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2"/10 If p = r s t

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2"/10 If p = r s t

by sanju09 » Fri Mar 04, 2011 12:42 am
If r, s, and t are all positive integers, what is the remainder of 2"/10 If p = r s t?

(1) s is even.

(2) p = 4 t.
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by BarryLi » Fri Mar 04, 2011 12:51 am
2p/10?

I don't understand what " is, please elaborate if it is not a typo.

In any case, thanks for thinking of and posting original math problems every night!
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by sanju09 » Fri Mar 04, 2011 12:59 am
BarryLi wrote:2p/10?

I don't understand what " is, please elaborate if it is not a typo.

In any case, thanks for thinking of and posting original math problems every night!
It's 2^p BarryLi

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by Anurag@Gurome » Fri Mar 04, 2011 1:57 am
sanju09 wrote:If r, s, and t are all positive integers, what is the remainder of 2^p/10 If p = rst?

(1) s is even.
(2) p = 4 t.
Note that the remainder when 2^p is divided by 10 is nothing but the units digit of 2^p. Now the units digit of powers of 2 has a cycle of four like 2, 4, 8, 6, 2, 4, 8, ....

Statement 1: s is even => p is even.
Hence, unit's digit of 2^p is either 4 or 6.

Not sufficient

Statement 2: p = 4t => p is a multiple of 4
Unit's digit of 2^p is always 6.

Sufficient

The correct answer is B.
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