Question

Take a two digit number 'ab'. The number is reversed, and difference between ab and its reverse is taken as cd. What is the value of c + d?

• A. 11
• B. 10
• C. 9
• D. 8

Answer 1

The correct option is C

9

We are taking a 2 digit number, the difference of original number and its reverse will always have two digits which is less than 99.

cd = (10a + b) - (10b + a) = 9(a - b)

There is an interesting pattern for multiples of 9.

9 × 1 = 9 = 10 × 0 + 1 × 9 → 0 + 9 = 9

9 × 2 = 18 = 10 × 1 + 1 × 8 → 8 + 1 = 9

9 × 3 = 27 = 10 × 2 + 1 × 7 → 2 + 7 = 9
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9 × 10 = 90 = 10 × 9 + 1 × 0 → 9 + 0 = 9

Since cd is a multiple of 9, c + d = 9 as observed from the above pattern.