# Aptitude - Number System

### MCQ

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Q 31.

If n is a whole number greater than 1 then, n2(n2 - 1) is always divisible by.

Options:

• 60

• 24

• 48

• 12

Put n = 2,

n2(n2 - 1) = 12 which is divisible by 12.

Put n = 3,

n2(n2 - 1) = 72 which is divisible by 12.

Put n = 4,

n2(n2 - 1) = 240 which is divisible by 12.

So, we can say that n2(n2 - 1) is always divisible by 12.

Q 32.

Find the remainder when 919 + 6 is divided by 8.

Options:

• 4

• 5

• 6

• 7

Given,

N = 919 + 6

= (1+8)19 + 6

N/8 = [(1+8)19 + 6]/8

= (1 + 6)/8

= 7/8

So, remainder = 7

Q 33.

If N is divided by 56 it gives 29 as remainder. Find the remainder when N is divided by 8.

Options:

• 3

• 4

• 5

• 6

As per question,

N = 56q + 29

= (8x7q) + (8x3) + 5

= 8(7q + 3) + 5

So, remainder = 5

Q 34.

Find the sum of first 6 multiples of 5.

Options:

• 105

• 100

• 95

• 90

Given, n = 6 and x = 5

Sum of first n multiples of x = x[n(n+1)/2]

= 5[6(6+1)/2]

= 105

Q 35.

Find the sum of first 5 odd numbers.

Options:

• 21

• 23

• 25

• 27

Given, n = 5

Sum of first n odd numbers = n2

= 52

= 25

Q 36.

Find the sum of first 5 even numbers.

Options:

• 28

• 30

• 32

• 34

Given, n = 5

Sum of first n even numbers = n(n+1)

= 5(5+1)

= 30

Q 37.

Find the sum of the cubes of the first 5 natural numbers.

Options:

• 223

• 224

• 225

• 226

Given, n = 5

Sum of the cubes of first n natural numbers = [n(n+1)/2]2

= [5(5+1)/2]2

= 225

Q 38.

Find the sum of the squares of first 10 natural numbers.

Options:

• 375

• 385

• 395

• 365

Given, n = 10

Sum of the sqaures of first n natural numbers = n(n+1)(2n+1)/6

= 10(10+1)(20+1)/6

= 385

Q 39.

Find the remainder when 41000 is divided by 7.

Options:

• 1

• 2

• 3

• 4

41000/7

= ((42)500)/7

= ((16)500)/7

= ((14 + 2)500)/7

= ((2)500)/7

= (22 x (23)166)/7

= (4 x (8)166)/7

= (4 x (7 + 1)166)/7

= (4 x (1)166)/7

= 4

Q 40.

If the sum and difference of the digits of a two digit number is 14 and 2 respectively. Find the product of the digits.

Options:

• 46

• 48

• 50

• Insufficient data

Let the two digits be x and y.

Given, x + y = 14 and x - y = 2

Therefore, x = 8 and y = 6

So, product = xy = 8x6 = 48

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