2"/10 If p = r s t

[sanju09]

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.

[BarryLi]

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!

[sanju09]

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

thank you every night

[Anurag@Gurome]

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.