Question

A positive integer is divided by 63, we get the remainder as 25. The remainder when the same number is divided by 9 is equal to

• A. 5
• B. 7
• C. 6
• D. 8

Answer 1

The correct option is B 7

Let x and q be the number and quotient, respectively, when divided by 63. So, by division algorithm
x = 63q + 25
⇒ x = (9 × 7) × q + (9 × 2 + 7)
⇒ x = 9 × (7q + 2) + 7
⇒ x = 9p + 7 (where p = 7q + 2)
Therefore, when the same number is divided by 9, the remainder is 7.
Hence, the correct answer is option (b).