X^4 is dividable by 32, what is the remainder when X is : GMAT Problem Solving (PS)
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# X^4 is dividable by 32, what is the remainder when X is

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Intern
Joined: 15 Oct 2012
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X^4 is dividable by 32, what is the remainder when X is [#permalink]

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15 Oct 2012, 15:50
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X^4 is dividable by 32, what is the remainder when X is divided by 32?
Magoosh GMAT Instructor
Joined: 28 Dec 2011
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Re: X^4 is divisible by 32 [#permalink]

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15 Oct 2012, 16:37
tingting85114 wrote:
X^4 is dividable by 32, what is the remainder when X is divided by 32?

I'm happy to help with this.

First of all, if I may give you a piece of advice --- please give your post a title that that is more relevant to the content. The title "I need help" tells the rest of us absolutely nothing about the content. When the title is reveals something about the content, that is very helpful for other GC users scanning down the list of posts deciding which one to read. Does that make sense?

This question is not a well-defined question. First of all, it's not in a standard GMAT question form. Also, it doesn't have a clear yes/no answer.

You see, X could equal 4 or any multiple of 4. As long as a number is divisible by 4, then the fourth power of that number will be divisible by 32. For some of those values of X, the remainder when divided by 32 will be zero, and for some, it will be something else.

What is the source of this question?

Mike
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Mike McGarry
Magoosh Test Prep

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15 Oct 2012, 16:59
tingting85114 wrote:
X^4 is dividable by 32, what is the remainder when X is divided by 32?

X^4 = 32 (K) where K is any integer

(X)(X)(X)(X) = (2)(2)(2)(2)(2)(K)

Therefore, the smallest value of K = (2)(2)(2)

Therefore, the smallest value of X = (2)(2)

X can be 4, 8, 16, 32, 64,.......

The question seems incomplete, there will be remainders if X < 32 but no remainder when X >= 32.
Magoosh GMAT Instructor
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15 Oct 2012, 18:41
nmdial wrote:
there will be remainders if X < 32 but no remainder when X >= 32.

Dear nmdial,

I just want to point out, if, say, X = 8, then we divided by 32, the remainder will be 8. When the dividend is less than the divisor, the quotient is zero, and the remainder is equal to the dividend.

Mike
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Mike McGarry
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15 Oct 2012, 20:19
mikemcgarry wrote:
nmdial wrote:
there will be remainders if X < 32 but no remainder when X >= 32.

Dear nmdial,

I just want to point out, if, say, X = 8, then we divided by 32, the remainder will be 8. When the dividend is less than the divisor, the quotient is zero, and the remainder is equal to the dividend.

Mike

Mike: Exactly my point!
Re: I need help!   [#permalink] 15 Oct 2012, 20:19
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