euclaise/mathqa_programs huggingface dataset:
Problem: during 2003 , a company produced an average of 3,000 products per month . how many products will the company need to produce from 2004 through 2007 in order to increase its monthly average for the period from 2003 through 2007 by 300 % over its 2003 average ?
Options: a ) 520,000 , b ) 540,000 , c ) 525,000 , d ) 530,000 , e ) 550,000
Rationale: "company produced 12 * 3000 = 36,000 products in 2003 . if company produces x products from 2004 to 2007 , then total amount of product produced in 4 years ( 2003 through 2007 ) is x + 36,000 . the gives the average of ( x + 36,000 ) / 4 . this average needs to be 300 % higher than that in 2003 . in math terms , 36,000 + 300 % ( 36,000 ) = 144,000 . so : ( x + 36,000 ) / 4 = 144,000 x + 36,000 = 576,000 x = 540,000 the answer is b ."
Answer: b
Python program:
a = 2007 - 2003
b = a / 2
c = 300 * b
Problem: what is the ratio of arun ' s monthly income in the year 2006 , suman ' s monthly income in the year 2007 and jyothi ' s monthly income in the year 2005 ?
Options: a ) 22 , b ) 67 , c ) 26 , d ) 18 , e ) 16
Rationale: answer : a
Answer: a
Python program:
a = 10 + 10 
b = a + 2
Problem: a runner runs the 40 miles from marathon to athens at a constant speed . halfway through the run she injures her foot , and continues to run at half her previous speed . if the second half takes her 5 hours longer than the first half , how many hours did it take the runner to run the second half ?
Options: a ) 8 , b ) 9 , c ) 10 , d ) 11 , e ) 12
Rationale: the runner runs the first 20 miles at speed v and the second 20 miles at speed v / 2 . the time t 2 to run the second half must be twice the time t 1 to run the first half . t 2 = 2 * t 1 = t 1 + 5 t 1 = 5 and so t 2 = 10 . the answer is c .
Answer: c
Python program:
a = 40 / 2
b = a / 5
c = 40 / b
Problem: there are 2 sections a and b in a class , consisting of 40 and 20 students respectively . if the average weight of section a is 50 kg and that of section b is 40 kg , find the average of the whole class ?
Options: a ) 50.78 kg , b ) 49.32 kg , c ) 46.66 kg , d ) 69.15 kg , e ) 70.89 kg
Rationale: "total weight of 40 + 20 students = 40 * 50 + 20 * 40 = 2000 + 800 average weight of the class is = 2800 / 60 = 46.66 kg answer is c"
Answer: c
Python program:
a = 40 * 50
b = 20 * 40
c = a + b 
d = 40 + 20 
e = c / d
Problem: on dividing 15 by a number , the quotient is 4 and the remainder is 3 . find the divisor ?
Options: a ) 3 , b ) 6 , c ) 9 , d ) 12 , e ) 15
Rationale: "d = ( d - r ) / q = ( 15 - 3 ) / 4 = 12 / 4 = 3 a )"
Answer: a
Python program:
a = 15 / 4
b = math.floor(a)
Problem: if | 4 x + 10 | = 46 , what is the sum of all the possible values of x ?
Options: a ) 2 , b ) - 2 , c ) 4 , d ) - 5 , e ) 6
Rationale: there will be two cases 4 x + 10 = 46 or 4 x + 10 = - 46 = > x = 9 or x = - 14 sum of both the values will be - 14 + 9 = - 5 answer is d
Answer: d
Python program:
a = 46 - 10
b = a / 4
Problem: if it takes a machine 2 ⁄ 5 minute to produce one item , how many items will it produce in 2 hours ?
Options: a ) 1 ⁄ 3 , b ) 4 ⁄ 3 , c ) 80 , d ) 120 , e ) 300
Rationale: "1 item takes 2 / 5 min so it takes 120 min to produce x 2 x / 5 = 120 the x = 300 answer : e"
Answer: e
Python program:
a = 2 * const_60
b = 2 / 5
c = a / b
Problem: a specialized type of sand consists of 40 % mineral x by volume and 60 % mineral y by volume . if mineral x weighs 1.5 grams per cubic centimeter and mineral y weighs 3 grams per cubic centimeter , how many grams does a cubic meter of specialized sand combination weigh ? ( 1 meter = 100 centimeters )
Options: a ) 2 , 400,000 , b ) 2 , 800,000 , c ) 55,000 , d ) 28,000 , e ) 280
Rationale: "let the volume be 1 m ^ 3 = 1 m * 1 m * 1 m = 100 cm * 100 cm * 100 cm = 1 , 000,000 cm ^ 3 by volume 40 % is x = 400,000 cm ^ 3 60 % is y = 600,000 cm ^ 3 by weight , in 1 cm ^ 3 , x is 1.5 gms in 400,000 cm ^ 3 , x = 1.5 * 400,000 = 600,000 grams in 1 cm ^ 3 , y is 3 gms in 600,000 cm ^ 3 , y = 3 * 600,000 = 1 , 800,000 gms total gms in 1 m ^ 3 = 600,000 + 1 , 800,000 = 2 , 400,000 answer : a"
Answer: a
Python program:
a = volume_cube / (
b = a * 10
c = b * 1
d = c + 1 
e = volume_cube / (
f = e * 10
g = 2 * 3
h = f * g
i = d - h
Problem: excluding stoppages , the speed of a bus is 82 kmph and including stoppages , it is 75 kmph . for how many minutes does the bus stop per hour ?
Options: a ) 5.12 , b ) 4.13 , c ) 6.15 , d ) 7.5 , e ) none of these
Rationale: "due to stoppages , it covers 7 km less . time taken to cover 7 km = ( ( 7 / 82 ) ã — 60 ) = 5.12 min . option ( a ) is correct"
Answer: a
Python program:
a = 82 - 75
b = a / 82
c = const_60 * b
Problem: 4 , 6 , 9 , 13.50 , 20.25 , ( . . . )
Options: a ) 60 , b ) 60.75 , c ) 58 , d ) 31.528 , e ) 30.375
Rationale: "4 ( 4 ã — 3 ) ã · 2 = 6 ( 6 ã — 3 ) ã · 2 = 9 ( 9 ã — 3 ) ã · 2 = 13.50 ( 13.50 ã — 3 ) ã · 2 = 20.25 ( 40.5 ã — 3 ) ã · 2 = 30.375 answer is e"
Answer: e
Python program:
a = negate - (
Problem: during a certain season , a team won 85 percent of its first 100 games and 50 percent of its remaining games . if the team won 70 percent of its games for the entire season , what was the total number of games that the team played ?
Options: a ) 180 , b ) 175 , c ) 156 , d ) 150 , e ) 105
Rationale: "we are first given that a team won 85 percent of its first 100 games . this means the team won 0.85 x 100 = 85 games out of its first 100 games . we are next given that the team won 50 percent of its remaining games . if we use variable t to represent the total number of games in the season , then we can say t – 100 equals the number of remaining games in the season . thus we can say : 0.5 ( t – 100 ) = number of wins for remaining games 0.5 t – 50 = number of wins for remaining games lastly , we are given that team won 70 percent of all games played in the season . that is , they won 0.7 t games in the entire season . with this we can set up the equation : number of first 100 games won + number of games won for remaining games = total number of games won in the entire season 85 + 0.5 t – 50 = 0.7 t 35 = 0.2 t 350 = 2 t 175 = t answer is b ."
Answer: b
Python program:
a = 85 - 70
b = 70 / 100
c = 50 / 100
d = b - c
e = a / d
f = 100 + e
Problem: a certain clock marks every hour by striking a number of times equal to the hour , and the time require for a stroke is exactly equal to the time interval between strokes . at 6 : 00 the time lapse between the beginning of the first stoke and the end of the last stroke is 22 seconds . at 8 : 00 , how many seconds elapse between the beginning of the first stroke and the end of the last stroke ?
Options: a ) 26 , b ) 30 , c ) 36 , d ) 38 , e ) 40
Rationale: "at 6 ' o clock , there would be 6 strikes . first strike , then a short interval , the second strike , then a short interval and so on till the 6 th strike . so there would be in all 5 intervals between 6 strikes . similarly , between 8 strikes , there would be 7 intervals . according to the question , the time spent in the strike and the interval is same . at 6 ' o clock , the 6 strikes and the 5 intervals together take 22 sec so each strike and each interval takes 2 secs . at 8 ' o clock , the 8 strikes and 7 intervals will take 2 * ( 8 + 7 ) = 30 secs b"
Answer: b
Python program:
a = 8 - 1
b = a + 8 
c = 6 - 1
d = c + 6 
e = 22 / d
f = b * e
Problem: a train is running at a speed of 4040 km / hr and it crosses a post in 1818 seconds . what is the length of the train ?
Options: a ) 190 metres , b ) 160 metres , c ) 200 metres , d ) 120 metres , e ) 150 metres
Rationale: "explanation : speed = 40 km / hr = 40 km / hr = 40 ã — 518 = 1009 m / s = 40 ã — 518 = 1009 m / s time = 18 = 18 seconds distance covered = 1009 ã — 18 = 200 m = 1009 ã — 18 = 200 m therefore , length of the train = 200 m answer is c"
Answer: c
Python program:
a = 4040 * const_0_2778
b = 1818 * a
Problem: if m and n are whole numbers such that mn = 121 , the value of ( m 1 ) n + 1 is :
Options: a ) 1 , b ) 10 , c ) 121 , d ) 100 , e ) 1000
Rationale: if m and n are whole numbers such that mn = 121 , the value of ( m - 1 ) n + 1 is : a . 1 b . 10 c . 121 d . 1000 sol . - we know that 112 = 121 . putting m = 11 and n = 2 , we get : ( m - 1 ) n + 1 = ( 11 - 1 ) ( 2 + 1 ) = 103 = 1000 . answer : e
Answer: e
Python program:
a = math.sqrt(121)
b = a - 1
c = b ** 3
Problem: if the sides of a triangle are 28 cm , 26 cm and 10 cm , what is its area ?
Options: a ) 120 cm 2 , b ) 112 cm 2 , c ) 776 cm 2 , d ) 130 cm 2 , e ) 886 cm 2
Rationale: "the triangle with sides 28 cm , 26 cm and 10 cm is right angled , where the hypotenuse is 28 cm . area of the triangle = 1 / 2 * 26 * 10 = 130 cm 2 answer : d"
Answer: d
Python program:
a = 26 * 10
b = a / 2
Problem: a train is 510 meter long is running at a speed of 45 km / hour . in what time will it pass a bridge of 140 meter length ?
Options: a ) 76 seconds , b ) 18 seconds , c ) 52 seconds , d ) 19 seconds , e ) 45 seconds
Rationale: "speed = 45 km / hr = 45 * ( 5 / 18 ) m / sec = 25 / 2 m / sec total distance = 510 + 140 = 650 meter time = distance / speed = 650 * ( 2 / 25 ) = 52 seconds answer : c"
Answer: c
Python program:
a = 510 + 140 
b = 45 * 1000
c = b / 3600
d = a / c
Problem: how many ounces of a 60 % salt solution must be added to 50 ounces of a 20 percent salt solution so that the resulting mixture is 40 % salt ?
Options: a ) 16.67 , b ) 30 , c ) 50 , d ) 60.33 , e ) 70
Rationale: "for 60 % salt solution ( x ) and 20 % salt solution ( y ) to give 40 % = ( 60 + 20 ) / 2 salt solution , we should mix equal amounts of x and y . answer : c ."
Answer: c
Python program:
a = 40 / 100
b = a * 50
c = 20 / 100
d = c * 50
e = b - d
f = 40 / 100
g = 20 / 100
h = f - g
i = e / h
Problem: a certain taxi company charges $ 3.50 for the first 1 / 5 of a mile plus $ 0.40 for each additional 1 / 5 of a mile . what would this company charge for a taxi ride that was 8 miles long ?
Options: a ) 15.6 , b ) 16.0 , c ) 17.5 , d ) 18.7 , e ) 19.1
Rationale: "a certain taxi company charges $ 3.50 for the first 1 / 5 of a mile plus $ 0.40 for each additional 1 / 5 of a mile . what would this company charge for a taxi ride that was 8 miles long ? a . 15.60 b . 16.00 c . 17.50 d . 18.70 e . 19.10 1 / 5 miles = 0.2 miles . the cost of 8 miles long ride would be $ 3.50 for the first 0.2 miles plus ( 8 - 0.2 ) / 0.2 * 0.4 = $ 3.5 + $ 15.6 = $ 18.7 . answer : e ."
Answer: e
Python program:
a = 1 / 5
b = 8 / a
c = b - 1
d = c * 0
e = 3 + 50
Problem: the ratio of red balls to blue balls is 3 : 7 . 70 % of the red balls and 30 % of the blue balls are tennis balls . how many of the balls are tennis balls ?
Options: a ) 44 % , b ) 40 % , c ) 45 % , d ) 42 % , e ) 48 %
Rationale: let total no of balls 100 , red ball 30 and blue ball 70 , so tennis ball for red and blue ball respectively 30 * 70 / 100 = 21 and 70 * 30 / 100 = 21 so total 42 tennis balls out of 100 balls . . so required % is 42 % answer : d
Answer: d
Python program:
a = 3 * 70
b = 7 * 30
c = a + b 
d = 3 + 7 
e = c / d
Problem: if ( c - a ) / ( c - b ) = 1 , then ( 5 b - 3 a ) / ( c - a ) =
Options: a ) 0.5 , b ) 1 , c ) 1.5 , d ) 2 , e ) 2.5
Rationale: "let ' s say c = 2 , b = 1 , a = 1 so that our 1 st expression holds true . now , ibsert those numbers in the second expression and we ' ll get 2 answer d ( hopefully ) ) )"
Answer: d
Python program:
a = 5 - 3
b = a * 3
Problem: xy = 1 then what is ( 3 ^ ( x + y ) ^ 2 ) / ( 3 ^ ( x - y ) ^ 2 )
Options: a ) 81 , b ) 4 , c ) 8 , d ) 16 , e ) 32
Rationale: "( x + y ) ^ 2 - ( x - y ) ^ 2 ( x + y + x - y ) ( x + y - x + y ) ( 2 x ) ( 2 y ) 4 xy 4 3 ^ 4 = 81 answer a"
Answer: a
Python program:
a = 4 * 1
b = 1 ** a
Problem: how much time does a train 125 metres long running at 60 km / hr take to pass a pole ?
Options: a ) 7.9 s , b ) 2.5 s , c ) 7.5 s , d ) 7.6 s , e ) 7.4 s
Rationale: "explanation : 60 km / hr = 60 * 5 / 18 = 16.67 m / s speed = distance / time ; v = d / t 16.67 = 125 / t t = 7.5 s answer : c"
Answer: c
Python program:
a = 125 / 1000
b = a / 60
c = b * 3600
Problem: what is the least number which when divided by 5 , 6 , 9 and 12 leaves remainder 4 in each care ?
Options: a ) 130 , b ) 140 , c ) 156 , d ) 184 , e ) 196
Rationale: explanation : lcm of 5 , 6 , 9 and 12 is 180 required number = 180 + 4 = 184 answer : option d
Answer: d
Python program:
a = math.lcm(5, 6)
b = math.lcm(9, 12)
c = math.lcm(a, b)
d = c + 4
Problem: sakshi can do a piece of work in 25 days . tanya is 25 % more efficient than sakshi . the number of days taken by tanya to do the same piece of work :
Options: a ) 15 , b ) 20 , c ) 18 , d ) 25 , e ) 10
Rationale: "solution ratio of times taken by sakshi and tanya = 125 : 100 = 5 : 4 . suppose tanya taken x days to do the work . 5 : 4 : : 25 : x ⇒ x = ( 25 x 4 / 5 ) ⇒ x = 20 days . hence , tanya takes 16 days is complete the work . answer b"
Answer: b
Python program:
a = 25 / 100
b = 1 + a 
c = 25 / b
Problem: at what price must an article costing rs . 47.50 be marked in order that after deducting 8 % from the list price . it may be sold at a profit of 25 % on the cost price ?
Options: a ) 64.54 , b ) 62.6 , c ) 62.1 , d ) 62.7 , e ) 62.2
Rationale: "cp = 47.50 sp = 47.50 * ( 125 / 100 ) = 59.375 mp * ( 92 / 100 ) = 59.375 mp = 64.54 answer : a"
Answer: a
Python program:
a = 47 * 50
b = a / 100
c = 47 + 50 
d = c * 100
e = 100 - 8
f = d / e
Problem: in a bag , there are two 6 - sided dice ( numbered 1 to 6 ) , 3 12 - sided dice ( numbered 1 to 12 ) , and two 20 - sided dice ( numbered 1 to 20 ) . if 4 of these dice are selected at random from the bag , and then the 4 are rolled and we find the sum of numbers showing on the 4 dice , how many different possible totals are there for this sum ?
Options: a ) 60 , b ) 50 , c ) 42 , d ) 84 , e ) 61
Rationale: as ' complex - looking ' as this question might appear , it ' s actually rather simple . pay careful attention to what the specific questions asks for - the number of different possible sums from 4 dice . since we ' re dealing with some ' special ' dice ( some 12 - sided and 20 - sided dice ) , we have to adjust out math accordingly , but the possibilities are rather limited : 1 ) the minimum number on any given die is 1 2 ) the maximum possible sum would only occur if we took the 4 biggest possible dice and rolled the highest possible number on each . with 4 dice , we could end up with any sum between : 4 ( if we rolled 1 s on all 4 dice ) to 64 ( if we rolled two 20 s on the 20 - sided dice and two 12 s on the 12 - sided dice ) . thus , there are only 61 possible sums . e
Answer: e
Python program:
a = 20 + 20 
b = 12 + 12 
c = a + b
Problem: convert 50 miles into yards ?
Options: a ) 25630 yards , b ) 35200 yards , c ) 88000 yards , d ) 42560 yards , e ) 41520 yards
Rationale: "1 mile = 1760 yards 50 miles = 50 * 1760 = 88000 yards answer is c"
Answer: c
Python program:
a = 3 + 2 
b = a * 2
c = 3 + 2 
d = c * 2
e = b * d
f = e * 50
g = 3 + 2 
h = g * 2
i = 3 + 2 
j = i * 2
k = h * j
l = f / k
Problem: a bus covers a distance of 12 km in 5 min . if it takes 5 sec to pass a telegraph post , then the length of the bus is ?
Options: a ) 120 m , b ) 180 m , c ) 240 m , d ) 200 m , e ) 280 m
Rationale: speed = ( 12 / 5 * 60 ) km / hr = ( 144 * 5 / 18 ) m / sec = 40 m / sec . length of the bus = 40 * 5 = 200 m . answer : d
Answer: d
Python program:
a = 1000 * 12
b = const_60 * 5
c = a / b
d = c * 5
Problem: a number is doubled and 9 is added . if the resultant is trebled , it becomes 69 . what is that number ?
Options: a ) 3.5 , b ) 6 , c ) 8 , d ) 7 , e ) 4
Rationale: "let the number be x . then , 3 ( 2 x + 9 ) = 69 2 x = 14 = > x = 7 answer : d"
Answer: d
Python program:
a = 3 * 9
b = 69 - a
c = 3 * 2
d = b / c
Problem: x can finish a work in 18 days . y can finish the same work in 15 days . yworked for 10 days and left the job . how many days does x alone need to finish the remaining work ?
Options: a ) 5 , b ) 4 , c ) 6 , d ) 7 , e ) 8
Rationale: "work done by x in 1 day = 1 / 18 work done by y in 1 day = 1 / 15 work done by y in 10 days = 10 / 15 = 2 / 3 remaining work = 1 – 2 / 3 = 1 / 3 number of days in which x can finish the remaining work = ( 1 / 3 ) / ( 1 / 18 ) = 6 c"
Answer: c
Python program:
a = 1 / 15
b = 10 * a
c = 1 - b
d = 1 / 18
e = c / d
Problem: n ^ ( n / 2 ) = 8 is true when n = 8 in the same way what is the value of n if n ^ ( n / 2 ) = 20 ?
Options: a ) 8 , b ) 14 , c ) 10 , d ) 20 , e ) 40
Rationale: n ^ ( n / 2 ) = 20 apply log n / 2 logn = log 20 nlogn = 2 log 20 = log 20 ^ 2 = log 400 logn = log 400 now apply antilog n = 400 / n now n = 20 . answer : d
Answer: d
Python program:
a = 20 ** 2
b = a / 20
Problem: amar takes as much time in running 12 meters as a car takes in covering 48 meters . what will be the distance covered by amar during the time the car covers 1.6 km ?
Options: a ) 600 m , b ) 200 m , c ) 300 m , d ) 400 m , e ) 100 m
Rationale: "d 400 m distance covered by amar = 12 / 4.8 ( 1.6 km ) = 2.5 ( 1600 ) = 400 m answer is d"
Answer: d
Python program:
a = 1 * 6
b = 12 * a
c = b / 48
Problem: find the unit ’ s digit in the product ( 76 ^ 41 ) * ( 41 ^ 14 ) * ( 14 ^ 87 ) * ( 87 ^ 76 )
Options: a ) 1 , b ) 2 , c ) 3 , d ) 4 , e ) 5
Rationale: units digit of 87 ^ 76 = 1 because 87 ^ 3 n + 1 has units place as 1 units digit of 14 ^ 87 = 4 because 14 ^ ( some odd no . ) has units place as 4 units digit of 41 ^ 14 = 1 because 41 ^ ( some even no . ) has units place as 1 units digit of 76 ^ 41 = 6 because 76 ^ ( any positive no . ) has units place as 6 so , units digit of the product is = ` ` 4 ` ` ( units digit of 1 * 4 * 1 * 6 ) answer : d
Answer: d
Python program:
a = 14 / 14
b = a + 3
Problem: a man ate 100 bananas in 5 days , each day eating 6 more than the previous day . how many bananas did he eat on the first day ?
Options: a ) 6 , b ) 7 , c ) 8 , d ) 9 , e ) 10
Rationale: let the number of bannanas in first day be x for consecutive five days it will be like x , x + 6 , x + 12 , x + 18 , x + 24 the sum of those are 100 , 5 x + 60 = 100 so , x = 8 answer : c
Answer: c
Python program:
a = 100 * 2
b = a / 5
c = 6 * 4
d = b - c
e = d / 2
Problem: what is the least value of x . so that 1894 x is divisible by 3 ?
Options: a ) 2 , b ) 5 , c ) 1 , d ) 6 , e ) 7
Rationale: the sum of the digits of the number is divisible by 3 , then the number is divisible by 3 . 1 + 8 + 9 + 4 + x = 22 + x least value of x may be 2 therefore 22 + 2 = 24 is divisible by 3 . a
Answer: a
Python program:
a = 1894 * 10
b = a + 1 
c = b + 1 
d = 1894 * 10
e = c - d
Problem: if takes 25.5 minutes to download a file using modem a . modem b work at 17 % of the speed of modem a . how long does it take to download a file using a modem b ?
Options: a ) 130 minutes , b ) 140 minutes , c ) 150 minutes , d ) 160 minutes , e ) 170 minutes
Rationale: let speed of modem a be k so speed of modem b is 17 / 100 * k time taken by modem a = 25.5 minutes let time taken by modem b = x k * 25.5 = 17 / 100 * k * x 0.17 * x = 25.5 x = 25.5 / 0.17 = 150 minutes answer : c
Answer: c
Python program:
a = 25 * 5
b = a / 17
Problem: the ratio of investments of two partners p and q is 7 : 5 and the ratio of their profits is 7 : 9 . if p invested the money for 5 months , find for how much time did q invest the money ?
Options: a ) 9 , b ) 17 , c ) 13 , d ) 10 , e ) 12
Rationale: "7 * 5 : 5 * x = 7 : 9 x = 9 answer : a"
Answer: a
Python program:
a = 7 / 5
b = 9 / 7
c = a * b
d = c * 5
Problem: on july 1 of last year , total employees at company e was decreased by 10 percent . without any change in the salaries of the remaining employees , the average ( arithmetic mean ) employee salary was 10 percent more after the decrease in the number of employees than before the decrease . the total of the combined salaries of all the employees at company e after july 1 last year was what percent w of thatbeforejuly 1 last year ?
Options: a ) 90 % , b ) 99 % , c ) 100 % , d ) 101 % , e ) 110 %
Rationale: "the total number of employees = n the average salary = x total salary to all emplyoees = xn after the total number of employees = n - 0.1 n = 0.9 n the average salary = x + 10 % of x = 1.1 x total salary to all emplyoees = 0.9 n ( 1.1 x ) total salary after as a % of total salary before w = [ 0.9 n ( 1.1 x ) ] / xn = 0.99 or 99 % = b"
Answer: b
Python program:
a = 10 * 10
Problem: what annual installment will discharge a debt of $ 100 due in 3 years at 10 % simple interest ?
Options: a ) 25.6 , b ) 50.2 , c ) 30.3 , d ) 45 , e ) 56
Rationale: let each installment be x [ x + ( x * 10 * 1 / 100 ) ] + [ x + ( x * 10 * 2 / 100 ) ] + x = 100 11 x / 10 + 12 x / 10 + x = 100 x = 30.3 answer is c
Answer: c
Python program:
a = 10 / 100
b = 100 * a
c = b * 3
Problem: a boat can travel with aspeed of 20 km / hr in still water . if the speed of the stream is 5 km / hr , find the time taken by the boat to go 125 km downstream .
Options: a ) 1 hr , b ) 2 hrs , c ) 3 hrs , d ) 4 hrs , e ) 5 hrs
Rationale: speed downstream = ( 20 + 5 ) km / hr = 25 km / hr . time taken to travel 125 km downstream = 125 / 25 hrs = 5 hrs . answer : e
Answer: e
Python program:
a = 20 + 5 
b = 125 / a
Problem: john bought 9.25 m of cloth for $ 397.75 . find the cost price per metre .
Options: a ) 46 , b ) 47 , c ) 58 , d ) 56 , e ) 43
Rationale: "cloth bought by john = 9.25 m cost of 9.25 m = $ 397.75 cost per metre = 397.75 ÷ 9.25 the cost of the cloth per metre = $ 43 answers : e"
Answer: e
Python program:
a = 397 / 75
Problem: a sum fetched total simple interest of 4016.25 at the rate of 13 p . c . p . a . in 5 years . what is the sum ?
Options: a ) 6178.85 , b ) 8032.5 , c ) 4462.5 , d ) 8900 , e ) none of these
Rationale: "let the sums be p . now , 65 % of p = 4016.25 or , p = 6178.85 answer a"
Answer: a
Python program:
a = 100 * 4016
b = 13 * 5
c = a / b
Problem: what could be the range of a set consisting of odd multiples of 3 ?
Options: a ) 21 , b ) 24 , c ) 35 , d ) 62 , e ) 70
Rationale: "range = the difference between the greatest and the smallest numbers in the sequence . our sequence is odd and is a multiple of 7 . every number in that sequence can be represented like this : 3 * ( 2 n + 1 ) where n is any positive integer . range = 3 * ( 2 m + 1 ) - 3 * ( 2 n + 1 ) = 3 * 2 * ( m - n ) = 6 * ( m - n ) . m , n - any positive integers the answer must be divisible by 6 , which is only 24 . the correct answer is b"
Answer: b
Python program:
a = 3 * 4
Problem: i walk a certain distance and ride back taking a total time of 37 minutes . i could walk both ways in 55 minutes . how long would it take me to ride both ways ?
Options: a ) 12 mins , b ) 10 mins , c ) 19 mins , d ) 15 mins , e ) 20 mins
Rationale: let the distance be x km . then , ( time taken to walk x km ) + ( time taken to ride x km ) = 37 min . ( time taken to walk 2 x km ) + ( time taken to ride 2 x km ) = 74 min . but , the time taken to walk 2 x km = 55 min . time taken to ride 2 x km = ( 74 - 55 ) min = 19 min . ans : c
Answer: c
Python program:
a = 55 - 37
b = 37 / 2
c = a + b 
d = 55 - 37
e = c - d
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 15 % next year . this year , the total amount paid for type a products was $ 4000 and the total price paid for type b products was $ 5300 . 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 ) $ 11,495 , c ) $ 16,000 , d ) $ 16,225 , e ) $ 17,155
Rationale: cost of type a products next year = 1.35 * 4000 = 5400 cost of type b products next year = 1.15 * 5300 = 6095 total 5400 + 6095 = 11495 answer : b
Answer: b
Python program:
a = 3 / 4
b = a * 1000
Problem: the area of a parallelogram is 242 sq m and its altitude is twice the corresponding base . then the length of the base is ?
Options: a ) 8 , b ) 9 , c ) 7 , d ) 11 , e ) 2
Rationale: "2 x * x = 242 = > x = 11 answer : d"
Answer: d
Python program:
a = 242 / 2
b = math.sqrt(a)