Question

If a, b, c are digits, then match the the number which divides the given numbers.

• A. 11
• B. 99
• C. 9
• D. 111

Answer 1

Writing the numbers in expanded form we have,
ab = 10a + b
ba = 10b+ a
abc = 100a + 10b + c
cab = 100c + 10a + b
bca = 100b + 10c + a

ab + ba = 10a + b + 10b + a = 11 (a + b)

ab - ba = 10a +b - 10b + a = 9 (a - b)

abc - cba = 100a + 10b + c - 100c - 10b - a= 99 (a - c)

abc + cab + bca = (100a + 10a + a) + (100b + 10b + b) + (100c + 10c + c)
= 111a + 111b + 111c = 111 (a + b + c)