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