euclaise/mathqa_programs huggingface dataset:
Problem: the price of 10 chairs is equal to that of 4 tables . the price of 15 chairs and 2 tables together is rs . 4000 . the total price of 12 chairs and 3 tables is :
Options: a ) rs . 3900 , b ) rs . 3990 , c ) rs . 4000 , d ) rs . 4100 , e ) rs . 4200
Rationale: "let the cost of a chair and that of a table be rs . x and rs . y respectively . then , 10 x = 4 y or y = 5 x . 2 15 x + 2 y = 4000 15 x + 2 x 5 x = 4000 2 20 x = 4000 x = 200 . so , y = 5 x 200 = 500 . 2 hence , the cost of 12 chairs and 3 tables = 12 x + 3 y = rs . ( 2400 + 1500 ) = rs . 3900 . a"
Answer: a
Python program:
a = 4 / 10
b = 15 * a
c = b + 2 
d = 4000 / c
e = d * 3
f = 4 / 10
g = 4 / 10
h = 15 * g
i = h + 2 
j = 4000 / i
k = f * j
l = k * 12
m = e + l
Problem: if the remainder is 15 when the integer n is divided by 28 , what is the remainder when 2 n is divided by 14 ?
Options: a ) 0 , b ) 1 , c ) 2 , d ) 3 , e ) 4
Rationale: "n = 28 k + 15 2 n = 2 ( 28 k + 15 ) = 4 k * 14 + 30 = 4 k * 14 + 2 * 14 + 2 = 14 j + 2 the answer is c ."
Answer: c
Python program:
a = 15 * 2
b = a - 28
Problem: rice weighing 25 / 2 pounds was divided equally and placed in 4 containers . how many ounces of rice were in each container ? ( note that 1 pound = 16 ounces )
Options: a ) 40 , b ) 50 , c ) 60 , d ) 70 , e ) 80
Rationale: "25 / 2 ÷ 4 = 25 / 8 pounds in each container 25 / 8 pounds * 16 ounces / pound = 50 ounces in each container the answer is b ."
Answer: b
Python program:
a = 25 / 2
b = a * 16
c = b / 4
Problem: a man sold 18 toys for rs . 21000 , gaining thereby the cost price of 3 toy find the cost price of a toy
Options: a ) s . 600 , b ) s . 800 , c ) s . 500 , d ) s . 900 , e ) s . 1000
Rationale: "let the cost of one toy = x . then , cost of 18 toys = 18 x . gain = 3 x . sp of 18 toys = rs . 21000 . gain = sp â € “ cp 3 x = 21000 â € “ 18 x 21 x = 21000 x = rs . 1000 . answer : option e"
Answer: e
Python program:
a = 18 + 3 
b = 21000 / a
Problem: in a school of 700 students , 45 % wear blue shirts , 23 % wear red shirts , 15 % wear green shirts , and the remaining students wear other colors . how many students wear other colors ( not blue , not red , not green ) ?
Options: a ) 109 , b ) 119 , c ) 129 , d ) 139 , e ) 149
Rationale: 45 + 23 + 15 = 83 % 100 – 83 = 17 % 700 * 17 / 100 = 119 the answer is b .
Answer: b
Python program:
a = 45 / 100
b = a * 700
c = 23 / 100
d = c * 700
e = b + d 
f = 15 / 100
g = f * 700
h = e + g 
i = 700 - h
Problem: two brother x and y appeared for an exam . the probability of selection of x is 1 / 7 and that of b is 2 / 9 . find the probability that both of them are selected .
Options: a ) 2 / 69 , b ) 2 / 60 , c ) 2 / 63 , d ) 2 / 29 , e ) 2 / 10
Rationale: "explanation : let a be the event that x is selected and b is the event that y is selected . p ( a ) = 1 / 7 , p ( b ) = 2 / 9 . let c be the event that both are selected . p ( c ) = p ( a ) × p ( b ) as a and b are independent events : = ( 1 / 7 ) × ( 2 / 9 ) = 2 / 63 answer : c ) 2 / 63"
Answer: c
Python program:
a = 1 / 7
b = 2 / 9
c = a * b
Problem: 150 metres long yard , 11 trees are palnted at equal distances , one tree being at each end of the yard . what is the distance between 2 consecutive trees
Options: a ) 10 , b ) 15 , c ) 14 , d ) 16 , e ) 17
Rationale: "11 trees have 10 gaps between them , required distance ( 150 / 10 ) = 15 b"
Answer: b
Python program:
a = 11 - 2
b = a + 1 
c = 150 / b
Problem: a sells a cricket bat to b at a profit of 20 % . b sells it to c at a profit of 25 % . if c pays $ 231 for it , the cost price of the cricket bat for a is :
Options: a ) 150 , b ) 120 , c ) 154 , d ) 160 , e ) 210
Rationale: 125 % of 120 % of a = 231 125 / 100 * 120 / 100 * a = 231 a = 231 * 2 / 3 = 154 . answer c
Answer: c
Python program:
a = 20 / 100
b = 1 + a 
c = 25 / 100
d = 1 + c 
e = b * d
f = 231 / e
Problem: a boat running up stram takes 4 hours to cover a certain distance , while it takes 8 hours to cover the same distance running down stream . what is the ratio between the speed of the boat and the speed of water current respectively ?
Options: a ) 2 : 3 , b ) 5 : 6 , c ) 4 : 5 , d ) 3 : 1 , e ) 8 : 1
Rationale: "explanation : let speed of boat is x km / h and speed stream is y km / hr 4 ( x + y ) = 8 ( x - y ) 4 x + 4 y = 8 x - 8 y 12 y = 4 x 3 y = x x / y = 3 / 1 3 : 1 answer : option d"
Answer: d
Python program:
a = 8 - 4
Problem: a farmer used 1,034 acres of land for beans , wheat , and corn in the ratio of 5 : 2 : 4 , respectively . how many w acres were used for corn ?
Options: a ) 188 , b ) 258 , c ) 376 , d ) 470 , e ) 517
Rationale: "consider 5 x acres of land used for bean consider 2 x acres of land used for wheat consider 4 x acres of land used for corn total given is 1034 acres 11 x = 1034 x = 94 land used for corn w = 4 * 94 = 376 correct option - c"
Answer: c
Python program:
a = 1000 * 1
b = 10 * 3
c = b + 4 
d = a + c 
e = 5 + 2 
f = e + 4 
g = d / f
h = g * 4
Problem: find the l . c . m of 22 , 25 , 44 and 20 .
Options: a ) 1240 , b ) 1600 , c ) 1320 , d ) 1150 , e ) 1100
Rationale: "explanation : 2 x 2 x 11 x 5 x 5 = 1100 answer : option e"
Answer: e
Python program:
a = 3 ** 3
b = 2 ** 3
c = 4 + 1 
d = c ** 2
e = b * d
f = a * e
g = 44 / 2
h = g / 2
i = h / 3
j = 4 + 1 
k = i / j
l = 4 + 1 
m = k / l
n = f * m
Problem: 3 models ( f , g , and h ) of cars are distributed among 3 showrooms . the number of cars in each showrooms must be equal and each model must be represented by at least one car in every showroom . there are 19 cars of model f , 17 cars of model g , and 15 cars of model h . what is the maximum number of cars of model f in any showroom ?
Options: a ) 17 , b ) 16 , c ) 15 , d ) 14 , e ) 13
Rationale: the total number of cars is 51 . so each showroom has 17 cars ( since the number of cars in each showrooms should be equal 51 / 3 = 17 ) . moreover that the number of model f is maximum means that the numbers of model g and h should be minimum . since each model must be represented by at least one car in every showroom that minimum number should be 1 . so maximum number of model f is 17 - 2 = 15 . the answer is ( c )
Answer: c
Python program:
a = 19 + 17 
b = a + 15 
c = b / 3
d = 3 - 1
e = c - d
Problem: the timing of a college is from 12 p . m to 5.00 p . m . five lectures are held in the given duration and a break of 5 minutes after each lecture is given to the students . find the duration of each lecture .
Options: a ) 56 minutes , b ) 45 minutes , c ) 30 minutes , d ) 48 minutes , e ) 44 minutes
Rationale: "explanation : total time a student spends in college = 5 hours 00 minutes = 300 minutes as there are 5 lectures , the number of breaks between lectures is 4 . total time of the break = 20 minutes hence , the duration of each lecture is = ( 300 â € “ 20 ) / 5 = 56 minutes answer a"
Answer: a
Python program:
a = 5 * 0
b = a / 5
Problem: if q = x ^ 4 + y ^ 4 = 100 , then the greatest possible value of x is between
Options: a ) 0 and 3 , b ) 3 and 6 , c ) 6 and 9 , d ) 9 and 12 , e ) 12 and 15
Rationale: my attempt : if q = x ^ 4 + y ^ 4 = 100 , then the greatest possible value of x would be when y is minimum . let y ^ 4 be 0 . now x ^ 4 = 100 . x should be definitely greater than 3 but less than 4 . the only option that fits this range is b hence answer is - - b ) 3 and 6 .
Answer: b
Python program:
a = 10 * 3
b = 4 + 2 
c = a + b
Problem: what is the units digit of 29 ! + 50 ! + 3 ! + 3 ! ?
Options: a ) 0 , b ) 2 , c ) 4 , d ) 6 , e ) 8
Rationale: "for all n greater than 4 , the units digit of n ! is 0 . the sum of the four units digits is 0 + 0 + 6 + 6 = 12 the units digit is 2 . the answer is b ."
Answer: b
Python program:
a = 4 + 3 
b = a + 2
Problem: a train 285 m long , running with a speed of 54 km / hr will pass a tree in
Options: a ) 19 sec , b ) 15 sec , c ) 16 sec , d ) 20 sec , e ) none
Rationale: "sol . speed = ( 54 x 5 / 18 ) m / sec . = 15 m / sec . time taken = ( 285 x 1 / 15 ) sec = 19 sec answer a"
Answer: a
Python program:
a = 54 * 1000
b = 285 / a
c = b * 3600
Problem: a group of 55 adults and 70 children go for trekking . if there is meal for either 70 adults or 90 children and if 7 adults have their meal , find the total number of children that can be catered with the remaining food .
Options: a ) 33 , b ) 54 , c ) 81 , d ) 17 , e ) 01
Rationale: "explanation : as there is meal for 70 adults and 7 have their meal , the meal left can be catered to 63 adults . now , 70 adults = 90 children 7 adults = 9 children therefore , 63 adults = 81 children hence , the meal can be catered to 81 children . answer : c"
Answer: c
Python program:
a = 70 - 7
b = 90 / 70
c = a * b
Problem: if 42 / 330 = 0.1272 , what is the 32 nd digit to the right of the decimal point of the fraction ?
Options: a ) 1 , b ) 4 , c ) 5 , d ) 7 , e ) 2
Rationale: "we are not concerned what 42 / 330 means . . we have to look at the decimal . . 0 . . 1272 means 0.1272727 . . . so leaving first digit to the right of decimal , all odd numbered are 7 and all even numbered are 2 . here 32 is even , so ans is 2 answer is e"
Answer: e
Python program:
a = 2 + 3
Problem: a began business with rs . 36000 and was joined afterwards by b with rs . 54000 . when did b join if the profits at the end of the year were divided in the ratio of 2 : 1 ?
Options: a ) 1 , b ) 6 , c ) 7 , d ) 8 , e ) 2
Rationale: "36 * 12 : 54 * x = 2 : 1 x = 4 12 - 4 = 8 answer : d"
Answer: d
Python program:
a = 4 * 3
b = 4 * 3
c = 36000 * b
d = c / 54000
e = d / 2
f = a - e
Problem: find the value of √ ( 25 / 16 ) .
Options: a ) 5 / 2 , b ) 3 / 4 , c ) 2 / 3 , d ) 1 / 3 , e ) 5 / 4
Rationale: "√ ( 25 / 16 ) = √ 25 / √ 16 = 5 / 4 answer is e ."
Answer: e
Python program:
a = 16 - 4
b = a * 25
Problem: how many of the positive factors of 24 are not factors of 25
Options: a ) 2 , b ) 3 , c ) 4 , d ) 1 , e ) 5
Rationale: "factors of 24 - 1 , 2 , 3 , 4 , 6 , 8 , 12,24 factors of 25 - 1,5 , 25 comparing both , we have 1 factor of 24 which are not factors of 25 - 1 answer : d"
Answer: d
Python program:
a = 25 / 24
Problem: a man can do a piece of work in 4 days , but with the help of his daughter , he can do it in 3 days . in what time can his daughter do it alone ?
Options: a ) 12 , b ) 28 , c ) 26 , d ) 19 , e ) 112
Rationale: explanation : daughter ’ s 1 day ’ s work = ( 1 / 3 – 1 / 4 ) = 1 / 12 daughter alone can do the work in 12 / 1 = 12 days answer : a
Answer: a
Python program:
a = 4 * 3
b = 4 - 3
c = a / b
Problem: john had a stock of 900 books in his bookshop . he sold 75 on monday , 50 on tuesday , 64 on wednesday , 78 on thursday and 135 on friday . what percentage of the books were not sold ?
Options: a ) 50.4 % , b ) 23.8 % , c ) 66.5 % , d ) 34.9 % , e ) 55.3 %
Rationale: "let n be the total number of books sold . hence n = 75 + 50 + 64 + 78 + 135 = 402 let m be the books not sold m = 900 - n = 900 - 402 = 498 percentage books not sold / total number of books = 498 / 900 = 0.553 = 55.3 % correct answer e"
Answer: e
Python program:
a = 75 + 50 
b = 64 + 78 
c = a + b 
d = c + 135 
e = 900 - d
f = e / 900
g = f * 100
Problem: a sum of money at simple interest amounts to rs . 825 in 3 years and to rs . 854 in 4 years . the sum is :
Options: a ) 647 , b ) 738 , c ) 654 , d ) 847 , e ) 976
Rationale: "s . i . for 1 year = rs . ( 854 - 825 ) = rs . 29 . s . i . for 3 years = rs . ( 29 x 3 ) = rs . 87 . principal = rs . ( 825 - 87 ) = rs . 738 answer : b"
Answer: b
Python program:
a = 854 - 825
b = a * 3
c = b / 4
d = 825 - c
Problem: the age of father 7 years ago was 5 times the age of his son . 5 years hence , father ' s age will be thrice that of his son . the ratio of their present ages is :
Options: a ) 67 : 19 , b ) 65 : 17 , c ) 61 : 19 , d ) 63 : 15 , e ) 67 : 17
Rationale: let the ages of father and son 7 years ago be 5 x and x years respectively . then , ( 5 x + 7 ) + 5 = 3 [ ( x + 7 ) + 5 ] 5 x + 12 = 3 x + 36 x = 12 . required ratio = ( 5 x + 7 ) : ( x + 7 ) = 67 : 19 . answer : option a
Answer: a
Python program:
a = 5 * 3
b = 7 * 5
c = b - 7
d = a + c 
e = d - 5
f = 5 - 3
g = e / f
h = 5 * g
i = 7 * 5
j = i - 7
k = h - j
l = 5 * 3
m = 7 * 5
n = m - 7
o = l + n 
p = o - 5
q = 5 - 3
r = p / q
s = k / r
Problem: huey ' s hip pizza sells two sizes of square pizzas : a small pizza that measures 14 inches on a side and costs $ 10 , and a large pizza that measures 21 inches on a side and costs $ 20 . if two friends go to huey ' s with $ 30 apiece , how many more square inches of pizza can they buy if they pool their money than if they each purchase pizza alone ?
Options: a ) 5 square inches , b ) 10 square inches , c ) 49 square inches , d ) 25 square inches , e ) 350 square inches
Rationale: "in the first case each can buy one pizza of $ 10 and one pizza of $ 20 . in square inches that would be ( 14 * 14 = 196 ) for the small pizza and ( 21 * 21 = 441 ) for the large pizza . in total sq inches that would be ( 196 + 441 ) * 2 = 1274 sq inches . in the second case if they pool their money together they can buy 3 large pizzas . in terms of square inches that would be 3 * 441 = 1323 sq inches . hence , the difference is 49 square inches more ( 1323 - 1274 ) . the correct answer is c"
Answer: c
Python program:
a = 21 ** 2
b = a * 3
c = 14 ** 2
d = 21 ** 2
e = c + d 
f = 14 ** 2
g = 21 ** 2
h = f + g 
i = e + h 
j = b - i
Problem: if the lcm of a and b is 72 and their hcf is 6 , what is the product of a & b ?
Options: a ) 432 , b ) 433 , c ) 434 , d ) 435 , e ) 436
Rationale: the most important property of lcm ( the least common multiple ) and gcd ( the greatest common divisors ) is : for any positive integers x and y , x ∗ y = gcd ( x , y ) ∗ lcm ( x , y ) so ab = 72 * 6 = 432 . answer : a
Answer: a
Python program:
a = 6 * 72
Problem: in a 120 meters race a beats b by 56 m or 7 seconds . a ' s time over the course is :
Options: a ) 22 seconds , b ) 12 seconds , c ) 10 seconds , d ) 8 seconds , e ) 28 seconds
Rationale: "b runs 56 m in 7 sec . = > b runs 120 m in 7 / 56 * 120 = 15 seconds since a beats b by 7 seconds , a runs 120 m in ( 15 - 7 ) = 8 seconds hence , a ' s time over the course = 8 seconds answer : d"
Answer: d
Python program:
a = 7 / 56
b = a * 120
c = b - 7
Problem: if x is a randomly chosen integer between 1 and 20 , inclusive , and y is a randomly chosen integer between 21 and 40 , inclusive , what is the probability that xy is a multiple of 4 ?
Options: a ) 1 / 4 , b ) 1 / 3 , c ) 3 / 8 , d ) 7 / 16 , e ) ½
Rationale: there are two ways that i see of getting a multiple of 4 1 ) x and / or y is a multiple of 4 2 ) x is a multiple of 2 and y is a multiple of 2 for 1 we have p ( option 1 ) = ( 5 / 20 ) ( 20 / 20 ) + ( 5 / 20 ) ( 20 / 20 ) - ( 5 / 20 ) ( 5 / 20 ) = 1 / 2 - 1 / 16 since 5 of the numbers in each range are divisible by 4 , and if either x or y is selected to be divisible by 4 the selection of the other variable does not matter . notice the last subtraction term which corrects the fact that we have counted the possibility of both being divisible by 4 twice ( e . g . p ( a union b ) = p ( a ) + p ( b ) - p ( a and b ) ) . notice at this point that the probability of option one is already 7 / 16 , the second largest available option . if we can come up with any other possibilities for getting xy divisble by 4 we must go with option e . of course this is the case because if we select a multiple of 2 that is not a multiple of 4 from both ranges of numbers , the product is divisible by 4 . we can formally compute this as : p ( option 2 ) = ( 5 / 20 ) * ( 5 / 20 ) = 1 / 16 since we do not wish to double count possibilities that fall into category 1 , we only count the probability of selecting even numbers from each set that are not divisible by 4 ( e . g . the other 5 even integers in each set ) . total probability is then p ( option 1 ) + p ( option 2 ) = 1 / 2
Answer: e
Python program:
a = 1 / 2
b = 1 / 2
c = a * b
d = 1 / 2
e = c * d
f = 1 / 2
g = 1 / 2
h = f * g
i = 1 / 2
j = 1 / 2
k = i * j
l = 1 / 2
m = k * l
n = h + m 
o = e + n 
p = 1 - o
Problem: the average of 20 number is zero of them at the most , how many may be greater than zero ?
Options: a ) 0 , b ) 1 , c ) 10 , d ) 19 , e ) 20
Rationale: solution average of 20 numbers = 0 . ∴ sum of 20 numbers = ( 0 × 20 ) = 0 . it is quite possible that 19 of these number may be positive and if their sum is a , then 20 th number is ( - a ) . answer d
Answer: d
Python program:
a = 20 - 1
Problem: find the principle on a certain sum of money at 5 % per annum for 2 2 / 5 years if the amount being rs . 1792 ?
Options: a ) 1600 , b ) 2777 , c ) 2889 , d ) 27670 , e ) 2771
Rationale: "1792 = p [ 1 + ( 5 * 12 / 5 ) / 100 ] p = 1600 . answer : a"
Answer: a
Python program:
a = 2 * 5
b = a + 2 
c = b / 5
d = c * 5
e = d / 100
f = e + 1 
g = 1792 / f
Problem: of the 13 employees in a certain department , 1 has an annual salary of 38,000 , 2 have an annual salary of 45,800 each , 2 have an annual salary of 42,500 each , 3 have an annual salary of 40,000 each and 5 have an annual salary of 48,500 each . what is the median annual salary for the 13 employees ?
Options: a ) 38,000 , b ) 40,000 , c ) 42,500 , d ) 45,800 , e ) 48,500
Rationale: "median is just the value in the middle when you arrange all values in the ascending order in this question , the 7 th value would be the median ( since there are 13 employees ) 38 , 40 , 40 , 40 , 42.5 , 42.5 , 45.8 so , answer is d ."
Answer: d
Python program:
a = 100 * 100
b = a * 4
Problem: there are 200 female managers in a certain company . find the total number r 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 ) r = 300 , b ) r = 400 , c ) r = 500 , d ) 600 , e ) none of these
Rationale: "{ managers } = { female managers } + { male managers } ; we are told that the total number of managers in the company is 2 / 5 of all the employees , thus { managers } = 2 / 5 ( m + f ) , where m and f are number of female and male employees , respectively . also , we know that 2 / 5 of all male employees are managers : { male managers } = 2 / 5 * mas well as there are total of 200 female managers : { female managers } = 200 ; thus : 2 / 5 ( m + f ) = 200 + 2 / 5 * m - - > f = 500 . answer : c ."
Answer: c
Python program:
a = 2 / 5
b = 200 / a
Problem: in a certain boys camp , 20 % of the total boys are from school a and 30 % of those study science . if there are 49 boys in the camp that are from school a but do not study science then what is the total number of boys in the camp ?
Options: a ) 70 , b ) 245 , c ) 150 , d ) 35 , e ) 350
Rationale: "since 30 % of the boys from school a study science , then 70 % of the boys from school a do not study science and since 20 % of the total number of boys are from school a , then 0.2 * 0.7 = 0.14 , or 14 % of the boys in the camp are from school a and do not study science . we are told that this number equals to 49 , so 0.14 * { total } = 49 - - > { total } = 350 . answer : e ."
Answer: e
Python program:
a = 100 - 30
b = a / 100
c = 20 / 100
d = b * c
e = 49 / d
Problem: how many litres of pure acid are there in 8 litres of a 20 % solution ?
Options: a ) 2 litres , b ) 1.4 litres , c ) 1 litres , d ) 1.6 litres , e ) none of these
Rationale: "explanation : quantity of pure acid = 8 × ( 20 / 100 ) = 1.6 answer : option d"
Answer: d
Python program:
a = 20 / 100
b = a * 8
Problem: a 1200 m long train crosses a tree in 120 sec , how much time will i take to pass a platform 500 m long ?
Options: a ) 266 sec , b ) 170 sec , c ) 776 sec , d ) 166 sec , e ) 997 sec
Rationale: "l = s * t s = 1200 / 120 s = 10 m / sec . total length ( d ) = 1700 m t = d / s t = 1700 / 10 t = 170 sec answer : b"
Answer: b
Python program:
a = 1200 + 500 
b = 1200 / 120
c = a / b
Problem: what is the least number which when divided by 6 , 7 , 9 and 18 leaves remainder 4 in each care ?
Options: a ) 130 , b ) 140 , c ) 136 , d ) 156 , e ) 166
Rationale: "explanation : lcm of 6 , 7 , 9 and 18 is 126 required number = 126 + 4 = 130 answer : option a"
Answer: a
Python program:
a = math.lcm(6, 7)
b = math.lcm(9, 18)
c = math.lcm(a, b)
d = c + 4
Problem: the profit earned by selling an article for rs . 832 is equal to the loss incurred when the same article is sold for rs . 448 . what should be the sale price for making 50 % profit ?
Options: a ) 277 , b ) 960 , c ) 277 , d ) 266 , e ) 121
Rationale: "let c . p . = rs . x . then , 832 - x = x - 448 2 x = 1280 = > x = 640 required s . p . = 150 % of rs . 640 = 150 / 100 * 640 = rs . 960 . answer : b"
Answer: b
Python program:
a = 832 - 448
b = a / 2
c = 832 - b
d = 50 / 100
e = 1 + d 
f = c * e
Problem: a room 14 m 21 cm long and 7 m 77 cm broad is to be paved with square tiles . find the least number of square tiles required to cover the floor .
Options: a ) 22636 , b ) 22640 , c ) 22647 , d ) 22533 , e ) 22675
Rationale: "explanation : area of the room = ( 1421 x 777 ) cm 2 . size of largest square tile = h . c . f . of 1421 cm and 777 cm = 7 cm . area of 1 tile = ( 7 x 7 ) cm 2 . number of tiles required = ( 1147 × 777 ) / ( 7 × 7 ) = 22533 answer : option d"
Answer: d
Python program:
a = 14 * 100
b = a + 21 
c = 7 * 100
d = c + 77 
e = b * d
f = 2 * 4
g = f + 2 
h = 21 - g
i = 2 * 4
j = i + 2 
k = 21 - j
l = h * k
m = e / l
Problem: roja and pooja start moving in the opposite directions from a pole . they are moving at the speeds of 5 km / hr and 3 km / hr respectively . after 4 hours what will be the distance between them ?
Options: a ) 32 km , b ) 20 km , c ) 65 km , d ) 18 km , e ) 16 km
Rationale: "distance = relative speed * time = ( 5 + 3 ) * 4 = 32 km [ they are travelling in the opposite direction , relative speed = sum of the speeds ] . answer : a"
Answer: a
Python program:
a = 5 + 3 
b = a * 4
Problem: the number which exceeds 16 % of it by 105 is :
Options: a ) 125 , b ) 52 , c ) 58 , d ) 60 , e ) 62
Rationale: solution solution let the number be x . x - 16 % of x = 105 x - 16 / 100 x = 105 x - 4 / 25 x = 105 21 / 25 x = 105 x = ( 105 x 25 / 21 ) = 125 answer a
Answer: a
Python program:
a = 105 * 100
b = 100 - 16
c = a / b
Problem: sachin is younger than rahul by 7 years . if the ratio of their ages is 6 : 9 , find the age of sachin
Options: a ) 24.5 , b ) 14 , c ) 24.21 , d ) 27 , e ) 25
Rationale: "explanation : if rahul age is x , then sachin age is x - 7 , so , 9 x - 63 = 6 x 3 x = 63 x = 21 so sachin age is 21 - 7 = 14 answer : b ) 14"
Answer: b
Python program:
a = 9 - 6
b = 7 / a
c = b * 6
Problem: a man has some hens and cows . if the number of heads be 44 and the number of feet equals 140 , then the number of hens will be :
Options: a ) 22 , b ) 23 , c ) 18 , d ) 26 , e ) 28
Rationale: "let hens be x and cows be y now , feet : x * 2 + y * 4 = 140 heads : x * 1 + y * 1 = 44 implies , 2 x + 4 y = 140 and x + y = 44 solving these two equations , we get x = 18 and y = 26 therefore , hens are 26 . answer : c"
Answer: c
Python program:
a = 44 * 4
b = a - 140
c = b / 2
Problem: in the x - y plane , there are 4 points ( 00 ) , ( 04 ) , ( 54 ) , and ( 50 ) . if these 4 points makes a rectangle , what is the probability that x + y < 4 ?
Options: a ) 2 / 3 , b ) 2 / 5 , c ) 3 / 4 , d ) 3 / 7 , e ) 5 / 8
Rationale: the line y = - x + 4 intersects the rectangle and these three points of intersection ( 0,0 ) , ( 0,4 ) and ( 4,0 ) form a triangle . the points below the line y = - x + 4 satisfy x + y < 4 . the area of this triangle is ( 1 / 2 ) ( 4 ) ( 4 ) = 8 the area of the rectangle is 20 . p ( x + y < 4 ) = 8 / 20 = 2 / 5 the answer is b .
Answer: b
Python program:
a = 4 / 2
b = 50 / 10
c = a / b
Problem: the probability of two events a and b are 0.25 and 0.35 respectively . the probability that both a and b occur is 0.15 . the probability that neither a nor b occur is _________
Options: a ) 0.55 , b ) 0.4 , c ) 0.5 , d ) 0.05 , e ) 0.6
Rationale: "we are apply that formula . . . . . . . . . . . . . . p ( aorb ) = p ( a ) + p ( b ) - p ( a and b ) = . 25 + . 35 - . 15 = . 45 but the probability of neither a nor b = 1 - . 45 = 0.55 answer : a"
Answer: a
Python program:
a = 0 + 25 
b = a - 0
c = 1 - b