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# QOTD#15 When m is divided by 11, the remainder is r.

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QOTD#15 When m is divided by 11, the remainder is r. [#permalink]  19 Aug 2016, 03:50
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Question Stats:

50% (00:51) correct 49% (00:56) wrong based on 55 sessions
$$m = 10^{32} + 2$$

When m is divided by 11, the remainder is r.

 Quantity A Quantity B r 3

A)The quantity in Column A is greater.
B)The quantity in Column B is greater.
C)The two quantities are equal.
D)The relationship cannot be determined from the information given.

Practice Questions
Question: 8
Page: 150
[Reveal] Spoiler: OA

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Re: QOTD#15 When m is divided by 11, the remainder is r. [#permalink]  23 Mar 2018, 12:47
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Explanation

m = 10^(32) + 2 = 100,000,000,000,000,000,000,000,000,000,002 so we certainly don't want to CALCULATE the remainder when m is divided by 11.
Instead, let's examine different powers of 10 and look for a pattern

1) 10^1 + 2 = 12. When we divide 12 by 11, we get remainder 1
2) 10^2 + 2 = 102. When we divide 102 by 11, we get remainder 3
3) 10^3 + 2 = 1002. When we divide 1002 by 11, we get remainder 1
4) 10^4 + 2 = 10,002. When we divide 10,002 by 11, we get remainder 3

So, when the exponent is ODD, the remainder is 1
And, when the exponent is EVEN, the remainder is 3

So, when we divide 10^32 +2 by 11, we get remainder 3

So, we have:
Quantity A: 3
Quantity B: 3

Cheers,
Brent
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Re: QOTD#15 When m is divided by 11, the remainder is r. [#permalink]  27 Nov 2018, 02:16
thank you very much
Re: QOTD#15 When m is divided by 11, the remainder is r.   [#permalink] 27 Nov 2018, 02:16
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