RMD007 wrote:

If a and b are non negative integers, what is remainder when \(\frac{(11^a)}{b}\)?

1. a = 2

2. b = 10

Dear

RMD007I'm happy to respond.

This is a great problem!

You may find the discussion in this blog article germane:

GMAT Quant: Difficult Units Digits QuestionsYou see, any two numbers with units digits both equal to 1 will have a product with a units digit of 1. Thus, for 11, 21, 91, or any other number with a units digit of 1, all the powers of that number will have units digits of 1. We know for a fact that, regardless of the value of a, every possible \(11^a\) will have a units digit of 1.

Statement #1 is obviously

insufficient, because we don't know B.

With statement #2, we are dividing some unknown power of 11 by 10. Since every power of 11 has a units digit of 1, the remainder when we divide by 10 has to be 1. With this statement, we get a definitive answer to the prompt question, so the second statement is

sufficient.

OA =

(B) Does all this make sense?

Mike

_________________

Mike McGarry

Magoosh Test Prep

Education is not the filling of a pail, but the lighting of a fire. — William Butler Yeats (1865 – 1939)