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Important properties: 0!=1 and any non-zero number to the power of 0 is 1.

Let's check the options: If \(p=-1\) then \((|p|!)^p = (|-1|!)^{-1}=1^{-1}=1\) and \(|p|!=|-1|!=1!=1\) so \(p\) could be -1; If \(p=0\) then \((|p|!)^p = (|0|!)^{0}=1^{0}=1\) and \(|0|!=0!=1\) so \(p\) could be 0; If \(p=1\) then \((|p|!)^p = (|1|!)^{1}=1^{1}=1\) and \(|p|!=|1|!=1\) so \(p\) could be 1.

Explanation: Statement (2): If \(p^p = p^2\) is true, \(p\) should be 1. Since \(p^2\) is positive for all non-zero values, \(p^p\) has to be also positive. \(0^0\) is undefined, so \(p\) can't equal 0. It can only be possible for \(p=1\). Therefore, \(p\) cannot be any other integer than 1. Sufficient.

There are a few errors here: As a side note: \(0^0\) is defined and is equal to 1.

p=2 (\(2^2 = 2^2\)) also works, so (2) can't be sufficient

(1)+(2): (1) tells us that -1, 0 and 1 are the only possible values, but with (2), only 1 fits the bill. So for me: Answer C

I agree that the answer should be C and I will correct it. +1. However, I don't think you're right when you say that \(0^0 = 1\). Mathematicians still argue whether it should be undefined or equal to 1. As I understand, \(0^0\) should not be tested on the GMAT. You can see this link which confirms my point: http://www.manhattangmat.com/np-exponents.cfm

Thanks for the feedback!

PadawanOfTheGMAT wrote:

There are a few errors here: As a side note: \(0^0\) is defined and is equal to 1.

p=2 (\(2^2 = 2^2\)) also works, so (2) can't be sufficient

(1)+(2): (1) tells us that -1, 0 and 1 are the only possible values, but with (2), only 1 fits the bill. So for me: Answer C

GMAT Diagnostic Test Question 15 Field: Modules, Powers Difficulty: 750

Rating:

If \(p\) is an integer, what is the value of \(p\)?

1. \((|p|!)^p = |p|!\) 2. \(p^p = p^2\)

(1)Using 0: |0|! = 1; 1^0 = 1 same is applicable to 1.........Insuff (0,1) .....did not bother testing further with -1 (2) tested with 1: 1^1 = 1^2 = 1 using 2: 2^2 = 2^2........Insuff (1,2)

combining (1) & (2) integer 1 is the ans. So, C _________________

KUDOS me if you feel my contribution has helped you.

Re: GMAT Diagnostic Test Question 15 [#permalink]
01 Jun 2010, 17:28

sheetalsanjana wrote:

but p^p = p^2

that means, p = 2...so we are done with the value of 'p'...then how come ans is 'C'

I agree with sheetal. Since the base p is same the power must be equal. Therefore p=2. There should be no other answer and I beleive the answer to this question should be B. _________________

P^P = P^2 Bases are same so P = 2. Am I using a wrong theory, that when bases are same , the powers can be equated?

The solution cannot be (B) because there are two values that can answer the question, "what is the value of p?" The values are 1 and 2. Try to substitute and you will see why. Hope that helps _________________

KUDOS me if you feel my contribution has helped you.

seems like this test love 0 he he... now i was tripped in 0^0=0 which should be 1(it said it is not tested still it is really difficult to tell what is tested and what is not ...in gmat...)

Re: GMAT Diagnostic Test Question 15 [#permalink]
19 Dec 2010, 08:06

How do i know what is not tested in GMAT ? I.e. 0^0. Is there a definitive list of things like this which are likely to throw you off ? (Not that the outcome of the problem changes, but it very well could in other problems). Thanks.

Re: GMAT Diagnostic Test Question 15 [#permalink]
19 Dec 2010, 08:21

Expert's post

TheBirla wrote:

How do i know what is not tested in GMAT ? I.e. 0^0. Is there a definitive list of things like this which are likely to throw you off ? (Not that the outcome of the problem changes, but it very well could in other problems). Thanks.

0^0, in some sources equals to 1, some mathematicians say it's undefined. Anyway you won't need this for GMAT because the case of 0^0 is not tested on the GMAT: http://www.manhattangmat.com/np-exponents.cfm

The fact that this concept is not tested on the GMAT means that you won't encounter a problem on the GMAT in which you should decide what 0^0 is equal to. So for example if there will be x^x in the problem then somehow the possibility of x being zero will be excluded, for example by saying that x is positive integer or by simply saying that x doesn't equal to zero. _________________

The first solution-explanation is incorrect. Theoretically, the factorial for a negative number is undefined. This is the basic definition for the factorial operand. So that leaves 0 and 1 as the two options from clue 1. Zero is the next one to be eliminated. I assume GMAT prefers to stay away from mathematical controversies. 0^0 is mathematically undefined. So after completely analyzing clue 1, we are left with 1 alone as the solution. Sufficient.

On the second statement, the explanation appears correct. 1 and 2 both seem plausible solutions. Not sufficient