euclaise/mathqa_programs huggingface dataset:
Problem: a 230 m long train running at the speed of 120 km / hr crosses another train running in opposite direction at the speed of 80 km / hr in 9 sec . what is the length of the other train ?
Options: a ) 230 , b ) 270 , c ) 260 , d ) 256 , e ) 298
Rationale: "relative speed = 120 + 80 = 200 km / hr . = 200 * 5 / 18 = 500 / 9 m / sec . let the length of the other train be x m . then , ( x + 2340 ) / 9 = 500 / 9 = > x = 270 . answer : b"
Answer: b
Python program:
a = 120 + 80 
b = a * const_0_2778
c = b * 9
d = c - 230
Problem: a candidate who gets 40 % of the marks fails by 40 marks . but another candidate who gets 60 % marks gets 20 marks more than necessary for passing . find the number of marks for passing ?
Options: a ) 100 marks , b ) 200 marks , c ) 160 marks , d ) 371 marks , e ) 827 marks
Rationale: "40 % - - - - - - - - - - - - 40 60 % - - - - - - - - - - - - 20 - - - - - - - - - - - - - - - - - - - - - - 20 % - - - - - - - - - - - - - 60 40 % - - - - - - - - - - - - - - ? 120 + 40 = 160 marks answer : c"
Answer: c
Python program:
a = 40 + 20 
b = 60 / 100
c = 40 / 100
d = b - c
e = a / d
f = 40 / 100
g = e * f
h = g + 40
Problem: two numbers are in the ratio of 1 : 2 . if 10 be added to both , their ratio changes to 3 : 5 . the greater number is
Options: a ) 20 , b ) 24 , c ) 28 , d ) 32 , e ) 40
Rationale: "let the ratio be x : y , given x / y = 1 / 2 , ( x + 10 ) / ( y + 10 ) = 3 / 5 = > x = 20 and y = 40 answer : e"
Answer: e
Python program:
a = 1 * 10
Problem: a train running at the speed of 90 km / hr crosses a pole in 9 sec . what is the length of the train ?
Options: a ) 288 , b ) 225 , c ) 277 , d ) 272 , e ) 150
Rationale: "speed = 90 * 5 / 18 = 25 m / sec length of the train = speed * time = 25 * 9 = 225 m answer : b"
Answer: b
Python program:
a = 90 * 1000
b = a / 3600
c = b * 9
Problem: rs . 850 is divided so that 4 times the first share , twice the 2 nd share and twice the third share amount to the same . what is the value of the first share ?
Options: a ) s 400 , b ) s 500 , c ) s 850 , d ) s 540 , e ) s 170
Rationale: "a + b + c = 850 4 a = 2 b = 2 c = x a : b : c = 1 / 4 : 1 / 2 : 1 / 2 = 1 : 2 : 2 1 / 5 * 850 = rs 170 answer : e"
Answer: e
Python program:
a = 4 + 2 
b = a + 3 
c = 850 / b
d = 4 * c
Problem: we bought 85 hats at the store . blue hats cost $ 6 and green hats cost $ 7 . the total price was $ 550 . how many green hats did we buy ?
Options: a ) a ) 36 , b ) b ) 40 , c ) c ) 41 , d ) d ) 42 , e ) e ) 44
Rationale: "let b be the number of blue hats and let g be the number of green hats . b + g = 85 . b = 85 - g . 6 b + 7 g = 550 . 6 ( 85 - g ) + 7 g = 550 . 510 - 6 g + 7 g = 550 . g = 550 - 510 = 40 . the answer is b ."
Answer: b
Python program:
a = 85 * 6
b = 550 - a
Problem: solve for x and check : 6 x = 54
Options: a ) 12 , b ) 15 , c ) 5 , d ) 9 , e ) none of these
Rationale: "solution : dividing each side by 6 , we obtain ( 6 x / 6 ) = ( 54 / 6 ) therefore : x = 9 check : 6 x = 54 ( 6 * 9 ) = 54 54 = 54 answer : d"
Answer: d
Python program:
a = 54 / 6
b = 6 * a
Problem: jackie has two solutions that are 2 percent sulfuric acid and 12 percent sulfuric acid by volume , respectively . if these solutions are mixed in appropriate quantities to produce 60 liters of a solution that is 5 percent sulfuric acid , approximately how many liters of the 12 percent solution will be required ?
Options: a ) 18 , b ) 20 , c ) 24 , d ) 36 , e ) 42
Rationale: let a = amount of 2 % acid and b = amount of 12 % acid . now , the equation translates to , 0.02 a + . 12 b = . 05 ( a + b ) but a + b = 60 therefore . 02 a + . 12 b = . 05 ( 60 ) = > 2 a + 12 b = 300 but b = 60 - a therefore 2 a + 12 ( 60 - a ) = 300 = > 10 a = 420 hence a = 42 . , b = 60 - 42 = 18 answer : a
Answer: a
Python program:
a = 60 / 10
b = 3 * a
Problem: excluding stoppages , the speed of a train is 45 kmph and including stoppages it is 36 kmph . of how many minutes does the train stop per hour ?
Options: a ) 16 , b ) 17 , c ) 12 , d ) 16 , e ) 16
Rationale: "t = 9 / 45 * 60 12 answer : c"
Answer: c
Python program:
a = 36 / 45
b = const_60 * a
c = const_60 - b
Problem: one - fourth of a number is greater than one - fifth of the number succeeding it by 1 . find the number .
Options: a ) 24 , b ) 42 , c ) 36 , d ) 48 , e ) 50
Rationale: number is 24 as 1 / 4 th of 24 = 6 1 / 5 th of 25 ( 24 + 1 ) = 5 6 = 5 + 1 answer : a
Answer: a
Python program:
a = 2 / 10
b = a + 1 
c = 1 / 4
d = 2 / 10
e = c - d
f = b / e
Problem: working at their respective constant rates , machine a makes 100 copies in 20 minutes and machine b makes 150 copies in 10 minutes . if these machines work simultaneously at their respective rates for 30 minutes , what is the total number of copies that they will produce ?
Options: a ) 250 , b ) 425 , c ) 675 , d ) 700 , e ) 600
Rationale: "machine a can produce 100 * 30 / 20 = 150 copies and , machine b can produce 150 * 30 / 10 = 450 copies total producing 600 copies . e is the answer"
Answer: e
Python program:
a = 100 / 20
b = 150 / 10
c = a + b 
d = c * 30
Problem: a car gets 40 kilometers per gallon of gasoline . how many gallons of gasoline would the car need to travel 160 kilometers ?
Options: a ) 8 gallons , b ) 4 gallons , c ) 6 gallons , d ) 5.5 gallons , e ) 10 gallons
Rationale: "each 40 kilometers , 1 gallon is needed . we need to know how many 40 kilometers are there in 160 kilometers ? 160 / 40 = 4 * 1 gallon = 4 gallons correct answer b"
Answer: b
Python program:
a = 160 / 40
Problem: a vessel of capacity 2 litre has 25 % of alcohol and another vessel of capacity 6 litre had 40 % alcohol . the total liquid of 8 litre was poured out in a vessel of capacity 10 litre and thus the rest part of the vessel was filled with the water . what is the new concentration of mixture ?
Options: a ) 31 % . , b ) 71 % . , c ) 49 % . , d ) 29 % . , e ) 51 % .
Rationale: 25 % of 2 litres = 0.5 litres 40 % of 6 litres = 2.4 litres therefore , total quantity of alcohol is 2.9 litres . this mixture is in a 10 litre vessel . hence , the concentration of alcohol in this 10 litre vessel is 29 % answer : d
Answer: d
Python program:
a = 25 / 100
b = a * 2
c = 40 / 100
d = c * 6
e = b + d 
f = e / 10
g = f * 100
Problem: cole drove from home to work at an average speed of 75 kmh . he then returned home at an average speed of 105 kmh . if the round trip took a total of 6 hours , how many minutes did it take cole to drive to work ?
Options: a ) 84 , b ) 136 , c ) 172 , d ) 210 , e ) 478
Rationale: "first round distance travelled ( say ) = d speed = 75 k / h time taken , t 2 = d / 75 hr second round distance traveled = d ( same distance ) speed = 105 k / h time taken , t 2 = d / 105 hr total time taken = 6 hrs therefore , 6 = d / 75 + d / 105 lcm of 75 and 105 = 525 6 = d / 75 + d / 105 = > 6 = 7 d / 525 + 5 d / 525 = > d = 525 / 2 km therefore , t 1 = d / 75 = > t 1 = 525 / ( 2 x 75 ) = > t 1 = ( 7 x 60 ) / 2 - - in minutes = > t 1 = 210 minutes . d"
Answer: d
Python program:
a = 105 * 6
b = 75 + 105 
c = a / b
d = c * const_60
Problem: the average of temperatures at noontime from monday to friday is 30 ; the lowest one is 20 , what is the possible maximum range of the temperatures ?
Options: a ) 20 , b ) 25 , c ) 40 , d ) 45 , e ) 10
Rationale: "average = 30 , sum of temperatures = 30 * 5 = 150 as the min temperature is 20 , max would be 150 - 4 * 20 = 30 - - > the range = 30 ( max ) - 20 ( min ) = 10 answer : e"
Answer: e
Python program:
a = 2 + 3 
b = 30 * a
c = 20 * 4
d = b - c
e = d - 20
Problem: find the c . i . on a sum of rs . 10000 for 6 months at 20 % per annum , interest being compounded halfyearly ?
Options: a ) 3010 , b ) 2010 , c ) 1000 , d ) 3100 , e ) 2100
Rationale: "c . i . = 10000 ( 11 / 10 ) ^ 1 - 10000 = 1000 answer : c"
Answer: c
Python program:
a = const_0_25 / 4
b = 1 + a 
c = const_0_25 / 4
d = 1 + c 
e = b * d
f = 10000 * e
g = f - 10000
Problem: if the population of a certain country increases at the rate of one person every 15 seconds , by how many persons does the population increase in 40 minutes ?
Options: a ) 80 , b ) 100 , c ) 160 , d ) 240 , e ) 300
Rationale: "since the population increases at the rate of 1 person every 15 seconds , it increases by 4 people every 60 seconds , that is , by 4 people every minute . thus , in 40 minutes the population increases by 40 x 4 = 160 people . answer . c ."
Answer: c
Python program:
a = const_60 / 15
b = a * 40
Problem: the average of 10 result is 42 . average of the first 7 of them is 30 and that of the last 7 is 80 . find the 8 th result ?
Options: a ) 35 , b ) 37 , c ) 70 , d ) 75 , e ) 50
Rationale: "sum of all the 10 results = 10 * 42 = 420 sum of the first 7 of them = 7 * 30 = 210 sum of the last 7 of them = 7 * 80 = 560 so , the 8 th number = 420 + 210 - 560 = 70 . c"
Answer: c
Python program:
a = 7 * 30
b = 7 * 80
c = a + b 
d = 10 * 42
e = c - d
Problem: a certain boxer has agreed to pay his opponent a fee of 3 % of his total purse for every pound over the specified weight limit he weighs in . if the boxer pays his opponent a fee of $ 26250 after weighing in 7 pounds over the specified limit , what was the boxer ' s purse ?
Options: a ) $ 65,625 , b ) $ 105,000 , c ) $ 125,000 , d ) $ 183,750 , e ) $ 1 , 050,000
Rationale: . 03 * 7 = . 21 26250 / . 21 = $ 125,000 answer : c
Answer: c
Python program:
a = 7 * 3
b = a / 100
c = 26250 / b
d = c / 1000
e = d - 10
f = e - 10
Problem: what is the maximum number q of 27 cubic centimetre cubes that can fit in a rectangular box measuring 8 centimetre x 9 centimetre x 12 centimetre ?
Options: a ) 36
b ) 32
c ) 24
d ) 21
e ) 15
Rationale: 27 cubic centimetre cubes gives side = 3 cm so if : l * w * h is 9 * 12 * 8 , then max . cube we can have are 3 * 4 * 2 = 24 l * w * h is 9 * 8 * 12 , then max . cube we can have are 3 * 2 * 4 = 24 l * w * h is 12 * 8 * 9 , then max . cube we can have are 4 * 2 * 3 = 24 l * w * h is 12 * 9 * 8 , then max . cube we can have are 4 * 3 * 2 = 24 l * w * h is 8 * 12 * 9 , then max . cube we can have are 2 * 4 * 3 = 24 l * w * h is 8 * 9 * 12 , then max . cube we can have are 2 * 3 * 4 = 24 in all cases we get q = 24 cubes . ans . c
Answer: c
Python program:
a = 2 * 3
b = volume_rectangular_prism / (
Problem: - 64 x 29 + 165 = ?
Options: a ) 2436 , b ) 2801 , c ) - 2801 , d ) - 1601 , e ) none of them
Rationale: "given exp . = - 64 x ( 30 - 1 ) + 165 = - ( 64 x 30 ) + 64 + 165 = - 1830 + 229 = - 1601 answer is d"
Answer: d
Python program:
a = 1 - 2
b = 64 * 29
c = b - 165
d = a * c
Problem: if ( c - a ) / ( c - b ) = 1 , then ( 5 b - 4 a ) / ( c - a ) =
Options: a ) 0.5 , b ) 1 , c ) 1.5 , d ) 2 , e ) 2.5
Rationale: "let ' s say c = 3 , b = 1 , a = 1 so that our 1 st expression holds true . now , ibsert those numbers in the second expression and we ' ll get 0.5 answer a ( hopefully ) ) )"
Answer: a
Python program:
a = 5 - 4
b = a * 4
Problem: two trains of length 100 m and 120 m are running towards each other on parallel lines at 42 kmph and 30 kmph respectively . in what time will they be clear of each other from the moment they meet ?
Options: a ) 11 sec , b ) 70 sec , c ) 21 sec , d ) 20 sec , e ) 19 sec
Rationale: "relative speed = ( 42 + 30 ) * 5 / 18 = 4 * 5 = 20 mps . distance covered in passing each other = 100 + 120 = 220 m . the time required = d / s = 220 / 20 = 11 sec . answer : a"
Answer: a
Python program:
a = 100 + 120 
b = 42 + 30 
c = b * const_0_2778
d = a / c
Problem: in an examination , a student scores 3 marks for every correct answer and loses 2 marks for every wrong answer . if he attempts all 100 questions and secures 300 marks , the number of questions he attempts correctly , is :
Options: a ) 150 , b ) 250 , c ) 400 , d ) 300 , e ) 100
Rationale: "let the number of correct answers be x . number of incorrect answers = ( 100 â € “ x ) . 3 x â € “ 2 ( 100 â € “ x ) = 300 or 5 x = 500 or x = 100 . answer : e"
Answer: e
Python program:
a = 300 + 100 
b = 3 + 2 
c = a / b
Problem: what is the % change in the area of a rectangle when its length increases by 30 % and its width decreases by 30 % ?
Options: a ) 0 % , b ) 20 % increase , c ) 20 % decrease , d ) 9 % decrease , e ) insufficient data
Rationale: "( 13 / 10 ) * ( 7 / 10 ) = 91 / 100 of original area 91 / 100 is a 9 % decrease from 100 / 100 - > d"
Answer: d
Python program:
a = 100 + 30 
b = 100 - 30
c = a * b
d = c / 100
e = 100 - d
Problem: what will be the cost of building a fence around a square plot with area equal to 289 sq ft , if the price per foot of building the fence is rs . 58 ?
Options: a ) rs . 3944
b ) rs . 3942
c ) rs . 3987
d ) rs . 3929
e ) rs . 3938
Rationale: let the side of the square plot be a ft . a 2 = 289 = > a = 17 length of the fence = perimeter of the plot = 4 a = 68 ft . cost of building the fence = 68 * 58 = rs . 3944 . answer : a
Answer: a
Python program:
a = math.sqrt(289)
b = square_perimeter * (
Problem: points a , b , c , and d , in that order , lie on a line . if ab = 3 cm , ac = 4 cm , and bd = 9 cm , what is cd , in centimeters ?
Options: a ) 1 , b ) 8 , c ) 3 , d ) 4 , e ) 5
Rationale: "putting a value to each point , lets use the following : a - 0 b - 3 ( ab = 3 ) c - 4 ( ac = 4 ) d - 12 ( bd = 9 ) cd is 12 - 4 = 8 . ans b"
Answer: b
Python program:
a = 4 - 3
Problem: robert is travelling on his cycle andhas calculated to reach point a at 2 pm . if he travels at 10 kmph , he will reach there at 12 pm if he travels at 15 kmph . at what speed musthe travel to reach a at 1 pm ?
Options: a ) 8 kmph , b ) 10 kmph , c ) 12 kmph , d ) 14 kmph , e ) 16 kmph
Rationale: "let the distance travelled by x km . then , x - x = 2 10 15 3 x - 2 x = 60 x = 60 km . time taken to travel 60 km at 10 km / hr = 60 hrs = 6 hrs . 10 so , robert started 6 hours before 2 p . m . i . e . , at 8 a . m . required speed = 60 kmph . = 12 kmph . 5 c"
Answer: c
Python program:
a = 1 / 10
b = 1 / 15
c = a - b
d = 2 / c
e = 1 / 10
f = 1 / 15
g = e - f
h = 2 / g
i = h / 10
j = i - 1
k = d / j
Problem: find the value of m 32519 x 9999 = m ?
Options: a ) 724533811 , b ) 353654655 , c ) 545463251 , d ) 725117481 , e ) 325157481
Rationale: "32519 x 9999 = 32519 x ( 10000 - 1 ) = 32519 x 10000 - 32519 x 1 = 325190000 - 32519 = 325157481 e"
Answer: e
Python program:
a = 9999 - 4
b = a * 32519
Problem: sheila works 8 hours per day on monday , wednesday and friday , and 6 hours per day on tuesday and thursday . she does not work on saturday and sunday . she earns $ 252 per week . how much does she earn in dollars per hour ?
Options: a ) 11 , b ) 10 , c ) 9 , d ) 8 , e ) 7
Rationale: "let sheila earn x dollars per hour so , on monday , wednesday and friday , she earns 8 x each and , on tuesday and thursday , she earns 6 x each in total , over the week she should earn , 3 ( 8 x ) + 2 ( 6 x ) = 36 x she earns $ 252 per week 36 x = 252 x = 7 correct option : e"
Answer: e
Python program:
a = 8 * 3
b = 6 * 2
c = a + b 
d = 252 / c
Problem: a can run 4 times as fast as b and gives b a start of 66 m . how long should the race course be so that a and b might reach in the same time ?
Options: a ) 88 m , b ) 60 m , c ) 80 m , d ) 65 m , e ) 75 m
Rationale: speed of a : speed of b = 4 : 1 means in a race of 4 m a gains 3 m . then in a race of 66 m he gains 66 * ( 4 / 3 ) i . e 88 m answer : a
Answer: a
Python program:
a = 66 / 4
b = 4 - 1
c = a / b
d = 4 * c
e = d + 66
Problem: how many multiples of 5 are there between 5 to 105 ?
Options: a ) 9 , b ) 18 , c ) 17 , d ) none of these , e ) 19
Rationale: "explanation : as you know , multiples of 5 are integers having 0 or 5 in the digit to the extreme right ( i . e . the units place ) . so the numbers are 10 , 15 , 20 , 25 , 30 , 35 , 40 , 45 , 50 , 55 , 60 , 65 , 70 , 75 , 80 , 85 , 90 , 95 , 100 . answer : e"
Answer: e
Python program:
a = 105 - 5
b = a / 5
c = b + 1
Problem: a and b go around a circular track of length 600 m on a cycle at speeds of 30 kmph and 54 kmph . after how much time will they meet for the first time at the starting point ?
Options: a ) 120 sec , b ) 360 sec , c ) 178 sec , d ) 187 sec , e ) 189 sec
Rationale: "time taken to meet for the first time at the starting point = lcm { length of the track / speed of a , length of the track / speed of b } = lcm { 600 / ( 30 * 5 / 18 ) , 600 / ( 54 * 5 / 18 ) } = 360 sec . answer : b"
Answer: b
Python program:
a = 54 * const_0_2778
b = 30 * const_0_2778
c = a - b
d = 600 / c
Problem: the ratio of male to female in a class is 2 : 3 . the career preference of the students in the class are to be represented in a circle graph . if the area of the graph allocated to each career preference is to be proportional to the number of students who have that career preference , how many degrees of the circle should be used to represent a career that is preferred by one of the males and one of the females in the class ?
Options: a ) a ) 160 degree
b ) b ) 168 degree
c ) c ) 191 degree
d ) d ) 72 degree
e ) e ) 204 degree
Rationale: let the common ratio be x . . so m = 2 x and f = 3 x and total = 5 x 1 of m = 2 x and 1 of f = 3 x . . total preferring that carrer = 5 x now 5 x = 360 , so x = 360 / 5 = 72 . . so x * 8 / 3 = 72 * 8 / 3 = 192 d
Answer: d
Python program:
a = 1 / 3
b = 2 + 3 
c = 3 / b
d = c * 360
e = a * d
Problem: by selling an article at rs . 800 , a shopkeeper makes a profit of 25 % . at what price should he sell the article so as to make a loss of 20 % ?
Options: a ) 228 , b ) 480 , c ) 512 , d ) 288 , e ) 276
Rationale: sp = 800 profit = 25 % cp = ( sp ) * [ 100 / ( 100 + p ) ] = 800 * [ 100 / 125 ] = 640 loss = 25 % = 25 % of 640 = rs . 128 sp = cp - loss = 640 - 128 = rs . 512 answer : c
Answer: c
Python program:
a = 800 * 100
b = 25 + 100 
c = a / b
d = 800 * 100
e = 25 + 100 
f = d / e
g = f * 20
h = g / 100
i = c - h
Problem: the length of a rectangular plot is 20 metres more than its breadth . if the cost of fencing the plot @ rs . 26.50 per metre is rs . 9540 , what is the length of the plot in metres ?
Options: a ) 20 , b ) 200 , c ) 300 , d ) 400 , e ) 100
Rationale: "let length of plot = l meters , then breadth = l - 20 meters and perimeter = 2 [ l + l - 20 ] = [ 4 l - 40 ] meters [ 4 l - 40 ] * 26.50 = 9540 [ 4 l - 40 ] = 9540 / 26.50 = 360 4 l = 400 l = 400 / 4 = 100 meters . answer : e"
Answer: e
Python program:
a = 9540 / 26
b = a / 2
c = 2 * 20
d = b - c
Problem: what is the greatest of 3 consecutive integers whose sum is 36 ?
Options: a ) 12 , b ) 13 , c ) 14 , d ) 15 , e ) 16
Rationale: "36 / 3 = 12 the three numbers are 11 , 12 , and 13 . the answer is b ."
Answer: b
Python program:
a = 36 - 3
b = a / 3
c = b + 2
Problem: each of the 43 points is placed either inside or on the surface of a perfect sphere . if 16 % or fewer of the points touch the surface , what is the maximum number of segments which , if connected from those points to form chords , could be the diameter of the sphere ?
Options: a ) 3 , b ) 11 , c ) 13 , d ) 23 , e ) 38
Rationale: "maximum number of points on the surface is 16 % * 43 = 6.88 . . . or 6 since it has to be an integer now note that if two points form a diameter , they can not be part of any other diameter . so in the best case we can pair up the points we have 6 points , so at best we can form 3 pairs ( 6 ) . so , answer is ( a )"
Answer: a
Python program:
a = 16 / 100
b = 43 * a
c = b / 2
Problem: xavier starts from p towards q at a speed of 60 kmph and after every 12 mins increases his speed by 10 kmph . if the distance between p and q is 60 km , then how much time does he take to cover the distance ?
Options: a ) 48 , b ) 59 , c ) 60 , d ) 56 , e ) 50
Rationale: "first 12 min = 60 * 12 / 60 = 12 km 2 nd 12 min = 70 * 12 / 60 = 14 km 3 rd 12 min = 80 * 12 / 60 = 16 km 4 th 12 min = 90 * 12 / 60 = 18 km total time 12.4 = 48 min a"
Answer: a
Python program:
a = 12 + 12 
b = a + 12 
c = b + 12
Problem: a & b started a partnership business . a ' s investment was thrice the investment of b and the period of his investment was two times the period of investments of b . if b received rs 6000 as profit , what is their total profit ?
Options: a ) 28000 , b ) 30000 , c ) 42000 , d ) 34000 , e ) none of these
Rationale: explanation : suppose b ' s investment = x . then a ' s investment = 3 x suppose bs period of investment = y , then a ' s period of investment = 2 y a : b = 3 x * 2 y : xy = 6 : 1 total profit * 1 / 7 = 6000 = > total profit = 6000 * 7 = 42000 . answer : option c
Answer: c
Python program:
a = 1 * 1
b = 3 * 2
c = 1 * 1
d = b + c 
e = a / d
f = 6000 / e
Problem: the average of 5 quantities is 11 . the average of 3 of them is 4 . what is the average of remaining 2 numbers ?
Options: a ) 21.5 , b ) 10.6 , c ) 8 , d ) 9.5 , e ) none of these
Rationale: "answer : a ( 5 x 11 - 3 x 4 ) / 2 = 21.5"
Answer: a
Python program:
a = 5 * 11
b = 3 * 4
c = a - b
d = c / 2
Problem: 10 % of a number is added to 45 , the result is the same number . find the number ?
Options: a ) 50 , b ) 288 , c ) 270 , d ) 129 , e ) 281
Rationale: "( 10 / 100 ) * x + 45 = x 9 x = 450 x = 50 answer : a"
Answer: a
Python program:
a = 45 / 100
b = 45 / a
Problem: if 4 x + y + z = 80 , 2 x - y - z = 4003 x + y - z = 20 for integers of x , y and z , find x = ?
Options: a ) 10 , b ) 20 , c ) 15 , d ) 26 , e ) 18
Rationale: 4 x + y + z = 80 - - - - - - - - - - 1 ) 2 x - y - z = 40 - - - - - - - - - - - - - 2 ) 3 x + y - z = 20 - - - - - - - - - - - - 3 ) from 1 ) and 2 ) 6 x = 120 x = 20 answer is b
Answer: b
Python program:
a = 80 / 4
Problem: calculate how much time could be saved if the train would run at its usual speed , given that it ran at 5 / 7 of its own speed and got to its destination in 15 hours ?
Options: a ) 1.29 hrs , b ) 2.29 hrs , c ) 4.29 hrs , d ) 5.29 hrs , e ) 3.29 hrs
Rationale: "new speed = 5 / 7 of usual speed new time = 5 / 7 of usual time 5 / 7 of usual time = 15 hrs usual time = 15 * 5 / 7 = 10.71 hrs time saved = 15 - 10.71 = 4.29 hrs answer is c"
Answer: c
Python program:
a = 15 * const_60
b = 5 / 7
c = 15 * b
d = c * const_60
e = a - d
f = reminder / (
g = f + 100
Problem: find the average of first 10 multiples of 7
Options: a ) 35.5 , b ) 37.5 , c ) 38.5 , d ) 40.5 , e ) none of these
Rationale: "explanation : = 7 ( 1 + 2 + 3 + . . . + 10 ) 10 = 7 ( 10 ( 10 + 1 ) ) 10 × 2 = 7 ( 110 ) 10 × 2 = 38.5 answer : option c"
Answer: c
Python program:
a = 10 + 1 
b = 10 + 1 
c = b + 2 
d = a + c 
e = 7 - 10
f = 7 - 2
g = e + f 
h = d + g 
i = h / 10
Problem: two numbers are in the ratio 3 : 5 . if 9 be subtracted from each , they are in the ratio of 9 : 17 . the first number ?
Options: a ) 36 , b ) 86 , c ) 27 , d ) 86 , e ) 27
Rationale: "( 3 x - 9 ) : ( 5 x - 9 ) = 9 : 17 x = 12 = > 3 x = 36 answer : a"
Answer: a
Python program:
a = 3 * 5
b = 9 / a
c = 3 * b
d = 3 * 5
e = 9 / d
f = 5 * e
g = c + f
Problem: john makes $ 30 a week from his job . he earns a raise and now makes $ 40 a week . what is the % increase ?
Options: a ) 16 % , b ) 16.66 % , c ) 18 % , d ) 21 % , e ) 33.33 %
Rationale: "increase = ( 10 / 30 ) * 100 = 33.33 % . e"
Answer: e
Python program:
a = 40 - 30
b = a / 30
c = b * 100
Problem: a truck covers a distance of 550 metres in 1 minute whereas a bus covers a distance of 33 kms in 45 minutes . the ratio of their speeds is ?
Options: a ) 1 : 2 , b ) 3 : 4 , c ) 2 : 5 , d ) 3 : 7 , e ) 1 : 3
Rationale: ratio of speeds = ( 550 / 60 ) 18 / 5 : 60 * 33 / 45 = 33 : 44 = 3 : 4 answer is b
Answer: b
Python program:
a = 33 / 45
b = a * 1000
c = 550 / b
Problem: a particular library has 150 books in a special collection , all of which were in the library at the beginning of the month . these book are occasionally loaned out through an inter - library program . if , by the end of the month , 65 percent of books that were loaned out are returned and there are 122 books in the special collection at that time , how many books of the special collection were loaned out during that month ?
Options: a ) 40 , b ) 60 , c ) 80 , d ) 100 , e ) 120
Rationale: "the total number of books is 150 . let x be the number of books which were loaned out . 65 % of books that were loaned out are returned . 35 % of books that were loaned out are not returned . now , there are 122 books , thus the number of un - returned books is 150 - 122 = 28 books . 0.35 x = 28 x = 80 the answer is c ."
Answer: c
Python program:
a = 150 - 122
b = 65 / 100
c = 1 - b
d = a / c