If a and b are non negative integers, what is remainder when 11^a/b

Question

If a and b are non negative integers, what is remainder when \frac{(11^a)}{b} ? 1. a = 2 2. b = 10 Source : Self Made

mikemcgarry · Answer

Dear RMD007 I'm happy to respond. :-)

This is a great problem! You may find the discussion in this blog article germane: GMAT Quant: Difficult Units Digits Questions You 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 :-)

chetan2u · Answer

Hi

Two points in such Qs..
Non negative integers would also include 0 and any number to the power of 0 will be 1..
If divisor is 2,5 or 10, it is sufficient to know just the units digit..

So here 11 to the power of anything, 0 and above, will have units digit as 1..
And when we are given denominator as 10, even if it was 2 or 5, remainder will be 1
Suff

B

Mo2men · Answer

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

1. a = 2

Let b=11 ..........11^2/11.....reminder is 0

Let b= 2............11^2/11.....reminder is 1

Insufficient

2. b = 10

let a= 1...............11/10..........reminder is 1

a=2................121/10........reminder is 1

Any power raised to 11 with make this number greater than 10 or its multiple of 10 by 1. Always reminder is 1

Sufficient

Answer: B

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If a and b are non negative integers, what is remainder when 11^a/b

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