Question

'X' a whole number which when divided by 23, gives the remainder 8. Then, the remainder when (4x + 15) is divided by 23, is –
1. 2
2. 1
3. 3
4. 4

Answer 1

Correct Answer - Option 2 : 1

CONCEPT:

Dividend = (Quotient × Divisor) + Remainder

CALCULATION:

Suppose divisor is k, then, x = 23k + 8

According to the question –

⇒ (4x + 15) = [4(23k + 8) + 15]

⇒ 92k + 32 + 15

⇒ 92k + 47

When (92k + 47) is divided by 23, then, 92k is completely divisible by 23 and leaves 1 as a remainder when 47 is divided by 23.

⇒ Rem[(92k + 47)/23] = Rem(47/23) = 1