When divided by 143 leaves 31 as remainder What will be the remainder when the same number is divided by 13?

A number when divided by 143 leaves 31 as remainder. What will be the remainder when the same number is divided by 13? (a) 0 (b) 1 (c) 3 (d) 5

Correct Answer: (d) 5

Explanation:

Dividend = Divisor × Quotient + Remainder.

Given,

Divisor = 143

Remainder = 13

The number is in the form of 143x + 31, where x is the quotient.

∴ 143x + 31 = 13 (11x) + (13 × 2) + 5 = 13 (11x + 2) + 5

The remainder will be 5 when the same number is divided by 13.

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