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Q: If pq is a two-digit number, then pq – qp will be completely divisible by:
  • A. 9
  • B. 7
  • C. 6
  • D. 5
Correct Answer: Option A - Let the two digit number (pq) = 10x + y Then, qp = 10y + x According to the question, pq – qp = 10x + y – (10y + x) = 10x + y – 10y – x = 9x – 9y = 9 (x – y) Hence pq – qp will be completely divisible by 9.
A. Let the two digit number (pq) = 10x + y Then, qp = 10y + x According to the question, pq – qp = 10x + y – (10y + x) = 10x + y – 10y – x = 9x – 9y = 9 (x – y) Hence pq – qp will be completely divisible by 9.

Explanations:

Let the two digit number (pq) = 10x + y Then, qp = 10y + x According to the question, pq – qp = 10x + y – (10y + x) = 10x + y – 10y – x = 9x – 9y = 9 (x – y) Hence pq – qp will be completely divisible by 9.