Remainder, exponents

[avenus]

If n is an integer and n^4 is divisible by 32, which of the following could be the remainder when n is divided by 32?

(A) 2
(B) 4
(C) 5
(D) 6
(E) 10

[ssmiles08]

I got 4.

Not sure if it is right but here is my explanation:

if n^4 is divisible by 32, the n^4 must have at least five 2's in it's product.

since n^4 = n^2* n^2

every prime number in n must occur in sets of 2.

2*2*2*2*2 = 32;

32 is 2^5, so three more 2's need to be added to make n have four sets of two 2's.

so the smallest value n could possibly be is 4

4/32, would give the remainder of 4.

I am not sure if I explained it really well. What is the OA?

[avenus]

OA D

[scoobydooby]

i get B too, worked out just like ssmiles08 did.
hey avenus,
do you have the OE? curious how they solved it

[Stuart@KaplanGMAT]

i get B too, worked out just like ssmiles08 did.
hey avenus,
do you have the OE? curious how they solved it

4^4 is 256, which is certainly divisible by 32.

4/32 is 0rem4, so it's definitely possible to get a remainder of 4. If the OA is 6, the OA is wrong.

[doclkk]

I got 4.

Not sure if it is right but here is my explanation:

if n^4 is divisible by 32, the n^4 must have at least five 2's in it's product.

since n^4 = n^2* n^2

every prime number in n must occur in sets of 2.

2*2*2*2*2 = 32;

32 is 2^5, so three more 2's need to be added to make n have four sets of two 2's.

so the smallest value n could possibly be is 4

4/32, would give the remainder of 4.

I am not sure if I explained it really well. What is the OA?

Could you explain this a little more. how does 4/32 provide R 4 ?

4/32 = 1/8... how can you have a remainder when the numerator is larger than the denominator.

[ssmiles08]

Could you explain this a little more. how does 4/32 provide R 4 ?

4/32 = 1/8... how can you have a remainder when the numerator is larger than the denominator.

If you draw out a long division on the paper: 4 would be inside and 32 is outside.

0 is the quotient which gives you 32*0 = 0; so 4-0 = 4: remainder

Hope that clarifies a little

[doclkk]

Could you explain this a little more. how does 4/32 provide R 4 ?

4/32 = 1/8... how can you have a remainder when the numerator is larger than the denominator.

If you draw out a long division on the paper: 4 would be inside and 32 is outside.

0 is the quotient which gives you 32*0 = 0; so 4-0 = 4: remainder

Hope that clarifies a little

Yea I got it now, just have never done this on a GMAT problem yet ...?