13 days
Rationale: "wc = 2 : 1 2 x + x = 1 / 9 x = 1 / 27 = > 27 days answer : d"
Answer: d
Python program:
a = 2 + 1 
b = 9 * a
c = b / 2
d = c * 2
Problem: tom read a book containing 480 pages by reading the same number of pages each day . if he would have finished the book 5 days earlier by reading 16 pages a day more , how many days did tom spend reading the book ?
Options: a ) 10 , b ) 12 , c ) 15 , d ) 16 , e ) 18
Rationale: "say the number of days tom spent reading the book was dd . then : the number of pages he read per day would be 480 / d the number of pages he would read per day with an increased speed would be 480 / d − 5 e are told that the number of pages for the second case was 16 pages per day more , so 480 / d = 480 / d − 5 − 16 at this point it ' s much better to plug answer choices rather than solve for dd . answer choice cc fits : 480 / 15 = 32 = 480 / 15 − 5 − 16 answer : c"
Answer: c
Python program:
a = 16 * 5
b = a * 4
c = 16 ** 2
d = b + c 
e = math.sqrt(d)
f = e - 16
g = f / 2
Problem: ajay and vijay have some marbles with them . ajay told vijay ` ` if you give me ' x ' marbles , both of us will have equal number of marbles ' ' . vijay then told ajay ` ` if you give me twice as many marbles , i will have 30 more marbles than you would ' ' . find ' x ' ?
Options: a ) 7 , b ) 5 , c ) 6 , d ) 4 , e ) 3
Rationale: if vijay gives ' x ' marbles to ajay then vijay and ajay would have v - x and a + x marbles . v - x = a + x - - - ( 1 ) if ajay gives 2 x marbles to vijay then ajay and vijay would have a - 2 x and v + 2 x marbles . v + 2 x - ( a - 2 x ) = 30 = > v - a + 4 x = 30 - - - ( 2 ) from ( 1 ) we have v - a = 2 x substituting v - a = 2 x in ( 2 ) 6 x = 30 = > x = 5 . answer : b
Answer: b
Python program:
a = 2 * 3
b = 30 / a
Problem: the average of temperatures at noontime from monday to friday is 45 ; the lowest one is 42 , what is the possible maximum range of the temperatures ?
Options: a ) 15 , b ) 25 , c ) 40 , d ) 45 , e ) 75
Rationale: "there are 5 days so the sum of temperature can be 45 * 5 = 225 lowest is 42 . to find the maximum range we can say the temperature was the lowest for 4 of the 5 days so 4 * 42 = 168 . on the fifth day it is 225 - 168 = 57 range is therefore 57 - 42 = 15 answer a"
Answer: a
Python program:
a = 2 + 3 
b = 45 * a
c = 42 * 4
d = b - c
e = d - 42
Problem: david is 12 years older than his daughter rosy . in 4 years david will be twice as old as rosy . what is rosy current age .
Options: a ) 9 , b ) 10 , c ) 11 , d ) 8 , e ) 12
Rationale: "now : rosy = x , david = x + 12 in 4 years rosy = x + 4 , david = x + 12 + 4 or 2 ( x + 4 ) x + 16 = 2 x + 8 x = 8 rosy is 8 years old answer : d"
Answer: d
Python program:
a = 12 + 4 
b = 2 * 4
c = a - b
Problem: one - third of 1200 is what percent of 236 ?
Options: a ) 169.49 , b ) 30 , c ) 120.32 , d ) 125.32 , e ) 15.152
Rationale: "answer let one - third of 1200 is n % of 236 . ∵ 1200 / 3 = ( n x 236 ) / 100 ∴ n = ( 400 x 100 ) / 236 = 169.49 correct option : a"
Answer: a
Python program:
a = 1200 / 3
b = a / 236
c = 100 * b
Problem: the population of a town is 8100 . it decreases annually at the rate of 10 % p . a . what was its population 2 years ago ?
Options: a ) 9000 , b ) 8000 , c ) 8500 , d ) 9500 , e ) 10000
Rationale: "formula : ( after = 100 denominator ago = 100 numerator ) 8100 × 100 / 90 × 100 / 90 = 10000 e )"
Answer: e
Python program:
a = 10 / 100
b = 8100 * a
c = 8100 - b
d = 10 / 100
e = 8100 * d
f = 8100 - e
g = 10 / 100
h = f * g
i = c - h
Problem: average age of students of an adult school is 48 years . 120 new students whose average age is 32 years joined the school . as a result the average age is decreased by 4 years . find the number of students of the school after joining of the new students .
Options: a ) 1200 , b ) 160 , c ) 360 , d ) 240 , e ) none of these
Rationale: explanation : let the original no . of students be x . according to situation , 48 x + 120 * 32 = ( x + 120 ) 36 ⇒ x = 40 so , required no . of students after joining the new students = x + 120 = 160 . answer : b
Answer: b
Python program:
a = 32 + 4 
b = a * 120
c = 120 * 32
d = b - c
e = 32 + 4 
f = 48 - e
g = d / f
h = g * 4
Problem: if 9 - 4 / x = 7 + 8 / x , then x =
Options: a ) 15 , b ) 6 , c ) 1 , d ) 5 , e ) 12
Rationale: we ' re given the equation 9 - 4 / x = 7 + 8 / x . we ' re asked for the value of x . the common - denominator of these 4 numbers is x , so we have to multiple 2 of the numbers to give them that denominator . . . 9 x - 4 x / x = 7 x + 8 x / x we can then eliminate that denominator , which gives us . . . . 9 x - 4 = 7 x + 8 12 = 2 x both 2 x and 12 have a common denominator of 2 , so we divide both sides by 2 for our final answer . . . 6 = x b
Answer: b
Python program:
a = 8 + 4 
b = 9 - 7
c = a / b
Problem: it costs $ 4 for the first 1 / 4 hour to use the laundry machine at the laundromat . after the first ¼ hour it costs $ 12 per hour . if a certain customer uses the laundry machine for 3 hours and 25 minutes , how much will it cost him ?
Options: a ) $ 25 , b ) $ 32 , c ) $ 36 , d ) $ 40 . , e ) $ 42 .
Rationale: "3 hrs 25 min = 205 min first 15 min - - - - - - > $ 4 time left is 190 min . . . now , 60 min costs $ 12 1 min costs $ 12 / 60 190 min costs $ 12 / 60 * 190 = > $ 38 so , total cost will be $ 38 + $ 4 = > $ 42 hene answer will be ( e ) $ 42"
Answer: e
Python program:
a = 12 * 3
b = a + 4 
c = 12 / const_60
d = 25 / 4
e = c * d
f = b + e
Problem: the ratio of money with ram and gopal is 7 : 17 and that with gopal and krishan is 7 : 17 . if ram has rs . 637 , krishan has ?
Options: a ) s . 2890 , b ) s . 2330 , c ) s . 3757 , d ) s . 1620 , e ) s . 2680
Rationale: "ram : gopal = 7 : 17 = 49 : 119 gopal : krishan = 7 : 17 = 119 : 289 ram : gopal : krishan = 49 : 119 : 289 ram : krishan = 49 : 289 thus , 49 : 289 = 637 : n & there n = 289 x 637 / 49 = rs . 3757 answer : c"
Answer: c
Python program:
a = 637 / 7
b = a * 17
c = b / 7
d = c * 17
Problem: last week david spent 40 percent of his wages on recreation . this week , his wages are 5 percent less than last week ʼ s wages and he spent 50 percent of his wages on recreation . the amount he spends on recreation this week is what percent of the amount he spent on recreation last week
Options: a ) 118.75 % , b ) 128.75 % , c ) 116.75 % , d ) 117.75 % , e ) 114.75 %
Rationale: say david ' s wages last week were $ 100 , so he spent 0.40 * 100 = $ 40 on recreation ; this week ' s wages is 0.95 * 100 = $ 95 , so he spends 0.5 * 95 = $ 47.5 on recreation ; 47.5 / 40 = 1.1875 , hence the amount he spends on recreation this week is 118.75 % of the amount he spent on recreation last week : 40 * 1.1875 = 47.5 answer : a
Answer: a
Python program:
a = 50 / 100
b = 5 / 100
c = 1 - b
d = a * c
e = 40 / 100
f = d / e
g = f * 100
Problem: the data a and b are equal to the data subtracted c ; the data b is 3 times the data a ; if the data a is equal to 12 what is the sum of the data a , b and c ?
Options: a ) 86 , b ) 92 , c ) 84 , d ) 102 , e ) 96
Rationale: the equations raised . a + b = c b = 3 a a = 12 then b = 36 and c = 48 a + b + c = 96 answer : e
Answer: e
Python program:
a = 12 * 3
b = 12 + a 
c = 12 * 3
d = b + c 
e = d + 12
Problem: the population of a town is 30000 . it decreases annually at the rate of 20 % p . a . what will be its population after 2 years ?
Options: a ) 4300 , b ) 19200 , c ) 5120 , d ) 5230 , e ) 5366
Rationale: "30000 × 80 / 100 × 80 / 100 = 19200 answer ; b"
Answer: b
Python program:
a = 20 / 100
b = 30000 * a
c = 30000 - b
d = 20 / 100
e = 30000 * d
f = 30000 - e
g = 20 / 100
h = f * g
i = c - h
Problem: a , b and c invest in the ratio of 3 : 4 : 5 . the percentage of return on their investments are in the ratio of 6 : 5 : 4 . find the total earnings , if b earns rs . 150 more than a :
Options: a ) 2348 , b ) 7250 , c ) 4350 , d ) 1998 , e ) 2771
Rationale: "explanation : a b c investment 3 x 4 x 5 x rate of return 6 y % 5 y % 4 y % return \ inline \ frac { 18 xy } { 100 } \ inline \ frac { 20 xy } { 100 } \ inline \ frac { 20 xy } { 100 } total = ( 18 + 20 + 20 ) = \ inline \ frac { 58 xy } { 100 } b ' s earnings - a ' s earnings = \ inline \ frac { 2 xy } { 100 } = 150 total earning = \ inline \ frac { 58 xy } { 100 } = 4350 answer : c ) rs . 4350"
Answer: c
Python program:
a = 3 * 6
b = 4 * 5
c = a + b 
d = 5 * 4
e = c + d 
f = 4 * 5
g = 3 * 6
h = f - g
i = 150 / h
j = e * i
Problem: a man can row downstream at 18 kmph and upstream at 6 kmph . find the speed of the man in still water and the speed of stream respectively ?
Options: a ) 3 , b ) 5 , c ) 6 , d ) 4 , e ) 9
Rationale: let the speed of the man in still water and speed of stream be x kmph and y kmph respectively . given x + y = 18 - - - ( 1 ) and x - y = 6 - - - ( 2 ) from ( 1 ) & ( 2 ) 2 x = 24 = > x = 12 , y = 6 . answer : c
Answer: c
Python program:
a = 18 + 6 
b = a / 2
c = b / 2
Problem: the ratio of 3 numbers is 1 : 2 : 4 and the sum of their squares is 1701 . the sum of the numbers is ?
Options: a ) a ) 10 , b ) b ) 12 , c ) c ) 15 , d ) d ) 14 , e ) e ) 9
Rationale: let the numbers be x , 2 x , 4 x then , x ^ 2 + 4 x ^ 2 + 16 x ^ 2 = 1701 21 x ^ 2 = 1701 x ^ 2 = 81 x = 9 answer is e
Answer: e
Python program:
a = 4 ** 2
b = 1 ** 2
c = 2 ** 2
d = b + c 
e = a + d 
f = 1701 / e
g = math.sqrt(f)
Problem: a lady builds 10 cm length , 18 cm width , and 4 cm height box using 12 cubic cm cubes . what is the minimum number of cubes required to build the box ?
Options: a ) 107 , b ) 70 , c ) 78 , d ) 60 , e ) 111
Rationale: "number of cubes required = volume of box / volume of cube = 10 * 18 * 4 / 12 = 60 cubes answer : d"
Answer: d
Python program:
a = 10 * 18
b = a * 4
c = b / 12
Problem: the sum of the first 80 positive even integers is 2,550 . what is the sum of the odd integers from 101 to 200 , inclusive ?
Options: a ) 5,050 , b ) 7,500 , c ) 10,500 , d ) 15,000 , e ) 19,600
Rationale: "101 + 103 + . . . . . . . 199 if we remove 100 from each of these it will be sum of 1 st 100 odd numbers . so 101 + 103 + . . . . . . . 199 = 80 * 100 + ( 1 + 3 + 5 + 7 + . . . . . . ) sum of 1 st 100 natural numbers = ( 100 * 101 ) / 2 = 5050 sum of 1 st 80 positive even integers = 2550 sum of 1 st 100 odd numbers = 5050 - 2550 = 2500 so 101 + 103 + . . . . . . . 199 = 80 * 100 + ( 1 + 3 + 5 + 7 + . . . . . . ) = 8000 + 2500 = 10500 c is the answer ."
Answer: c
Python program:
a = 200 + 101 
b = a / 2
c = 200 - 101
d = c / 2
e = d + 1 
f = b * e
Problem: a 300 m long train crosses a platform in 45 sec while it crosses a signal pole in 18 sec . what is the length of the platform ?
Options: a ) 287 , b ) 350 , c ) 828 , d ) 450 , e ) 122
Rationale: "speed = 300 / 18 = 50 / 3 m / sec . let the length of the platform be x meters . then , ( x + 300 ) / 45 = 50 / 3 3 x + 900 = 2250 = > x = 450 m . answer : d"
Answer: d
Python program:
a = speed * (
b = a - 45