euclaise/mathqa_programs huggingface dataset:
Problem: a water tank is three - fifths full . pipe a can fill a tank in 10 minutes and pipe b can empty it in 6 minutes . if both the pipes are open , how long will it take to empty or fill the tank completely ?
Options: a ) 6 min , b ) 8 min , c ) 7 min , d ) 9 min , e ) 1 min
Rationale: "the combined rate of filling / emptying the tank = 1 / 10 - 1 / 6 = - 1 / 15 since the rate is negative , the tank will be emptied . a full tank would take 15 minutes to empty . since the tank is only three - fifths full , the time is ( 3 / 5 ) * 15 = 9 minutes the answer is d ."
Answer: d
Python program:
a = 2 + 3 
b = 4 / a
c = 1/(6)
d = 1/(10)
e = c - d
f = b / e
Problem: two vessels p and q contain 62.5 % and 87.5 % of alcohol respectively . if 4 litres from vessel p is mixed with 8 litres from vessel q , the ratio of alcohol and water in the resulting mixture is ?
Options: a ) 19 : 1 , b ) 19 : 4 , c ) 19 : 8 , d ) 38 : 10 , e ) 38 : 2
Rationale: "quantity of alcohol in vessel p = 62.5 / 100 * 4 = 5 / 2 litres quantity of alcohol in vessel q = 87.5 / 100 * 8 = 7 / 1 litres quantity of alcohol in the mixture formed = 5 / 2 + 7 / 1 = 19 / 2 = 9.50 litres as 12 litres of mixture is formed , ratio of alcohol and water in the mixture formed = 9.50 : 2.50 = 38 : 10 . answer : d"
Answer: d
Python program:
a = 62 * 5
b = a / 100
c = 87 * 5
d = c / 100
e = b + d 
f = 62 * 5
g = f / 100
h = 4 - g
i = 87 * 5
j = i / 100
k = 8 - j
l = h + k 
m = e / l
Problem: ( 228 % of 1265 ) ÷ 6 = ?
Options: a ) a ) 125 , b ) b ) 175 , c ) c ) 481 , d ) d ) 375 , e ) e ) 524
Rationale: "explanation : ? = ( 228 x 1265 / 100 ) ÷ 6 = 288420 / 600 = 481 answer : option c"
Answer: c
Python program:
a = 228 / 100
b = a * 1265
c = b / 6
Problem: the first year , two cows produced 8100 litres of milk . the second year their production increased by 15 % and 10 % respectively , and the total amount of milk increased to 9100 litres a year . how many litres were milked from one cow ?
Options: a ) 2178 lt , b ) 3697 lt , c ) 6583 lt , d ) 4370 lt , e ) 5548 lt
Rationale: "let x be the amount of milk the first cow produced during the first year . then the second cow produced ( 8100 − x ) litres of milk that year . the second year , each cow produced the same amount of milk as they did the first year plus the increase of 15 % 15 % or 10 % so 8100 + 15100 ⋅ x + 10100 ⋅ ( 8100 − x ) = 9100 therefore 8100 + 320 x + 110 ( 8100 − x ) = 9100 120 x = 190 x = 3800 therefore , the cows produced 3800 and 4300 litres of milk the first year , and 4370 and 4730 litres of milk the second year , = > one cow produced 4370 litres correct answer is d ) 4370 lt"
Answer: d
Python program:
a = 10 / 100
b = 1 + a 
c = b * 8100
d = 9100 - c
e = 15 / 100
f = 1 + e 
g = 10 / 100
h = 1 + g 
i = f - h
j = d / i
k = 8100 - j
Problem: the average height of 40 girls out of a class of 50 is 169 cm . and that of the remaining girls is 167 cm . the average height of the whole class is :
Options: a ) 138.9 cms , b ) 149.2 cms , c ) 168.6 cms , d ) 159.2 cms , e ) 142.5 cms
Rationale: "explanation : average height of the whole class = ( 40 × 169 + 10 × 167 / 50 ) = 168.6 cms answer c"
Answer: c
Python program:
a = 169 * 40
b = 167 * 10
c = a + b 
d = c / 50
Problem: equal amount of water were poured into two empty jars of different capacities , which made one jar 1 / 7 full and other jar 1 / 6 full . if the water in the jar with lesser capacity is then poured into the jar with greater capacity , what fraction of the larger jar will be filled with water ?
Options: a ) 1 / 7 , b ) 7 / 12 , c ) 1 / 2 , d ) 2 / 7 , e ) 2 / 3
Rationale: "same amount of water made bigger jar 1 / 7 full , then the same amount of water ( stored for a while in smaller jar ) were added to bigger jar , so bigger jar is 1 / 7 + 1 / 7 = 2 / 7 full . answer : d ."
Answer: d
Python program:
a = 2 / 7
Problem: given f ( x ) = 3 x – 5 , for what value of x does 2 * [ f ( x ) ] – 10 = f ( x – 2 ) ?
Options: a ) 1 , b ) 2 , c ) 3 , d ) 4 , e ) 5
Rationale: "2 ( 3 x - 5 ) - 10 = 3 ( x - 2 ) - 5 3 x = 9 x = 3 the answer is c ."
Answer: c
Python program:
a = 2 * 5
b = a + 10 
c = 3 * 2
d = c + 5 
e = b - d
f = 2 * 3
g = 3 * 1
h = f - g
i = e / h
Problem: the population of a town is 10000 . it increases annually at the rate of 40 % p . a . what will be its population after 2 years ?
Options: a ) 14000 , b ) 14400 , c ) 19600 , d ) 14600 , e ) 14700
Rationale: "formula : 10000 × 140 / 100 × 140 / 100 = 19600 answer : c"
Answer: c
Python program:
a = 10000 * 40
b = a / 100
c = b * 2
d = 10000 + c
Problem: for any integer n greater than 1 , # n denotes the product of all the integers from 1 to n , inclusive . how many prime numbers e are there between # 6 + 2 and # 6 + 6 , inclusive ?
Options: a ) none , b ) one , c ) two , d ) three , e ) four
Rationale: "none is the answer . a . because for every k 6 ! + k : : k , because 6 ! : : k , since k is between 2 and 6 . a"
Answer: a
Python program:
a = 1 + 1
Problem: the unit digit in the product ( 784 x 618 x 917 x 463 ) is :
Options: a ) 5 , b ) 9 , c ) 16 , d ) 2 , e ) 42
Rationale: "explanation : unit digit in the given product = unit digit in ( 4 x 8 x 7 x 3 ) = ( 672 ) = 2 d"
Answer: d
Python program:
a = 784 * 618
b = a * 917
c = b * 463
d = 784 * 618
e = d * 917
f = e * 463
g = 4 + 4 
h = f - g
i = c - h
Problem: the diameter of a cylindrical tin is 8 cm and height is 5 cm . find the volume of the cylinder ?
Options: a ) 33 , b ) 45 , c ) 66 , d ) 80 , e ) 21
Rationale: "r = 4 h = 5 π * 4 * 4 * 5 = 80 π cc answer : d"
Answer: d
Python program:
a = 8 / 2
b = volume_cylinder / (
Problem: whats the reminder when 54,879 , 856,985 , 421,547 , 895,689 , 874,525 , 826,547 is divided by 2
Options: a ) 1 , b ) 7 . , c ) 2 . , d ) 3 , e ) 9
Rationale: "a number ending in a 0 is divisible by 2 . given the obscene number , you should immediately be convinced that you will need to focus on a very small part of it . 54,879 , 856,985 , 421,547 , 895,689 , 874,525 , 826,547 = 54,879 , 856,985 , 421,547 , 895,689 , 874,525 , 826,540 + 7 the first number is divisible by 16 . you just have to find the remainder when you divide 5287 by 16 . that will be the remainder when you divide the original number by 2 . 7 / 16 gives remainder 1 . answer ( a )"
Answer: a
Python program:
a = 4 * 2
b = 10 - 1
c = b * 100
d = 3 + 2 
e = d * 100
f = e * 10
g = c + f 
h = 3 + 2 
i = 12 + h 
j = 3 + 2 
k = i * j
l = g + k 
m = a + reminder
Problem: each of the dogs in a certain kennel is a single color . each of the dogs in the kennel either has long fur or does not . of the 45 dogs in the kennel , 26 have long fur , 30 are brown , and 8 are neither long - furred nor brown . how many long - furred dogs are brown ?
Options: a ) 26 , b ) 19 , c ) 11 , d ) 8 , e ) 6
Rationale: "no of dogs = 45 long fur = 26 brown = 30 neither long fur nor brown = 8 therefore , either long fur or brown = 45 - 8 = 37 37 = 26 + 30 - both both = 19 answer b"
Answer: b
Python program:
a = 26 + 30 
b = 45 - 8
c = a - b
Problem: a person bought 114 glass bowls at a rate of rs . 13 per bowl . he sold 108 of them at rs . 17 and the remaining broke . what is the percentage gain for a ?
Options: a ) 40 , b ) 3000 / 11 , c ) 5900 / 247 , d ) 2790 / 11 , e ) 2709 / 8
Rationale: "cp = 114 * 13 = 1482 and sp = 108 * 17 = 1836 gain % = 100 * ( 1836 - 1482 ) / 1482 = 5900 / 247 answer : c"
Answer: c
Python program:
a = 108 * 17
b = 114 * 13
c = a - b
d = 114 * 13
e = c / d
f = e * 100
Problem: a boat can travel with a speed of 16 km / hr in still water . if the rate of stream is 5 km / hr , then find the time taken by the boat to cover distance of 147 km downstream .
Options: a ) 4 hours , b ) 5 hours , c ) 6 hours , d ) 7 hours , e ) 8 hours
Rationale: "explanation : it is very important to check , if the boat speed given is in still water or with water or against water . because if we neglect it we will not reach on right answer . i just mentioned here because mostly mistakes in this chapter are of this kind only . lets see the question now . speed downstream = ( 16 + 5 ) = 21 kmph time = distance / speed = 147 / 21 = 7 hours option d"
Answer: d
Python program:
a = 16 + 5 
b = 147 / a
Problem: the average age of 38 students in a group is 14 years . when teacher â € ™ s age is included to it , the average increases by one . what is the teacher â € ™ s age in years ?
Options: a ) 31 , b ) 36 , c ) 53 , d ) 58 , e ) none
Rationale: "sol . age of the teacher = ( 39 ã — 15 â € “ 38 ã — 14 ) years = 53 years . answer c"
Answer: c
Python program:
a = 38 + 1
Problem: the area of a square is 4761 sq cm . find the ratio of the breadth and the length of a rectangle whose length is twice the side of the square and breadth is 24 cm less than the side of the square .
Options: a ) 5 : 28 , b ) 5 : 19 , c ) 15 : 12 , d ) 5 : 13 , e ) 15 : 46
Rationale: "let the length and the breadth of the rectangle be l cm and b cm respectively . let the side of the square be a cm . a 2 = 4761 a = 69 l = 2 a and b = a - 24 b : l = a - 24 : 2 a = 45 : 138 = 15 : 46 answer : e"
Answer: e
Python program:
a = math.sqrt(4761)
b = a - 24
c = math.sqrt(4761)
d = c * 2
e = b / d
Problem: a positive integer n is a perfect number provided that the sum of all the positive factors of n , including 1 and n , is equal to 2 n . what is the sum of the reciprocals of all the positive factors of the perfect number 28 ?
Options: a ) 1 / 4 , b ) 56 / 27 , c ) 2 , d ) 3 , e ) 4
Rationale: soln : 28 = 1 * 28 2 * 14 4 * 7 sum of reciprocals = 1 + 1 / 28 + 1 / 2 + 1 / 14 + 1 / 4 + 1 / 7 = 56 / 28 = 2 answer : c
Answer: c
Python program:
a = 1 / 28
b = 2 * a
c = b * 28
Problem: two trains 200 m and 150 m long are running on parallel rails at the rate of 40 kmph and 46 kmph respectively . in how much time will they cross each other , if they are running in the same direction ?
Options: a ) 72 sec , b ) 210 sec , c ) 192 sec , d ) 252 sec , e ) none
Rationale: "solution relative speed = ( 46 - 40 ) kmph = 6 kmph = ( 6 x 5 / 18 ) m / sec = ( 30 / 18 ) m / sec time taken = ( 350 x 18 / 30 ) sec = 210 sec . answer b"
Answer: b
Python program:
a = 200 + 150 
b = a / 1000
c = 46 - 40
d = b / c
e = 3600 * d
Problem: an employee ’ s annual salary was increased 50 % . if her old annual salary equals $ 80,000 , what was the new salary ?
Options: a ) $ 128,000 , b ) $ 120,000 , c ) $ 110,000 , d ) $ 139,000 , e ) $ 125,000
Rationale: "old annual salary = $ 80,000 salary increase = 50 % . original salary = $ 80,000 * 50 / 100 = $ 40,000 new salary = $ 80,000 + $ 40,000 = $ 120,000 hence b ."
Answer: b
Python program:
a = 100 - 10
b = a * 1000
c = 100 - 10
d = c * 1000
e = const_0_25 * 100
f = e * 1000
g = d - f
h = b / g
i = h - 1
j = i * 100
Problem: a can do a job in 15 days and b in 20 days . if they work on it together for 8 days , then the fraction of the work that is left is ?
Options: a ) 2 / 15 , b ) 8 / 15 , c ) 3 / 11 , d ) 1 / 12 , e ) 1 / 15
Rationale: "a ' s 1 day work = 1 / 15 b ' s 1 day work = 1 / 20 a + b 1 day work = 1 / 15 + 1 / 20 = 7 / 60 a + b 8 days work = 7 / 60 * 8 = 14 / 15 remaining work = 1 - 14 / 15 = 1 / 15 answer is e"
Answer: e
Python program:
a = 1 / 15
b = 1 / 20
c = a + b 
d = 8 * c
e = 1 - d
Problem: a dishonest milkman wants to make a profit on the selling of milk . he would like to mix water ( costing nothing ) with milk costing rs . 33 per litre so as to make a profit of 20 % on cost when he sells the resulting milk and water mixture for rs . 36 in what ratio should he mix the water and milk ?
Options: a ) 1 : 20 , b ) 1 : 10 , c ) 1 : 8 , d ) 1 : 4 , e ) 6 : 11
Rationale: cost needed to net a 20 % profit : ( 36 - x ) / x = . 2 x = 30 actual cost : 33 solution ( x = liters of water needed to be added to the 1 liter of milk ) : 33 / ( 1 + x ) = 30 x = 1 / 10 so to get the cost down to 30 milk : water 1 : 1 / 10 or ( 10 / 10 ) : ( 1 / 10 ) answer : b
Answer: b
Python program:
a = 20 / 2
b = 1 / a
Problem: a dishonest shopkeeper professes to sell pulses at the cost price , but he uses a false weight of 980 gm . for a kg . his gain is … % .
Options: a ) 2.04 % , b ) 5.36 % , c ) 4.26 % , d ) 6.26 % , e ) 7.26 %
Rationale: "his percentage gain is 100 * 20 / 980 as he is gaining 20 units for his purchase of 980 units . so 2.04 % . . answer : a"
Answer: a
Python program:
a = 4 + 1 
b = a * 2
c = b * 100
d = 980 / c
e = 1/(d)
f = e - 1
g = f * 100
Problem: if 20 % of a number = 400 , then 120 % of that number will be ?
Options: a ) 20 , b ) 120 , c ) 360 , d ) 2400 , e ) 2820
Rationale: "let the number x . then , 20 % of x = 400 x = ( 400 * 100 ) / 20 = 2000 120 % of x = ( 120 / 100 * 2000 ) = 2400 . answer : d"
Answer: d
Python program:
a = 120 * 400
b = a / 20
Problem: at a certain resort , each of the 39 food service employees is trained to work in a minimum of 1 restaurant and a maximum of 3 restaurants . the 3 restaurants are the family buffet , the dining room , and the snack bar . exactly 17 employees are trained to work in the family buffet , 18 are trained to work in the dining room , and 12 are trained to work in the snack bar . if 4 employees are trained to work in exactly 2 restaurants , how many employees are trained to work in all 3 restaurants ?
Options: a ) 2 , b ) 3 , c ) 4 , d ) 5 , e ) 6
Rationale: "39 = 17 + 18 + 12 - 4 - 2 x 2 x = 17 + 18 + 12 - 4 - 39 = 43 - 39 = 4 x = 2 a"
Answer: a
Python program:
a = 17 + 18 
b = a + 12 
c = b - 4
d = c - 39
e = d / 2
Problem: a cistern is filled by pipe a in 20 hours and the full cistern can be leaked out by an exhaust pipe b in 25 hours . if both the pipes are opened , in what time the cistern is full ?
Options: a ) 50 hrs , b ) 60 hrs , c ) 70 hrs , d ) 80 hrs , e ) 100 hrs
Rationale: "time taken to full the cistern = ( 1 / 20 - 1 / 25 ) hrs = 1 / 100 = 100 hrs answer : e"
Answer: e
Python program:
a = 1 / 20
b = 1 / 25
c = a - b
d = 1 / c
Problem: the population of a town increased from 1 , 75,000 to 2 , 27,500 in a decade . the average percent increase of population per year is
Options: a ) 4.37 % , b ) 5 % , c ) 3 % , d ) 8.75 % , e ) none
Rationale: "solution increase in 10 years = ( 227500 - 175000 ) = 52500 . increase % = ( 52500 / 175000 ã — 100 ) % = 30 % . required average = ( 30 / 10 ) % = 3 % . answer c"
Answer: c
Python program:
a = 10 * 1000
b = a * 10
c = b - 1000
d = c - 1000
e = 2 + 3 
f = e * 100
g = d - f
h = 3 + 4 
i = h * 10
j = 2 + 3 
k = i + j 
l = k * 1000
m = g / l
n = m - 1
o = n / 10
p = o * 100
q = p + 4
Problem: - 54 x 29 + 100 = ?
Options: a ) - 1466 , b ) 2801 , c ) - 2801 , d ) - 2071 , e ) none of them
Rationale: given exp . = - 54 x ( 30 - 1 ) + 100 = - ( 54 x 30 ) + 54 + 100 = - 1620 + 154 = - 1466 answer is a
Answer: a
Python program:
a = 1 - 2
b = 54 * 29
c = b - 100
d = a * c
Problem: if 50 % of 100 is greater than 20 % of a number by 47 , what is the number ?
Options: a ) 60 , b ) 30 , c ) 15 , d ) 75 , e ) 100
Rationale: "explanation : 50 / 100 * 100 - 20 / 100 * x = 47 50 - 20 / 100 * x = 47 3 = 20 / 100 * x 3 * 100 / 20 = x 15 = x answer : option c"
Answer: c
Python program:
a = 50 / 100
b = a * 100
c = b - 47
d = 20 / 100
e = c / d
Problem: running at the same constant rate , 6 identical machines can produce a total of 270 bottles per minute . at this rate , how many bottles could 14 such machines produce in 4 minutes ?
Options: a ) 2520 , b ) 1800 , c ) 2700 , d ) 10800 , e ) none of these
Rationale: "solution let the required number of bottles be x . more machines , more bottles ( direct proportion ) more minutes , more bottles ( direct proportion ) â ˆ ´ 6 ã — 1 ã — x = 14 ã — 4 ã — 270 â ‡ ” x = 14 x 4 x 270 / 6 = 2520 . answer a"
Answer: a
Python program:
a = 270 / 6
b = a * 4
c = b * 14
Problem: a tank holds x gallons of a saltwater solution that is 20 % salt by volume . one fourth of the water is evaporated , leaving all of the salt . when 6 gallons of water and 12 gallons of salt are added , the resulting mixture is 33 1 / 3 % salt by volume . what is the value of x ?
Options: a ) 37.5 , b ) 75 , c ) 100 , d ) 150 , e ) 90
Rationale: nope , 150 . i can only get it by following pr ' s backsolving explanation . i hate that . original mixture has 20 % salt and 80 % water . total = x out of which salt = 0.2 x and water = 0.8 x now , 1 / 4 water evaporates and all salt remains . so what remains is 0.2 x salt and 0.6 x water . now 12 gallons salt is added and 6 gallons of water is added . so salt now becomes - > ( 0.2 x + 12 ) and water - - > ( 0.6 x + 6 ) amount of salt is 33.33 % of total . so amount of water is 66.66 % . so salt is half of the volume of water . so ( 0.2 x + 12 ) = ( 0.6 x + 6 ) / 2 = > 0.4 x + 24 = 0.6 x + 6 - > 0.2 x = 18 solving , x = 90 answer : e
Answer: e
Python program:
a = 12 * 2
b = a - 6
c = 20 / 100
d = 1 - c
e = 20 / 100
f = 1 - e
g = 1 / 4
h = f * g
i = d - h
j = 20 / 100
k = 2 * j
l = i - k
m = b / l
Problem: there are 250 female managers in a certain company . find the total number of female employees in the company , if 2 / 5 of all the employees are managers and 2 / 5 of all male employees are managers .
Options: a ) 325 , b ) 425 , c ) 625 , d ) 700 , e ) none of these
Rationale: as per question stem 2 / 5 m ( portion of men employees who are managers ) + 250 ( portion of female employees who are managers ) = 2 / 5 t ( portion of total number of employees who are managers ) , thus we get that 2 / 5 m + 250 = 2 / 5 t , or 2 / 5 ( t - m ) = 250 , from here we get that t - m = 625 , that would be total number of female employees and the answer ( c )
Answer: c
Python program:
a = 2 / 5
b = 250 / a
Problem: income and expenditure of a person are in the ratio 15 : 8 . if the income of the person is rs . 15000 , then find his savings ?
Options: a ) 6999 , b ) 7000 , c ) 7001 , d ) 7002 , e ) 7003
Rationale: "let the income and the expenditure of the person be rs . 15 x and rs . 8 x respectively . income , 15 x = 15000 = > x = 1000 savings = income - expenditure = 15 x - 8 x = 7 x = 7 ( 1000 ) so , savings = rs . 7000 . answer : b"
Answer: b
Python program:
a = 8 / 15
b = a * 15000
c = 15000 - b
Problem: ashok secured average of 78 marks in 6 subjects . if the average of marks in 5 subjects is 74 , how many marks did he secure in the 6 th subject ?
Options: a ) 66 , b ) 74 , c ) 78 , d ) 98 , e ) none of these
Rationale: "explanation : number of subjects = 6 average of marks in 6 subjects = 78 therefore total marks in 6 subjects = 78 * 6 = 468 now , no . of subjects = 5 total marks in 5 subjects = 74 * 5 = 370 therefore marks in 6 th subject = 468 – 370 = 98 answer d"
Answer: d
Python program:
a = 78 * 6
b = 74 * 5
c = a - b
Problem: a man performs 1 / 2 of the total journey by rail , 1 / 3 by bus and the remaining 4 km on foot . his total journey is
Options: a ) 16 km , b ) 10 km , c ) 12 km , d ) 24 km , e ) 25 km
Rationale: "explanation : let the journey be x km then , 1 x / 2 + 1 x / 3 + 4 = x 5 x + 24 = 6 x x = 24 km answer : option d"
Answer: d
Python program:
a = 3 * 4
Problem: a hat company ships its hats , individually wrapped , in 8 - inch by 10 - inch by 12 - inch boxes . each hat is valued at $ 7.50 . if the company ’ s latest order required a truck with at least 384,000 cubic inches of storage space in which to ship the hats in their boxes , what was the minimum value of the order ?
Options: a ) $ 3,000 , b ) $ 1,350 , c ) $ 1,725 , d ) $ 2,050 , e ) $ 2,250
Rationale: number of boxes = total volume / volume of one box = 384,000 / ( 8 * 10 * 12 ) = 400 one box costs 7.50 , so 400 box will cost = 400 * 7.5 = 3000 a is the answer
Answer: a
Python program:
a = 3 * 100
b = 8 * 10
c = a + b 
d = c + 4 
e = d * 1000
f = 8 * 10
g = f * 12
h = e / g
i = h * 7
j = i / 1000
Problem: if p / q = 3 / 5 , then 2 p + q = ?
Options: a ) 12 , b ) 11 , c ) 13 , d ) 15 , e ) 16
Rationale: "let p = 3 , q = 5 then 2 * 3 + 5 = 11 so 2 p + q = 11 . answer : b"
Answer: b
Python program:
a = 3 * 2
b = a + 5
Problem: fred and sam are standing 100 miles apart and they start walking in a straight line toward each other at the same time . if fred walks at a constant speed of 5 miles per hour and sam walks at a constant speed of 5 miles per hour , how many miles has sam walked when they meet ?
Options: a ) 5 , b ) 9 , c ) 25 , d ) 30 , e ) 75
Rationale: "relative distance = 100 miles relative speed = 5 + 5 = 10 miles per hour time taken = 100 / 10 = 15 hours distance travelled by sam = 15 * 5 = 75 miles = e"
Answer: e
Python program:
a = 5 + 5 
b = 100 / a
c = 5 * b
Problem: the difference between a two digit number and the number obtained by interchanging the digits is 36 . what is the difference between the sum and the difference of the digits of the number if the ratio between the digits of the number is 1 : 2 ?
Options: a ) 4 , b ) 8 , c ) 12 , d ) 16 , e ) 18
Rationale: sol . since the number is greater than the number obtained on reversing the digits , so the ten ' s is greater than the unit ' s digit . let the ten ' s and units digit be 2 x and x respectively . then , ( 10 × 2 x + x ) - ( 10 x + 2 x ) = 36 ⇔ 9 x = 36 ⇔ x = 4 . ∴ required difference = ( 2 x + x ) - ( 2 x - x ) = 2 x = 8 . answer b
Answer: b
Python program:
a = 3 - 1
b = 10 * 2
c = b + 1 
d = 10 + 2 
e = c - d
f = 36 / e
g = a * f
Problem: 40 + 5 * 12 / ( 180 / 3 ) = ?
Options: a ) 23 , b ) 78 , c ) 27 , d ) 61 , e ) 41
Rationale: "explanation : 40 + 5 * 12 / ( 180 / 3 ) = 40 + 5 * 12 / ( 60 ) = 40 + ( 5 * 12 ) / 60 = 40 + 1 = 41 . answer : e"
Answer: e
Python program:
a = 5 * 12
b = 180 / 3
c = a / b
d = 40 + c
Problem: on dividing 13787 by a certain number , we get 89 as quotient and 14 as remainder . what is the divisor ?
Options: a ) 743 , b ) 155 , c ) 852 , d ) 741 , e ) 785
Rationale: "divisor * quotient + remainder = dividend divisor = ( dividend ) - ( remainder ) / quotient ( 13787 - 14 ) / 89 = 155 answer ( b )"
Answer: b
Python program:
a = 13787 - 14
b = a / 89
Problem: in a mixture 60 litres , the ra ɵ o of milk and water 2 : 1 . if the this ra ɵ o is to be 1 : 2 , then the quanity of water to be further added is
Options: a ) 20 liters , b ) 30 liters , c ) 50 liters , d ) 60 liters , e ) none of these
Rationale: explanation : quantity of milk = 60 * ( 2 / 3 ) = 40 liters quantity of water = 60 - 40 = 20 liters answer : d
Answer: d
Python program:
a = 60 * 2
b = 2 + 1 
c = a / b
d = c * 2
e = 60 * 2
f = 2 + 1 
g = e / f
h = 60 - g
i = d - h
Problem: a scale 6 ft . 8 inches long is divided into 4 equal parts . find the length of each part
Options: a ) 17 inches , b ) 20 inches , c ) 15 inches , d ) 18 inches , e ) 19 inches
Rationale: "explanation : total length of scale in inches = ( 6 * 12 ) + 8 = 80 inches length of each of the 4 parts = 80 / 4 = 20 inches answer : b"
Answer: b
Python program:
a = 6 * 12
b = a + 8 
c = b / 4
Problem: ramu bought an old car for rs . 42000 . he spent rs . 12000 on repairs and sold it for rs . 64900 . what is his profit percent ?
Options: a ) 12 % , b ) 16 % , c ) 20.18 % , d ) 82 % , e ) 23 %
Rationale: "total cp = rs . 42000 + rs . 12000 = rs . 54000 and sp = rs . 64900 profit ( % ) = ( 64900 - 54000 ) / 54000 * 100 = 20.18 % answer : c"
Answer: c
Python program:
a = 42000 + 12000 
b = 64900 - a
c = 42000 + 12000 
d = b / c
e = d * 100
Problem: there are 79 people that own pets . 15 people own only dogs , 10 people own only cats , 5 people own only cats and dogs , 3 people own cats , dogs and snakes . how many total snakes are there ?
Options: a ) 2 , b ) 4 , c ) 8 , d ) 49 , e ) 32
Rationale: lets assign variables to all the areas in venn diagram of three . three different units are dog , cat , snake = total = 79 only dog = d = 15 only cat = c = 10 only snake = s exactly dog and cat = 5 exactly dog and snake = x exactly cat and snake = y all three = 3 so 79 = 15 + 10 + 5 + 3 + x + y + s we need to know total snakes = x + y + s + 3 = 49 answer : d
Answer: d
Python program:
a = 15 + 10 
b = a + 5 
c = b + 3 
d = 79 - c
e = d + 3