euclaise/mathqa_programs huggingface dataset:
Problem: excluding stoppages , the speed of a train is 45 kmph and including stoppages it is 32 kmph . of how many minutes does the train stop per hour ?
Options: a ) 17 , b ) 83 , c ) 12 , d ) 83 , e ) 28
Rationale: "explanation : t = 13 / 45 * 60 = 17 answer : option a"
Answer: a
Python program:
a = 32 / 45
b = const_60 * a
c = const_60 - b
Problem: a and b together can do a piece of work in 8 days . if a alone can do the same work in 12 days , then b alone can do the same work in ?
Options: a ) 49 , b ) 99 , c ) 24 , d ) 88 , e ) 21
Rationale: b = 1 / 8 – 1 / 2 = 1 / 24 = > 24 days answer : c
Answer: c
Python program:
a = 1/(8)
b = 1/(12)
c = a - b
d = 1/(c)
Problem: company z has 48 employees . if the number of employees having birthdays on wednesday is more than the number of employees having birthdays on any other day of the week , each of which have same number of birth - days , what is the minimum number of employees having birthdays on wednesday .
Options: a ) 6 , b ) 7 , c ) 8 , d ) 9 , e ) 12
Rationale: "say the number of people having birthdays on wednesday is x and the number of people having birthdays on each of the other 6 days is y . then x + 6 y = 48 . now , plug options for x . only a and e give an integer value for y . but only for e x > y as needed . answer : e ."
Answer: e
Python program:
a = 4 + 3 
b = 48 / a
c = math.floor(b)
d = c + 1 
e = 4 + d
Problem: in a fuel station the service costs $ 2.05 per car , every liter of fuel costs 0.6 $ . assuming that you fill up 3 mini - vans and 2 trucks , how much money will the fuel cost to all the cars owners total , if a mini - van ' s tank is 65 liters and a truck ' s tank is 120 % bigger and they are all empty - ?
Options: a ) 122.6 $ , b ) 128.9 $ , c ) 243.7 $ , d ) 298.85 $ , e ) 312.12 $
Rationale: "mini van cost = 65 * 0.6 + 2.05 truck capacity = 65 ( 1 + 120 / 100 ) = 143 lts . cost of truck = 143 + 0.6 + 2.05 total cost = 3 * 41.05 ( car ) + 2 * 87.85 ( truck ) = 298.85 answer : d"
Answer: d
Python program:
a = 65 * 120
b = a / 100
c = 65 + b 
d = c * 2
e = d * 0
f = 65 * 3
g = f * 0
h = e + g
Problem: a two - digit number is such that the product of the digits is 8 . when 18 is added to the number , then the digits are reversed . the number is :
Options: a ) 32 , b ) 24 , c ) 12 , d ) 7 , e ) 45
Rationale: "answer : option b let the ten ' s and unit ' s digit be x and 8 / x respectively . then , ( 10 x + 8 / x ) + 18 = 10 * 8 / x + x 9 x 2 + 18 x - 72 = 0 x 2 + 2 x - 8 = 0 ( x + 4 ) ( x - 2 ) = 0 x = 2 so , ten ' s digit = 2 and unit ' s digit = 4 . hence , required number = 24 ."
Answer: b
Python program:
a = 10 - 1
b = 18 / a
Problem: by selling 95 pens , a trader gains the cost of 19 pens . find his gain percentage ?
Options: a ) 20 % , b ) 21 % , c ) 22 % , d ) 23 % , e ) 24 %
Rationale: "let the cp of each pen be rs . 1 . cp of 95 pens = rs . 95 profit = cost of 19 pens = rs . 19 profit % = 19 / 95 * 100 = 20 % answer : a"
Answer: a
Python program:
a = 19 / 95
b = a * 100
Problem: there are 193 items that are members of set u . of these items , 41 are members of set b , 59 are not members of either of set a or set b , and 23 are members of both sets a and b . how many of the members of set u are members of set a ?
Options: a ) 116 , b ) 85 , c ) 94 , d ) 98 , e ) 108
Rationale: "you had the answer almost right . the x = 93 refers to only set a . however what ' s being asked is how many members are part of set a . this will include : 1 . only set a 2 . set a and set b so the answer is set a = 93 + set ab = 93 + 23 = 116 a"
Answer: a
Python program:
a = 193 - 59
b = a + 23 
c = b - 41
Problem: a machine can filled a tank in 25 minutes and another machine can empty it in 50 minutes . if the tank is already half full and both the taps are opened together , then the tank is filled in how many minutes ?
Options: a ) 25 min , b ) 20 min , c ) 10 min , d ) 15 min , e ) 30 min
Rationale: t = 1 / 2 ( 25 * 50 / 50 - 25 ) = 25 minutes tank is filled in 25 minutes answer is a
Answer: a
Python program:
a = 1 / 25
b = 1 / 50
c = a - b
d = 1 / c
e = d / 2
Problem: a hall 36 m long and 15 m broad is to be paved with stones , each measuring 8 dm by 5 dm . the number of stones required is :
Options: a ) 180 , b ) 1800 , c ) 18 , d ) 18000 , e ) 1350
Rationale: "area of the hall = 3600 * 1500 area of each stone = ( 80 * 50 ) therefore , number of stones = ( 3600 * 1500 / 80 * 50 ) = 1350 answer : e"
Answer: e
Python program:
a = 36 * 15
b = 8 * 5
c = b / 100
d = a / c
Problem: at company x , senior sales representatives visit the home office once every 16 days , and junior sales representatives visit the home office once every 12 days . the number of visits that a junior sales representative makes in a 2 - year period is approximately what percent greater than the number of visits that a senior representative makes in the same period ?
Options: a ) 10 % , b ) 25 % , c ) 33 % , d ) 50 % , e ) 67 %
Rationale: each 48 - day period , senior representatives visit the home office 3 times while junior representatives visit 4 times , thus 33 % more . the answer is c .
Answer: c
Python program:
a = 1 + 10 
b = 16 - 12
c = b - 1
d = a * c
Problem: in n is a positive integer less than 200 , and 14 n / 60 is an integer , then n has how many different positive prime factors q ?
Options: a ) 2 , b ) 3 , c ) 5 , d ) 6 , e ) 8
Rationale: "i like to put the numbers in prime factors so it is easier and faster to visualize . 14 * n / 60 if we write the factors of 14 - - > 2 , 7 , and the factors of 60 - - > 2 , 2 , 3 , 5 , we have ( 2 * 7 * n ) / ( 2 ^ 2 * 3 * 5 ) simplifying 7 * n / ( 2 * 3 * 5 ) the only way the equation above has an integer value is if n has at least the factors 2 , 3 and 5 , so we can simplify again and we have the number 7 . the number could be 2 * 3 * 5 , or 2 * 3 * 5 * 2 , or 2 * 3 * 5 * . . . . . however to be less than 200 we can not add any prime number . 2 * 3 * 5 = 120 if we added the next prime factor 7 , we would have q = 2 * 3 * 5 * 7 = 840 thus , answer b ."
Answer: b
Python program:
a = 1 + 4 
b = 60 / 2
c = b / 2
d = c / 3
e = a / d
f = e + 2
Problem: the two lines y = x and x = - 9 intersect on the coordinate plane . what is the value of the area of the figure formed by the intersecting lines and the x - axis ?
Options: a ) 32.5 , b ) 36.5 , c ) 40.5 , d ) 44.5 , e ) 48.5
Rationale: the point of intersection is ( - 9 , - 9 ) . the triangle has a base of length 9 and a height of 9 . area = ( 1 / 2 ) * base * height = ( 1 / 2 ) * 9 * 9 = 40.5 the answer is c .
Answer: c
Python program:
a = 9 * 9
b = a / 2
Problem: at a certain food stand , the price of each apple is 40 ¢ and the price of each orange is 60 ¢ . mary selects a total of 10 apples and oranges from the food stand , and the average ( arithmetic mean ) price of the 10 pieces of fruit is 54 ¢ . how many oranges must mary put back so that the average price of the pieces of fruit that she keeps is 50 ¢ ?
Options: a ) 1 , b ) 2 , c ) 3 , d ) 4 , e ) 5
Rationale: "if the average price is 54 , then mary has 7 oranges and 3 apples ( a ratio of 7 : 3 ) . for the average price to be 50 , the ratio should be 1 : 1 . mary must put back 4 oranges . the answer is d ."
Answer: d
Python program:
a = 60 * 10
b = 54 * 10
c = a - b
d = 60 - 40
e = c / d
f = e * 40
g = 60 * 10
h = 54 * 10
i = g - h
j = 60 - 40
k = i / j
l = 10 - k
m = l * 60
n = f + m 
o = 50 * 10
p = n - o
q = 60 - 50
r = p / q
Problem: a store has 10 bottles of juice , including 5 bottles of apple juice . in the evening , 6 bottles of juice are sold one by one . what is the probability of selling 4 bottles of apple juice among the 6 bottles ? assume that every bottle has an equal chance of being bought .
Options: a ) 2 / 7 , b ) 3 / 11 , c ) 4 / 15 , d ) 5 / 21 , e ) 6 / 25
Rationale: "the total number of ways to sell 6 bottles from 10 is 10 c 6 = 210 . the number of ways to sell 4 bottles of apple juice is 5 c 4 * 5 c 2 = 5 * 10 = 50 p ( selling 4 bottles of apple juice ) = 50 / 210 = 5 / 21 the answer is d ."
Answer: d
Python program:
a = math.comb(5, 4)
b = math.comb(10, 5)
c = a / b
Problem: a student got 71 % in math and 81 % in history . to get an overall average of 75 % , how much should the student get in the third subject ?
Options: a ) 63 % , b ) 75 % , c ) 77 % , d ) 79 % , e ) 81 %
Rationale: "71 + 81 + x = 3 * 75 x = 73 the answer is a ."
Answer: a
Python program:
a = 3 * 75
b = 71 + 81 
c = a - b
Problem: m and n are the x and y coordinates , respectively , of a point in the coordinate plane . if the points ( m , n ) and ( m + p , n + 9 ) both lie on the line defined by the equation x = ( y / 3 ) - ( 2 / 5 ) , what is the value of p ?
Options: a ) 1 , b ) 2 , c ) 3 , d ) 4 , e ) 5
Rationale: "x = ( y / 3 ) - ( 2 / 5 ) , and so y = 3 x + 6 / 5 . the slope is 3 . ( n + 9 - n ) / ( m + p - m ) = 3 p = 3 the answer is c ."
Answer: c
Python program:
a = 9 / 3
Problem: at an international conference , “ red ” world countries and “ blue ” world countries are the only participants . the ratio of “ red ” world participants to “ blue ” world participants is 5 : 5 . if one - third of “ red ” world participants are left - handed and two - thirds of “ blue ” world participants are left - handed , then what is the fraction of the participants who are left - handed ?
Options: a ) 1 / 4 , b ) 1 / 8 , c ) 1 / 6 , d ) 1 / 2 , e ) 1
Rationale: "red : blue = 5 : 5 let red = 5 x and blue = 5 x 1 / 3 of red are left handed = > 1 / 3 * 5 x = 5 x / 3 red left handed 2 / 3 of blue are left handed = > 2 / 3 * 5 x = 10 x / 3 blue left handed fraction of participants who are left handed = total left handed / total participants = ( red left handed + blue left handed ) / total participants = ( 5 x / 3 + 10 x / 3 ) / ( 5 x + 5 x ) = ( 15 x / 30 x ) = 1 / 2 answer : d"
Answer: d
Python program:
a = 5 * const_0_33
b = 2 / 3
c = 5 * b
d = a + c 
e = 5 + 5 
f = d / e
Problem: what is the remainder when 42 * 49 is divided by 8 ?
Options: a ) 1 , b ) 2 , c ) 4 , d ) 5 , e ) 7
Rationale: "we can make use of the rule : remainder of { ( a * b ) / n } } = remainder of ( a / n ) * remainder of ( b / n ) here remainder of { 42 * 49 ) / 8 } } = remainder of ( 42 / 8 ) * remainder of ( 49 / 8 ) = 2 * 1 = 2 answer : b"
Answer: b
Python program:
a = 8 / 2
b = 42 * 42
c = a - b
Problem: 1 + 2 + 3 + . . . + 12 = ?
Options: a ) 76 , b ) 68 , c ) 78 , d ) 66 , e ) 67
Rationale: 1 + 2 + 3 + ⋯ + n = ∑ n = n ( n + 1 ) / 2 1 + 2 + 3 + ⋯ + 12 = n ( n + 1 ) / 2 = ( 12 ( 12 + 1 ) ) / 2 = ( 12 × 13 ) / 2 = 6 × 13 = 78 answer is c
Answer: c
Python program:
a = 12 + 1 
b = 12 * a
c = b / 2
Problem: a room of 6 m 44 cm long and 3 m 00 cm broad is to be paved with square tiles . find the least number of square tiles required to cover the floor .
Options: a ) 12076 , b ) 12070 , c ) 12077 , d ) 12075 , e ) 12074
Rationale: "explanation : area of the room = 644 * 300 sq cm size of largest square tile = h . c . f of 644 cm and 300 cm = 4 cm area of 1 tile = 4 * 4 sq cm no . of tiles required = ( 644 * 300 ) / ( 4 * 4 ) = 12075 answer : d ) 12075"
Answer: d
Python program:
a = 6 * 100
b = a + 44 
c = 3 * 100
d = c + 0 
e = b * d
f = 6 * 100
g = f + 44 
h = 2 ** 4
i = g / h
j = i ** 2
k = e / j
Problem: 7 people average age is 30 . youngest person age is 6 . find average of the people when youngest was born .
Options: a ) 23 , b ) 24 , c ) 25 , d ) 26 , e ) 27
Rationale: "average age of people = 30 so have total age = 210 before 7 years we have to deduct each person age by seven years 210 - 42 = 161 so average age would be 161 / 7 = 24 answer : b"
Answer: b
Python program:
a = 30 * 7
b = 6 * 7
c = a - b
d = c / 7
Problem: if 4 men can reap 40 acres of land in 15 days , how many acres of land can 16 men reap in 30 days ?
Options: a ) 320 , b ) 240 , c ) 369 , d ) 489 , e ) 125
Rationale: "4 men 40 acres 15 days 16 men ? 30 days 40 * 16 / 4 * 30 / 15 40 * 4 * 2 40 * 8 = 320 answer : a"
Answer: a
Python program:
a = 16 / 4
b = 30 / 15
c = a * b
d = 40 * c
Problem: in the excel manufacturing company , 46 percent of the employees are men . if 60 percent of the employees are unionized and 70 percent of these are men , what percent of the non - union employees are women ?
Options: a ) 90 % , b ) 87.5 % , c ) 66.7 % , d ) 50 % , e ) 36 %
Rationale: lets say there are total 100 employees then men = 46 & women = 54 unionized emp = 60 & non unionized emp = 40 men unionized = . 7 * 60 = 42 women unionized = 18 women non - unionized = 54 - 18 = 36 percentage of women non unionized = 36 / 40 * 100 = 90 % the answer is option a
Answer: a
Python program:
a = 100 - 46
b = 70 / 100
c = b * 60
d = 60 - c
e = a - d
f = 100 - 60
g = e / f
h = g * 100
Problem: a library branch originally contained 18360 volumes , 30 % of which were fiction novels . 1 / 3 of the volumes were transferred to another location and 1 / 4 of the volumes transferred were fiction novels . what percent of the remaining collection was fiction novels ?
Options: a ) 2.5 % , b ) 17.67 % , c ) 28.3 % , d ) 45.2 % , e ) 32.5 %
Rationale: "fiction novels = 5,508 transferred to another location = 6,120 transferred fiction novels = 1,530 non transferred fiction novels = 3,978 percent of the remaining collection was fiction novels = 3978 / ( 18360 - 6120 ) * 100 = > 32.5 % hence answer will be ( e )"
Answer: e
Python program:
a = 30 / 100
b = 1 / 4
c = 1 - b
d = a * c
e = 1 / 3
f = 1 - e
g = d / f
h = g * 100
Problem: a man was asked to state his age in years . his reply was , ` ` take my age 6 years hence , multiply it by 6 and subtract 6 times my age 6 years ago and you will know how old i am . ' ' what was the age of the person ?
Options: a ) 18 , b ) 92 , c ) 72 , d ) 26 , e ) 19
Rationale: explanation : let the present age of person be x years . then , 6 ( x + 6 ) - 6 ( x - 6 ) = x < = > ( 6 x + 36 ) - ( 6 x - 36 ) = x < = > x = 72 . . answer : c
Answer: c
Python program:
a = 6 + 6 
b = a * 6
Problem: if the average ( arithmetic mean ) of x and y is 40 , and z – x = 60 , what is the average of y and z ?
Options: a ) 20 , b ) 50 , c ) 65 , d ) 70 , e ) 140
Rationale: "x + y / 2 = 40 = > x + y = 80 x = z - 60 . . . sub this value z - 60 + y = 80 = > z + y = 140 = > z + y / 2 = 70 . answer : d"
Answer: d
Python program:
a = 60 * 2
b = 40 * 2
c = a - b
Problem: find the simple interest on rs . 235 for 3 months at 8 paisa per month ?
Options: a ) s . 57.8 , b ) s . 56.4 , c ) s . 29.3 , d ) s . 33 , e ) s . 74
Rationale: "explanation : i = ( 235 * 3 * 8 ) / 100 = 56.4 answer : option b"
Answer: b
Python program:
a = 3 / 100
b = 235 * a
Problem: a , b and c started a business with capitals of rs . 8000 , rs . 10000 and rs . 12000 respectively . at the end of the year , the profit share of b is rs . 1800 . the difference between the profit shares of a and c is ?
Options: a ) 720 , b ) 266 , c ) 155 , d ) 600 , e ) 441
Rationale: "ratio of investments of a , b and c is 8000 : 10000 : 12000 = 4 : 5 : 6 and also given that , profit share of b is rs . 1800 = > 5 parts out of 15 parts is rs . 1800 now , required difference is 6 - 4 = 2 parts required difference = 2 / 5 ( 1800 ) = rs . 720 answer : a"
Answer: a
Python program:
a = 12000 / 10000
b = 8000 / 10000
c = a - b
d = c * 1800
Problem: the length of a bridge in meters , which a train 120 - meters long and traveling at 45 km / hr can cross in 30 seconds is ?
Options: a ) 255 , b ) 285 , c ) 315 , d ) 345 , e ) 375
Rationale: "45 km / h = 45000 m / 3600 s = 12.5 m / s in 30 seconds , the train can go 30 ( 12.5 ) = 375 meters let x be the length of the bridge . x + 120 = 375 meters x = 255 meters the answer is a ."
Answer: a
Python program:
a = 45 * 1000
b = a / 3600
c = b * 30
d = c - 120
Problem: of 70 players on a football team , 49 are throwers . the rest of the team is divided so one third are left - handed and the rest are right handed . assuming that all throwers are right handed , how many right - handed players are there total ?
Options: a ) 54 , b ) 59 , c ) 63 , d ) 71 , e ) 92
Rationale: total = 70 thrower = 49 rest = 70 - 49 = 21 left handed = 21 / 3 = 7 right handed = 14 if all thrower are right handed then total right handed is 49 + 14 = 63 so c . 63 is the right answer
Answer: c
Python program:
a = 1 / 3
b = 1 - a
c = 70 - 49
d = b * c
e = d + 49
Problem: jack has two dice , one has 6 equally probable sides , labeled 1 , 2 , 3 , 4 , 5 , 6 , and the other has 7 equally probable sides , labeled 1 , 2 , 3 , 4 , 5 , 6 , 7 . if jack rolls both dice what is the probability that both of the numbers will be 3 ?
Options: a ) 3 / 14 , b ) 2 / 7 , c ) 1 / 3 , d ) 1 / 42 , e ) 12 / 21
Rationale: method - 1 probability that the number on first die is 3 = 1 / 6 probability that the number on second die is 3 = 1 / 7 probability that both dice result in odd numbers = ( 1 / 6 ) * ( 1 / 7 ) = 1 / 42 answer : option d
Answer: d
Python program:
a = 1 / 6
b = 1 / 7
c = a * b
Problem: a number divided by 44 leaves remainder 12 what is the remainder when same number divided by 12
Options: a ) 7 , b ) 8 , c ) 9 , d ) 10 , e ) 11
Rationale: "add 44 + 12 = 56 now 56 divided by 12 so we get 8 as reaminder answer : b"
Answer: b
Python program:
a = 12 - 12
b = 12 - 12
c = a / b
Problem: a person walks at a speed of 4 km / hr and runs at a speed of 8 km / hr . how many hours will the person require to cover a distance of 16 km , if the person completes half of the distance by walking and the other half by running ?
Options: a ) 2 , b ) 2.5 , c ) 3 , d ) 3.5 , e ) 4
Rationale: time = 8 / 4 + 8 / 8 = 3 hours the answer is c .
Answer: c
Python program:
a = 16 / 2
b = a / 4
c = 16 / 2
d = c / 8
e = b + d
Problem: change the below lagarithm log 255 = 1 / 2 to exponential form
Options: a ) 5 , b ) 8 , c ) 7 , d ) 10 , e ) 11
Rationale: solution : log 255 = 251 / 2 = 5 answer is a
Answer: a
Python program:
a = 255 - 100
b = a - 100
c = 10 * 4
d = b - c
e = d - 10
Problem: the length of a rectangle is twice its breadth . if its length is decreased by 5 cm and breadth is increased by 5 cm , the area of the rectangle is increased by 75 sq . cm . find the length of the rectangle ?
Options: a ) 10 cm , b ) 40 cm , c ) 20 cm , d ) 30 cm , e ) 50 cm
Rationale: "let the breadth of the given rectangle be x then length is 2 x . thus area of the given rect is \ fn _ jvn { \ color { black } 2 x ^ { 2 } } after dec 5 cm from length and inc 5 cm breadth , new lenght becomes 2 x - 5 and breadth is x + 5 . thus new area = ( 2 x - 5 ) ( x + 5 ) = \ fn _ jvn { \ color { black } 2 x ^ { 2 } + 5 x - 25 } since new area is 75 units greater than original area thus \ fn _ jvn { \ color { black } 2 x ^ { 2 } + 75 = 2 x ^ { 2 } + 5 x - 25 } 5 x = 75 + 25 5 x = 100 therefore x = 20 hence length of the rectangle is 40 cm . answer : b"
Answer: b
Python program:
a = 100 / 3
Problem: by selling 16 pencils for a rupee a man loses 10 % . how many for a rupee should he sell in order to gain 20 % ?
Options: a ) 8 , b ) 9 , c ) 12 , d ) 89 , e ) 81
Rationale: "90 % - - - 16 120 % - - - ? 90 / 120 * 16 = 12 answer : c"
Answer: c
Python program:
a = 100 + 20 
b = 100 - 10
c = 1 / b
d = a * c
e = 1 / d
f = e * 16
Problem: if it takes a machine 2 ⁄ 3 minute to produce one item , how many items will it produce in 1 hours ?
Options: a ) 1 ⁄ 3 , b ) 4 ⁄ 3 , c ) 90 , d ) 120 , e ) 180
Rationale: "1 item takes 2 / 3 min so it takes 60 min to produce x 2 x / 3 = 60 the x = 90 answer : c"
Answer: c
Python program:
a = 1 * const_60
b = 2 / 3
c = a / b
Problem: a batsman makes a score of 65 runs in the 17 th inning and thus increases his average by 3 . find his average after 17 th inning .
Options: a ) 17 , b ) 39 , c ) 42 , d ) 45 , e ) none of the above
Rationale: let the average after 17 th inning = x . then , average after 16 th inning = ( x – 3 ) . ∴ 16 ( x – 3 ) + 65 = 17 x or x = ( 65 – 48 ) = 17 . answer a
Answer: a
Python program:
a = 17 * 3
b = 65 - a
c = b + 3
Problem: an article is bought for rs . 675 and sold for rs . 1200 , find the gain percent ?
Options: a ) 87 % , b ) 88 % , c ) 78 % , d ) 75 % , e ) 73 %
Rationale: "675 - - - - 525 100 - - - - ? = > = 78 % answer : c"
Answer: c
Python program:
a = 1200 * 100
b = a / 675
c = 100 - b
Problem: the distance between two cities a and b is 1410 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 pm , b ) 07 pm , c ) 11 pm , d ) 05 am , e ) 03 am
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 ] = 1410 . therefore , 60 x + 75 ( x - 1 ) = 1410 . = > x = 3 . so , they meet at ( 8 + 11 ) i . e , 7 pm . answer : b"
Answer: b
Python program:
a = 1410 + 75 
b = 60 + 75 
c = a / b
d = c + 8
Problem: tom opened a shop investing rs . 3000 . jose joined him 2 months later , investing rs . 4000 . they earned a profit of rs . 4230 after completion of one year . what will be jose ' s share of profit ?
Options: a ) 2000 , b ) 2200 , c ) 2309 , d ) 2350 , e ) 3250
Rationale: "sol = ~ s - so anju ’ s share = [ 5 / 9 ] x 4230 = 2350 d"
Answer: d
Python program:
a = 2 * 3
b = 2 * a
c = 3000 * b
d = 2 * 3
e = 2 * d
f = e - 2
g = 4000 * f
h = 2 * 3
i = 2 * h
j = 3000 * i
k = g + j 
l = c / k
m = 1 - l
n = 4230 * m
Problem: a student got twice as many sums wrong as he got right . if he attempted 54 sums in all , how many did he solve correctly ?
Options: a ) 12 , b ) 16 , c ) 18 , d ) 24 , e ) 26
Rationale: "explanation : suppose the boy got x sums right and 2 x sums wrong . then , x + 2 x = 54 3 x = 54 x = 18 . answer : c"
Answer: c
Python program:
a = 1 + 2 
b = 54 / a
Problem: the instructions state that deepthi needs 4 / 17 square yards of one type of material and 3 / 10 square yards of another type of material for a project . she buys exactly that amount . after finishing the project , however , she has 9 / 30 square yards left that she did not use . what is the total amount of square yards of material deepthi used ?
Options: a ) 1 / 12 , b ) 4 / 17 , c ) 2 / 3 , d ) 1 1 / 9 , e ) 2 1 / 9
Rationale: total bought = 4 / 17 + 3 / 10 left part 9 / 30 - - - > 3 / 10 so used part 4 / 17 + 3 / 10 - 3 / 10 = 4 / 17 answer : b
Answer: b
Python program:
a = 4 / 17
b = 3 / 10
c = a + b 
d = 9 / 30
e = c - d
Problem: a certain city with a population of 108,000 is to be divided into 11 voting districts , and no district is to have a population that is more than 10 percent greater than the population of any other district what is the minimum possible population that the least populated district could have ?
Options: a ) a ) 10,700 , b ) b ) 10,800 , c ) c ) 9,000 , d ) d ) 11,000 , e ) e ) 11,100
Rationale: "let x = number of people in smallest district x * 1.1 = number of people in largest district x will be minimised when the number of people in largest district is maximised 10 * x * 1.1 = 11 x = total number of people in other districts so we have 11 x + x = 108 k x = 9,000 answer : c"
Answer: c
Python program:
a = 4 * 2
b = a * 100
Problem: company p had 15 percent more employees in december than it had in january . if company p had 470 employees in december , how many employees did it have in january ?
Options: a ) 391 , b ) 408 , c ) 410 , d ) 423 , e ) 445
Rationale: "d = number of employees in december j = number of employees in january j x 1.15 = d j x 1.15 = 470 j = 470 / 1.15 j = 47,000 / 115 = 408 thus b is the correct answer ."
Answer: b
Python program:
a = 15 / 100
b = 1 + a 
c = 470 / b
Problem: a , b and c can do a piece of work in 5 days , 10 days and 15 days respectively . how long will they taken , if all the three work together ?
Options: a ) 2 , b ) 4 , c ) 2 8 / 11 , d ) 67 , e ) 9
Rationale: "1 / 5 + 1 / 10 + 1 / 15 = 11 / 30 = > 30 / 11 = > 2 8 / 11 days answer : c"
Answer: c
Python program:
a = 1/(15)
b = 1/(5)
c = 1/(10)
d = b + c 
e = a + d 
f = 1/(e)
Problem: find the annual income derived by investing $ 6800 in 60 % stock at 136 .
Options: a ) 550 , b ) 3000 , c ) 250 , d ) 300 , e ) 400
Rationale: "by investing $ 136 , income obtained = $ 60 . by investing $ 6800 , income obtained = $ [ ( 60 / 136 ) * 6800 ] = $ 3000 . answer b ."
Answer: b
Python program:
a = 6800 * 60
b = a / 136