euclaise/mathqa_programs huggingface dataset:
Problem: a retail appliance store priced a video recorder at 20 percent above the wholesale cost of $ 200 . if a store employee applied the 30 percent employee discount to the retail price to buy the recorder , how much did the employee pay for the recorder ?
Options: a ) $ 198 , b ) $ 216 , c ) $ 220 , d ) $ 230 , e ) $ 168
Rationale: "wholesale cost of video recorder = 200 $ video recorder was priced at 20 percent above 200 = 240 $ % discount given by store employee = 30 emlpoyee paid = . 7 * 240 = 168 $ answer e"
Answer: e
Python program:
a = 200 / 100
b = a * 20
c = 200 + b 
d = 200 / 100
e = d * 20
f = 200 + e 
g = f / 100
h = g * 30
i = c - h
Problem: if an integer n is to be chosen at random from the integers 1 to 92 , inclusive , what is the probability that n ( n + 1 ) ( n + 2 ) will be divisible by 8 ?
Options: a ) 1 / 4 , b ) 3 / 8 , c ) 1 / 2 , d ) 29 / 46 , e ) 3 / 4
Rationale: "n ( n + 1 ) ( n + 2 ) will be divisible by 8 when n is a multiple of 2 or when ( n + 1 ) is a multiple of 8 . thus when n is even , this whole expression will be divisible by 8 . from 1 to 96 , there are 46 even integers . now when ( n + 1 ) is multiple by 8 , we have 12 such values for ( n + 1 ) probability that n ( n + 1 ) ( n + 2 ) will be divisible by 8 = ( 46 + 12 ) / 92 = 58 / 96 = 29 / 46 ans is d"
Answer: d
Python program:
a = 92 / 2
b = 92 / 8
c = a + b 
d = c / 92
Problem: on dividing a number by 56 , we get 27 as remainder . on dividing the same number by 8 , what will be the remainder ?
Options: a ) 2 , b ) 3 , c ) 4 , d ) 5 , e ) 6
Rationale: "number = 56 x + 27 ( ∵ since the number gives 27 as remainder on dividing by 56 ) = ( 7 × 8 × x ) + ( 3 × 8 ) + 3 hence , if the number is divided by 8 , we will get 3 as remainder . answer : b"
Answer: b
Python program:
a = 27 ** 2
b = a / 56
c = 27 ** 2
d = c / 56
e = math.floor(d)
f = b - e
g = f * 56
Problem: what sum of money will produce rs . 90 as simple interest in 4 years at 3 1 / 2 percent ?
Options: a ) 263 , b ) 500 , c ) 367 , d ) 642.9 , e ) 339
Rationale: "90 = ( p * 4 * 7 / 2 ) / 100 p = 642.9 answer : d"
Answer: d
Python program:
a = 1 / 2
b = 3 + a 
c = 4 * b
d = c / 100
e = 90 / d
Problem: a and b enter into a partnership . a contributed rs . 5000 for 8 months and b rs . 6000 for 5 months . find a ' s share in a total profit of rs . 8400 .
Options: a ) rs . 4800 , b ) rs . 2400 , c ) rs . 3600 , d ) rs . 5600 , e ) none of these
Rationale: explanation : ratio of capitals of a and b = ratio of their investments = 5000 × 8 : 6000 × 5 = 40000 : 30000 = 4 : 3 . : a ' s share = rs . [ ( 4 / 7 ) × 8400 ] = rs . 4800 answer : option a
Answer: a
Python program:
a = 5000 * 8
b = 5000 * 8
c = 6000 * 5
d = b + c 
e = a / d
f = 8400 * e
Problem: two vessels a and b contain spirit and water in the ratio 5 : 2 and 7 : 6 respectively . find the ratio in which these mixtures be mixed to obtain a new mixture in vessel c containing spirit and water in the ratio 8 : 5 ?
Options: a ) 3 : 4 , b ) 4 : 3 , c ) 9 : 7 , d ) 7 : 9 , e ) 8 : 1
Rationale: "explanation : let cost price ( cp ) of 1 litre spirit be rs . 1 quantity of spirit in 1 litre mixture from vessel a = 5 / 7 cost price ( cp ) of 1 litre mixture from vessel a = rs . = 5 / 7 quantity of spirit in 1 litre mixture from vessel b = 7 / 13 cost price ( cp ) of 1 litre mixture from vessel b = rs . = 7 / 13 quantity of spirit to be obtained in 1 litre mixture from vessel c = 8 / 13 cost price ( cp ) of 1 litre mixture from vessel c ( mean price ) = rs . = 8 / 13 = > mixture from vessel a : mixture from vessel b = 1 / 13 : 9 / 91 = 7 : 9 answer is d"
Answer: d
Python program:
a = 2 + 7 
b = 7 / a
Problem: company a imported 10,000 widgets made of either brass or aluminum . the widgets are painted blue , red or green . if 20 percent of the widgets are made of brass and of those 20 percent are painted green and 40 percent are painted red how many brass widgets painted blue were imported ?
Options: a ) 420 , b ) 840 , c ) 800 , d ) 1680 , e ) 2100
Rationale: "answer a . we are told that 10 % of all imported widgets are made of brass and of those , 20 % are green and 40 % are red . since we know that there are only three colors , the remaining 40 % must be blue . 40 % blue of 20 % brass widgets leads to 8 % blue brass widgets out of the total 10,550 widgets . 10,000 / 100 * 8 = 800 . answer c ."
Answer: c
Python program:
a = 20 / 100
b = 40 / 100
c = a * b
d = 20 + 2 
e = d / 20
f = c * e
g = f * 100
h = g * 100
Problem: a honey bee flies for 10 seconds , from a daisy to a rose . it immediately continues to a poppy , flying for 6 additional seconds . the distance the bee passed , flying from the daisy to the rose is 6 meters longer than the distance it passed flying from the rose to the poppy . the bee flies to the poppy at 3 meters per second faster than her speed flying to the rose . the bee flies how many meters per second from the daisy to the rose ?
Options: a ) 3 , b ) 5 , c ) 6 , d ) 8 , e ) 10
Rationale: "let the speed be ' s ' and let the distance between rose and poppy be ' x ' the problem boils down to : rose to poppy : s + 3 = x / 6 - - - - - - - 1 daisy to rose : s = ( x + 6 ) / 10 - - - - - - 2 so from 1 we can re write x as x = 6 s + 18 substitute the value of x in 2 gives us s = 3 m / s a"
Answer: a
Python program:
a = 6 * 3
b = a + 6 
c = b / 10
Problem: a rectangular lawn of dimensions 80 m * 40 m has two roads each 10 m wide running in the middle of the lawn , one parallel to the length and the other parallel to the breadth . what is the cost of traveling the two roads at rs . 3 per sq m ?
Options: a ) 2288 , b ) 2779 , c ) 3300 , d ) 3900 , e ) 2781
Rationale: "area = ( l + b â € “ d ) d ( 80 + 40 â € “ 10 ) 10 = > 1100 m 2 1100 * 3 = rs . 3300 answer : c"
Answer: c
Python program:
a = 80 + 40 
b = a - 10
c = b * 10
d = c * 3
Problem: there is enough provisions for 1200 girls in a hostel for 50 days . if there were 600 girls less , how long will the provision last ?
Options: a ) 75 , b ) 80 , c ) 90 , d ) 95 , e ) 100
Rationale: "we have , m 1 d 1 = m 2 d 2 1200 * 50 = 600 * d 2 d 2 = 1200 * 50 / 600 = 100 days . answer : e"
Answer: e
Python program:
a = 1200 * 600
b = a / 10
c = b + 50
Problem: a 50 kg metal bar made of alloy of tin and silver lost 5 kg of its weight in the water . 10 kg of tin loses 1.375 kg in the water ; 5 kg of silver loses 0.375 kg . what is the ratio of tin to silver in the bar ?
Options: a ) 1 / 4 , b ) 2 / 5 , c ) 1 / 2 , d ) 3 / 5 , e ) 2 / 3
Rationale: "you can simply use this formula to avoid confusion : w 1 / w 2 = ( a 2 - aavg ) / ( avg - a 1 ) here is how you will find the values of a 1 an a 2 . we have an overall loss ( average loss ) . the average loss is 5 kg when 50 kg alloy is immersed . this is a loss of ( 5 / 50 ) * 100 = 10 % . this is aavg the loss of tin is 1.375 kg for every 10 kg . this means it loses ( 1.375 / 10 ) * 100 = 13.75 % of its weight in water . this is a 1 . the loss of silver is . 375 kg for every 5 kg . this means it loses ( . 375 / 5 ) * 100 = 7.5 % of its weight in water . this is a 2 . weight of tin / weight of silver = ( silver ' s loss - avg loss ) / ( avg loss - tin ' s loss ) x / y = ( 7.5 - 10 ) / ( 10 - 13.75 ) = 2 / 3 e"
Answer: e
Python program:
a = 0 / 375
b = a * 50
c = 5 - b
d = 1 / 375
e = 0 / 375
f = d - e
g = c / f
h = 0 / 375
i = h * 50
j = 5 - i
k = 1 / 375
l = 0 / 375
m = k - l
n = j / m
o = 50 - n
p = g / o
Problem: a , b and c have rs . 300 between them , a and c together have rs . 200 and b and c rs . 350 . how much does c have ?
Options: a ) a ) 250 , b ) b ) 249 , c ) c ) 248 , d ) d ) 247 , e ) e ) 246
Rationale: "a + b + c = 300 a + c = 200 b + c = 350 - - - - - - - - - - - - - - a + b + 2 c = 550 a + b + c = 300 - - - - - - - - - - - - - - - - c = 250 answer : a"
Answer: a
Python program:
a = 200 + 350 
b = a - 300
Problem: united telephone charges a base rate of $ 7.00 for service , plus an additional charge of $ 0.25 per minute . atlantic call charges a base rate of $ 12.00 for service , plus an additional charge of $ 0.20 per minute . for what number of minutes would the bills for each telephone company be the same ?
Options: a ) 200 minutes , b ) 100 minutes , c ) 120 minutes , d ) 140 minutes , e ) 160 minutes
Rationale: "lets take number of minutesx . given that , 7 + 0.25 x = 12 + 0.2 x - > 0.05 x = 2 - > x = 100 minutes ans b"
Answer: b
Python program:
a = 12 - 0
b = 0 - 25
c = a / b
Problem: there are 50 students in a class . if 12 % are absent on a particular day , find the number of students present in the class .
Options: a ) 43 , b ) 36 , c ) 28 , d ) 129 , e ) 44
Rationale: "number of students absent on a particular day = 12 % of 50 i . e . , 12 / 100 × 50 = 6 therefore , the number of students present = 50 - 6 = 44 students . answer : e"
Answer: e
Python program:
a = 12 / 100
b = 1 - a
c = b * 50
Problem: how many gallons of milk that is 10 percent butter - fat must be added to 8 gallons of milk that is 50 percent butterfat to obtain milk that is 20 percent butterfat ?
Options: a ) 6 , b ) 12 , c ) 14 , d ) 24 , e ) 28
Rationale: "equate the fat : 0.1 x + 0.5 * 8 = 0.2 ( x + 8 ) - - > x = 24 . answer : d ."
Answer: d
Python program:
a = 50 - 20
b = a * 8
c = b / 10
Problem: can c and can в are both right circular cylinders . the radius of can c is twice the radius of can b , while the height of can c is half the height of can b . if it costs $ 4.00 to fill half of can b with a certain brand of gasoline , how much would it cost to completely fill can c with the same brand of gasoline ?
Options: a ) $ 1 , b ) $ 2 , c ) $ 4 , d ) $ 8 , e ) $ 16
Rationale: let x be the radius of b and 2 h be the height of b . therefore , radius of c = 2 x and height = h vol of b = 3.14 * x ^ 2 * 2 h vol of a = 3.14 * 4 x ^ 2 * h cost to fill half of b = $ 4 - - > cost to fill full b = $ 8 - - > 3.14 * x ^ 2 * 2 h = 8 - - > 3.14 * x ^ 2 * h = 4 - - > 4 * ( 3.14 * x ^ 2 * h ) = $ 16 ans e
Answer: e
Python program:
a = 2 * 4
b = a * 2
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 3 years ago ?
Options: a ) 11 , b ) 10 , c ) 12 , d ) 14 , e ) 16
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 3 years ago ? i . e . d - 4 = 14 - 3 = 11 years answer : a"
Answer: a
Python program:
a = 6 + 8 
b = a - 3
Problem: 6 years ago , the ratio of the ages of vimal and saroj was 6 : 5 . 4 years hence , the ratio of their ages will be 11 : 10 . what is saroj ' s age at present ?
Options: a ) 12 , b ) 14 , c ) 16 , d ) 18 , e ) 15
Rationale: given that , six years ago , the ratio of the ages of vimal and saroj = 6 : 5 hence we can assume that age of vimal six years ago = 6 x age of saroj six years ago = 5 x after 4 years , the ratio of their ages = 11 : 10 ⇒ ( 6 x + 10 ) : ( 5 x + 10 ) = 11 : 10 ⇒ 10 ( 6 x + 10 ) = 11 ( 5 x + 10 ) ⇒ 5 x = 10 ⇒ x = 105 = 2 saroj ' s present age = ( 5 x + 6 ) = 5 × 2 + 6 = 16 answer is c .
Answer: c
Python program:
a = 11 * 10
b = 10 * 10
c = a - b
d = 10 * 6
e = 11 * 5
f = d - e
g = c / f
h = 5 * g
i = h + 6
Problem: a boat can travel with a speed of 13 km / hr in still water . if the speed of the stream is 5 km / hr , find the time taken by the boat to go 70 km downstream .
Options: a ) 4.25 hr , b ) 3.8 hr , c ) 8.25 hr , d ) 2.25 hr , e ) 2.50 hr
Rationale: "speed of boat in still water = 13 km / hr speed of the stream = 5 km / hr speed downstream = ( 13 + 5 ) = 18 km / hr time taken to travel 70 km downstream = 70 â  „ 18 = 3.8 hours answer is b"
Answer: b
Python program:
a = 13 + 5 
b = 70 / a
Problem: if 60 % of ( x - y ) = 20 % of ( x + y ) , then what percent of x is y ?
Options: a ) 50 % , b ) 44.4 % , c ) 22.2 % , d ) 33.3 % , e ) 25 %
Rationale: "60 % of ( x - y ) = 20 % of ( x + y ) 60 / 100 ( x - y ) = 20 / 100 ( x + y ) 4 x = 8 y required percentage = y / x * 100 = 4 y / 8 y * 100 = 50 % answer is a"
Answer: a
Python program:
a = 60 - 20
b = 60 + 20 
c = a / b
d = c * 100
Problem: a and b undertake to do a piece of work for rs . 600 . a alone can do it in 6 days while b alone can do it in 8 days . with the help of c , they finish it in 3 days . ! find the share of each .
Options: a ) 25 , b ) 50 , c ) 75 , d ) 80 , e ) none of them
Rationale: c ' s 1 day ' s work = 1 / 3 - ( 1 / 6 + 1 / 8 ) = 24 a : b : c = ratio of their 1 day ' s work = 1 / 6 : 1 / 8 : 1 / 24 = 4 : 3 : 1 . a ’ s share = rs . ( 600 * 4 / 8 ) = rs . 300 , b ' s share = rs . ( 600 * 3 / 8 ) = rs . 225 . c ' s share = rs . [ 600 - ( 300 + 225 » ) = rs . 75 . answer is c
Answer: c
Python program:
a = 4 + 3 
b = a + 1 
c = 1 / b
d = c * 600
Problem: how many even integers n , such that 20 < = n < = 220 are of the form 3 k + 4 , where k is any natural number ?
Options: a ) 28 , b ) 31 , c ) 34 , d ) 37 , e ) 40
Rationale: "the first number is 22 = 16 + 6 ( 1 ) . we can continue adding 6 to make a list : 22 , 28 , 34 , . . . the last number is 220 = 16 + 6 ( 34 ) there are 34 numbers in the list . the answer is c ."
Answer: c
Python program:
a = 220 - 2
b = 20 + 2 
c = a - b
d = 2 + 4 
e = c / d
f = e + 1
Problem: the edges of three metal cubes are 1 cm , 3 cm , and 4 cm respectively . a new cube is made by melting these three cubes together . what is the edge of the new cube ( in centimeters ) ?
Options: a ) 3.9 , b ) 4.2 , c ) 4.5 , d ) 4.8 , e ) 5.1
Rationale: the total volume is 1 ^ 3 + 3 ^ 3 + 4 ^ 3 = 92 the edge of the new cube is the cube root of 92 which is about 4.5 cm . the answer is c .
Answer: c
Python program:
a = 4 ** 3
b = 3 ** 3
c = 1 + b 
d = a + c 
e = d ** const_0_33
Problem: an inspector rejects 10 % of the meters as defective . how many will he examine to reject 12 ?
Options: a ) a ) 100 , b ) b ) 120 , c ) c ) 250 , d ) d ) 200 , e ) e ) 160
Rationale: "then , 10 % of x = 12 ( 10 / 100 ) x = 12 x = ( 12 * 100 * ) / 10 = 120 answer is b"
Answer: b
Python program:
a = 12 * 100
b = a / 10
Problem: a survey was sent to 60 customers , 7 of whom responded . then the survey was redesigned and sent to another 72 customers , 9 of whom responded . by approximately what percent did the response rate increase from the original survey to the redesigned survey ?
Options: a ) 2 % , b ) 7 % , c ) 14 % , d ) 28 % , e ) 63 %
Rationale: "rate of first survey = 7 / 60 rate of second survey = 9 / 72 % response rate increase ( 9 / 72 - 7 / 60 ) / ( 7 / 60 ) = 7 % answer is b = 7 %"
Answer: b
Python program:
a = 9 / 72
b = 7 / 60
c = a - b
d = c * 100
e = math.floor(d)
Problem: if the sides of a square are multiplied by 5 , the area of the original square is how many times as large as the area of the resultant square ?
Options: a ) 4 % , b ) 25 % , c ) 50 % , d ) 200 % , e ) 400 %
Rationale: "let x be the original length of one side . then the original area is x ^ 2 . the new square has sides of length 5 x , so the area is 25 x ^ 2 . the area of the original square is 1 / 25 = 4 % times the area of the new square . the answer is a ."
Answer: a
Python program:
a = 5 * 5
b = a / 100
Problem: car a runs at the speed of 50 km / hr & reaches its destination in 6 hr . car b runs at the speed of 100 km / h & reaches its destination in 1 h . what is the respective ratio of distances covered by car a & car b ?
Options: a ) 11 : 5 , b ) 3 : 1 , c ) 13 : 7 , d ) 15 : 7 , e ) 16 : 9
Rationale: "sol . distance travelled by car a = 50 × 6 = 300 km distance travelled by car b = 100 × 1 = 100 km ratio = 300 / 100 = 3 : 1 answer : b"
Answer: b
Python program:
a = 50 * 6
b = 100 * 1
c = a / b
Problem: a cubical block of metal weighs 8 pounds . how much will another cube of the same metal weigh if its sides are twice as long ?
Options: a ) 48 , b ) 32 , c ) 24 , d ) 18 , e ) 64
Rationale: "for example our cube have a side 1 meter , so we have 1 cubical meter in this cube and this cubical meter weigth 6 pounds if we take cube with side 2 meters we will have 8 cubical meters in this cube 8 meters * 8 pounds = 64 pounds so answer is e and similar but more theoretical approach : if we have sides a and b than they have equal ration with their areas : a / b = a ^ 2 / b ^ 2 and they have equal ration with their volumes : a / b = a ^ 3 / b ^ 3 we have two sides 1 / 2 so their volume will be in ratio 1 / 8 weight of one cube * volume of another cube 8 * 8 = 64 so answer is e"
Answer: e
Python program:
a = 2 * 4
b = 8 * a
Problem: of the final grades received by the students in a certain math course , 1 / 5 are a ' s , 1 / 4 are b ' s , 1 / 2 are c ' s , and the remaining 20 grades are d ' s . what is the number of students in the course ?
Options: a ) 80 , b ) 110 , c ) 160 , d ) 200 , e ) 400
Rationale: "we start by creating a variable for the total number of students in the math course . we can say : t = total number of students in the math course next , we can use variable t in an equation that we translate from the given information . we are given that , of the final grades received by the students in a certain math course , 1 / 5 are a ' s , 1 / 4 are b ' s , 1 / 2 are c ' s , and the remaining 20 grades are d ' s . since this represents all the grades in the class , it represents all the students in the class . thus we know : # a ’ s + # b ’ s + # c ’ s + # d ’ s = total number of students in the class 1 / 5 ( t ) + ¼ ( t ) + ½ ( t ) + 20 = t we can multiply the entire equation by 20 to cancel out the denominators of the fractions and we have : 4 t + 5 t + 10 t + 400 = 20 t 19 t + 400 = 20 t 400 = t there are a total of 400 students in the math class . answer is e ."
Answer: e
Python program:
a = 1 / 5
b = 1 / 4
c = a + b 
d = 1 / 2
e = c + d 
f = 1 - e
g = 20 / f
Problem: how many pieces of 0.85 meteres can be cut from a rod 42.5 meteres long
Options: a ) 30 , b ) 40 , c ) 50 , d ) 60 , e ) 70
Rationale: explanation : we need so simple divide 42.5 / 0.85 , = ( 4250 / 85 ) = 50 option c
Answer: c
Python program:
a = 42 / 5
Problem: ratio between rahul and deepak is 5 : 2 , after 6 years rahul age will be 26 years . what is deepak present age .
Options: a ) 14 , b ) 15 , c ) 8 , d ) 22 , e ) 24
Rationale: "explanation : present age is 5 x and 2 x , = > 5 x + 6 = 26 = > x = 4 so deepak age is = 2 ( 4 ) = 8 option c"
Answer: c
Python program:
a = 26 - 6
b = a * 2
c = b / 5
Problem: in what time will a train 400 m long cross an electric pole , it its speed be 144 km / hr ?
Options: a ) 2.5 sec , b ) 12.9 sec , c ) 11.3 sec , d ) 21.9 sec , e ) 10.0 sec
Rationale: "speed = 144 * 5 / 18 = 40 m / sec time taken = 400 / 40 = 10.0 sec . answer : e"
Answer: e
Python program:
a = 144 * const_0_2778
b = 400 / a
Problem: set a consists of all the prime numbers between 62 and 85 . what is the range of set a ?
Options: a ) 12 , b ) 13 , c ) 16.6 , d ) 16 , e ) 23
Rationale: the range of a set of data is the difference between the highest and lowest values in the set in this set , highest number = 83 lowest number = 67 range = highest - lowest = 83 - 67 = 16 option d
Answer: d
Python program:
a = 85 - 2
b = 62 + 4 
c = b + 1 
d = a - c
Problem: s ( n ) is a n - digit number formed by attaching the first n perfect squares , in order , into one integer . for example , s ( 1 ) = 1 , s ( 2 ) = 14 , s ( 3 ) = 149 , s ( 4 ) = 14916 , s ( 5 ) = 1491625 , etc . how many digits w are in s ( 99 ) ?
Options: a ) w = 350 , b ) w = 353 , c ) w = 354 , d ) 356 , e ) 357
Rationale: "focus on the points where the number of digits in squares change : 1 , 2 , 3 - single digit squares . first 2 digit number is 10 . 4 , 5 , . . . 9 - two digit squares . to get 9 , the last number with two digit square , think that first 3 digit number is 100 which is 10 ^ 2 . so 9 ^ 2 must be the last 2 digit square . 10 , 11 , 12 , . . . 31 - three digit squares . to get 31 , think of 1000 - the first 4 digit number . it is not a perfect square but 900 is 30 ^ 2 . 32 ^ 2 = 2 ^ 10 = 1024 , the first 4 digit square . 32 - 99 - four digit squares . to get 99 , think of 10,000 - the first 5 digit number which is 100 ^ 2 . so number of digits in s ( 99 ) = 3 * 1 + 6 * 2 + 22 * 3 + 68 * 4 = 3 + 12 + 66 + 272 = 353 . b"
Answer: b
Python program:
a = const_60 + 4 
b = a + 4 
c = const_60 + 4 
d = c + 4 
e = d * 4
f = b + e 
g = 3 * 1
h = 3 * 2
i = h * 2
j = g + i 
k = f + j
Problem: a candidate got 35 % of the votes and lost to the rival by 1650 votes . how many votes were cast ?
Options: a ) 5000 , b ) 5500 , c ) 6000 , d ) 6500 , e ) 7000
Rationale: "35 % - - - - - - - - - - - l 65 % - - - - - - - - - - - w - - - - - - - - - - - - - - - - - - 30 % = 1650 10 % = 550 100 % of the votes = 5500 answer : b"
Answer: b
Python program:
a = 35 / 100
b = 1 - a
c = 35 / 100
d = b - c
e = 1650 / d
Problem: a certain car traveled twice as many miles from town a to town b as it did from town b to town c . from town a to town b , the car averaged 8 miles per gallon , and from town b to town c , the car averaged 18 miles per gallon . what is the average miles per gallon that the car achieved on its trip from town a through town b to town c ?
Options: a ) 13 , b ) 15.5 , c ) 14 , d ) 14.5 , e ) 15
Rationale: "ans is b given d _ ab = 2 * d _ bc let d _ ab = d and d _ bc = x so d = 2 x for average miles per gallon = ( d + x ) / ( ( d / 8 ) + ( x / 18 ) ) = 15.5 ( formula avg speed = total distance / total time )"
Answer: b
Python program:
a = 18 * 10
b = 18 * 10
c = b / 2
d = a + c 
e = 18 * 10
f = e / 8
g = 18 * 10
h = g / 2
i = h / 18
j = f + i 
k = d / j
Problem: the total age of a and b is 10 years more than the total age of b and c . c is how many years younger than a . ?
Options: a ) 16 , b ) 12 , c ) 10 , d ) 20 , e ) 10
Rationale: "( a + b ) - ( b - c ) = 10 a - c = 10 answer is c"
Answer: c
Python program:
a = 10 * 1
Problem: excluding stoppages , the speed of a train is 67 kmph and including stoppages it is 51 kmph . of how many minutes does the train stop per hour ?
Options: a ) 82 , b ) 17 , c ) 14 , d ) 82 , e ) 18
Rationale: "explanation : t = 16 / 67 * 60 = 14 answer : option c"
Answer: c
Python program:
a = 51 / 67
b = const_60 * a
c = const_60 - b
Problem: the sides of a square region , measured to the nearest centimeter , are 9 centimeters long . the least possible value of the actual area of the square region is
Options: a ) 60.25 sq cm , b ) 66.25 sq cm , c ) 56.25 sq cm , d ) 72.25 sq cm , e ) 58.25 sq cm
Rationale: "though there might be some technicalities concerning the termnearest ( as 7.5 is equidistant from both 7 and 8 ) the answer still should be : 7.5 ^ 2 = 56.25 . answer : c"
Answer: c
Python program:
a = 9 - const_0_25
b = a - const_0_25
c = b ** 2
Problem: the average runs of a cricket player of 8 innings was 24 . how many runs must he make in his next innings so as to increase his average of runs by 8 ?
Options: a ) 12 , b ) 42 , c ) 64 , d ) 96 , e ) 84
Rationale: "explanation : average after 9 innings = 32 required number of runs = ( 32 * 9 ) – ( 24 * 8 ) = 288 – 192 = 96 answer d"
Answer: d
Python program:
a = 8 + 1 
b = 24 + 8 
c = a * b
d = 24 * 8
e = c - d
Problem: if jack walked 4 miles in 1 hour and 15 minutes , what was his rate of walking in miles per hour ?
Options: a ) 3.2 , b ) 4.5 , c ) 6 , d ) 6.25 , e ) 15
Rationale: distance walked in 1 hour and 15 mins = 4 miles speed per hour = distance / time = 4 / ( 5 / 4 ) = 3.2 miles per hour answer a
Answer: a
Python program:
a = 4 * const_60
b = 15 + const_60 
c = a / b
Problem: yesterday it took robert 6 hours to drive from city a to city b . today it took robert 4.5 hours to drive back from city в to city a along the same route . if he had saved 30 minutes in both trips , the speed for the round trip would be 90 miles per hour . what is the distance between city a and city b ?
Options: a ) 90 , b ) 120 , c ) 150 , d ) 440 , e ) 430
Rationale: 2 d / 90 = 9.5 ( because time = 6 + 4.5 - 1 hrs ) = > d = 430 answer - e
Answer: e
Python program:
a = 6 + 4 
b = a - 1
c = 90 * b
d = c / 2