Question 1

62976 ÷? = 123

Accepted Answer

Let 62976/N = 123 Then N = 62976 / 123 = 512.

Question 2

If x/y =3/4, then the value of [6/7 + (y - x) / (y + x)] equals?

Accepted Answer

Given Exp. = 6/7 + [(y - x)/(y + x)] = 6/7 + [1 - (x/y) / 1 + (x/y)] = 6/7 + [1 - (3/4)] / [1 + (3/4)] = 6/7 + 1/7 =1.

Question 3

If the three-four of a number is subtracted from the number, the value so obtained is 163.What is the number?

Accepted Answer

Let the number be N. According to the question, N - (N x 3/4) =163 ⇒ N/4 =163 ∴ N=652

Question 4

The positive number, when increased by 10 equals 200 times its reciprocal. What is the number?

Accepted Answer

Let the positive number be N. According to the question, N + 10 = 200 / N ⇒ N2 + 10N = 200 ⇒ N2 +10N - 200 =0 ⇒ (N - 10)(N + 20) = 0 ∴ N = 10 & N= -20 But N not equal to -20 since N is a positive number So, the required number is 10

Question 5

A man has given one -fourth part of his property to his daughter half part to his sons and one fifth part given as charity. How much part of his his property he has given?

Accepted Answer

Total share given by the person = (1/4) + (1/2) + (1/5) = (5 + 10 + 4) / 20 =19/20

Question 6

The sum of two number is 10 Their product is 20. Find the sum of the reciprocals of the two numbers.

Accepted Answer

Let the number be a and b Then a + b = 10 ..........(i) ab = 20 ........(ii) Sum of reciprocal = 1/a + 1/b = (a + b) / ab = 10/20 = 1/2

Question 7

A chocolate has 12 equal to pieces Manju gave 1/4 th of it to anju 1/3 th of it to raj and 1/6 th of to fiza The number of pieces of chocolate left with manju is

Accepted Answer

the number of pieces of chocolate left with manju =1- [(1/4) + (1/3) + (1/6)] = 1 - [ (3 + 4 + 2)/12) = 1 - (9/12) = 3/12 Hence number of piece of chocolate left with in manju is 3

Question 8

How many factors does 120 contains?

Accepted Answer

Factors of composite number = (P1 +1)(P2+1)(P3+1)......(Pn+1). Where P1,P2,P3... Pn are the powers of respective prime factors. So, 120= 23 x 31 x 51 Factors=(3+1)(1+1)(1+1)=16.

Question 9

If n is any odd number greater than 1, then n( n 2 -1 ) is

Accepted Answer

Solving the question by taking two odd numbers greater than 1 i.e. 3 and 5, for n =3, n( n2 -1 ) = 3( 9 - 1) = 24 for n = 5 n( n2 -1 ) = 5( 25 - 1) = 120 Using option we find that both the number are divisible by 24.

Question 10

7 6n - 6 6n, where n is an integer greater than 0, is divisible by

Accepted Answer

For n =1 76n - 66n = 76 - 66 ⇒ ( 73 )2 - ( 63 )2 ⇒ ( 73 - 63 )( 73 + 63 ) = ( 343 - 216 )( 343 + 216 ) = 127 x 559 ∴ it is clearly divisible by 127.

Question 11

Find the sum of first 25 natural numbers.

Accepted Answer

Sum of first n natural numbers = n(n+1)/2 = 25 ( 25 + 1 ) / 2 = ( 25 x 26 ) / 2 = 325

Question 12

Find the sum of square of first 35 natural numbers.

Accepted Answer

Sum of the square of first n natural numbers = n(n+1)(2n+1) / 6 Given n = 35 ∴ Required sum = ( 35 x 36 x 71 ) / 6 = 14910

Question 13

Find the sum of cube of first 15 natural numbers.

Accepted Answer

Sum of cubes of first n natural numbers = [ n(n+1) ]2 Given n = 15 ∴ Required sum = [ ( 15 x 16 ) / 2 ] 2 = (15 x 8 )2 = 1202 = 14400

Question 14

Find the sum of first 84 even numbers

Accepted Answer

Sum of first n even numbers = n( n +1 ) Given n = 84 ∴ Required sum = 84 ( 84 + 1 ) = 84 x 85 = 7140

Question 15

Find the sum of first 37 odd numbers

Accepted Answer

Sum of first n odd number = n2 Given, n = 37 ∴ Required sum = 372 = 37 x 37 = 1369

Question 16

Sum of first 15 multiple of 8 is

Accepted Answer

First 15 multiple of 8 are 8, 16, 24, ......, 120 Sum = 8 (1 + 2 + 3 + 4 ......+ 15) = 8 [ n(n + 1) / 2] = 8 x 15 x 8 960

Question 17

What is the unit digit in the ( 6817 ) 754?

Accepted Answer

Required unique digit = Unique digit in (7)754 = Unique digit in { (74)188 x 72 } = Unique digit in ( 1 x 49 ) = 9

Question 18

What is th unit digit in ( 3 65+6 59+7 71 )?

Accepted Answer

Unit digit in 34 = 1 ∴ Unit digit in ( 34 )16 = 1 ∴ Unit digit in 365 = 3 Unit digit in 659 = 6 Unit digit in 771 = 3 ∴ Required unit digit = Unit digit in ( 3 x 6 x 3 ) = Unit digit in 54 = 4

Question 19

A number divided by 56 gives 29 as remainder. If the same number is divided by 8, the remainder will be ..

Accepted Answer

Let the number be N According to question N = 56k + 29 Then, N = ( 8 x 7k ) + ( 8 x 3 ) + 5 Therefore if N will be divided by 8 the required remainder will = 5

Question 20

On dividing a certain number by 357, the remainder is 39. On dividing the same number by 17, what will be the remainder?

Accepted Answer

Let the given number be N Therefore N = 357k + 39 Then, 357 k + 39 = ( 17 x 21k ) + ( 17 x 2 ) + 5 ∴ Required remainder = 5

Number System Questions