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

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

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New post Updated on: 21 Jan 2017, 21:06
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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 :)

Originally posted by RMD007 on 21 Jan 2017, 10:03.
Last edited by RMD007 on 21 Jan 2017, 21:06, edited 1 time in total.
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Re: If a and b are non negative integers, what is remainder when 11^a/b  [#permalink]

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New post 21 Jan 2017, 18:03
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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 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 :-)
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Re: If a and b are non negative integers, what is remainder when 11^a/b  [#permalink]

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New post 21 Jan 2017, 19:55
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1
RMD007 wrote:
If a and b are non negative integers, what is remainder when \(\frac{(11^a)}{b}\)?

1. a = 2
2. b = 10



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
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3) effects of arithmetic operations : https://gmatclub.com/forum/effects-of-arithmetic-operations-on-fractions-269413.html


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Re: If a and b are non negative integers, what is remainder when 11^a/b  [#permalink]

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New post 22 Jan 2017, 04:21
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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Re: If a and b are non negative integers, what is remainder when 11^a/b  [#permalink]

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New post 23 Aug 2018, 01:53
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Re: If a and b are non negative integers, what is remainder when 11^a/b &nbs [#permalink] 23 Aug 2018, 01:53
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