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GMAT Diagnostic Test Question 15 [#permalink]
 06 Jun 2009, 22:31
GMAT Diagnostic Test Question 15Field: Modules, Powers Difficulty: 750
If p is an integer, what is the value of p? 1. (|p|!)^p = |p|!2. p^p = p^2
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Re: GMAT Diagnostic Test Question 15 [#permalink]
01 Jul 2009, 11:28
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Explanation:
Official Answer: CStatement (1): If (|p|!)^p = |p|! is true, the possible values for p are -1, 0 or 1. Not sufficient by itself. 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 not tested on the GMAT, so p can't equal 0. The expression holds for p=1 and p=2. We cannot determine what p is. Not sufficient. Statement (1) + Statement (2): From Statement (1), we have three possible values for p: -1, 0, 1. From Statement (2), we have two possible values: 1 and 2. It's clear that p=1. Sufficient.
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Re: GMAT Diagnostic Test Question 15 [#permalink]
06 Aug 2009, 22:23
can someone illustrate this using a #?
If (|p|!)^p = |p|!
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Re: GMAT Diagnostic Test Question 15 [#permalink]
07 Aug 2009, 00:43
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As said in the OE, all three numbers can be the values of p. Here's why: (|p|!)^p = |p|!p=-1: (|-1|!)^{-1} = |-1|!(1!)^{-1} = 1!\frac{1!}{1} = 1!\frac{1}{1} = 1p=0: (|0|!)^{0} = |0|!(0!)^{0} = 0!1^{0} = 11 = 1p=1: (|1|!)^{1} = |1|!(1!)^{1} = 1!1^{1} = 11 = 1Hope this helps chicagocubsrule wrote: can someone illustrate this using a #?
If (|p|!)^p = |p|!
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Re: GMAT Diagnostic Test Question 15 [#permalink]
19 Dec 2009, 14:55
This mostly test the number property of 0. I messed up because I thought 0 power of 1 is 0, using the logic that 1 power of 1 is 1.
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Re: GMAT Diagnostic Test Question 15 [#permalink]
01 Apr 2010, 05:19
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dzyubam wrote: 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
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Re: GMAT Diagnostic Test Question 15 [#permalink]
01 Apr 2010, 06:10
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.cfmThanks 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 _________________
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Re: GMAT Diagnostic Test Question 15 [#permalink]
02 Apr 2010, 11:36
bb wrote: GMAT Diagnostic Test Question 15Field: Modules, Powers Difficulty: 750
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
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Re: GMAT Diagnostic Test Question 15 [#permalink]
01 Jun 2010, 15:28
but p^p = p^2 that means, p = 2...so we are done with the value of 'p'...then how come ans is 'C'
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Re: GMAT Diagnostic Test Question 15 [#permalink]
01 Jun 2010, 18:28
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.
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Re: GMAT Diagnostic Test Question 15 [#permalink]
02 Jun 2010, 02:04
sheetalsanjana, valencia:Statement 2 holds for both 2 and 1: 2^2 = 2^2 = 41^1 = 1^2 = 1Remember that 1 raised to any (as far as GMAT is concerned) power equals 1.
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Re: GMAT Diagnostic Test Question 15 [#permalink]
18 Jul 2010, 13:52
Still not sure why it is not 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?
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Re: GMAT Diagnostic Test Question 15 [#permalink]
18 Jul 2010, 15:04
indranilb wrote: Still not sure why it is not 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
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Re: GMAT Diagnostic Test Question 15 [#permalink]
03 Sep 2010, 20:19
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...)
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Re: GMAT Diagnostic Test Question 15 [#permalink]
03 Sep 2010, 23:06
It is easier to get a clearer picture of what GMAT tests through adequate practice; at least, you now know what 0! is. Good luck in your practicing.
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Re: GMAT Diagnostic Test Question 15 [#permalink]
04 Dec 2010, 08:34
This is a really bad question for GMAT. You can't just assume that "0^0 is not tested on the GMAT, so p can't equal 0". This should be clearly stated.
Thanx!
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Re: GMAT Diagnostic Test Question 15 [#permalink]
19 Dec 2010, 09:06
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.
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Re: GMAT Diagnostic Test Question 15 [#permalink]
19 Dec 2010, 09:21
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.cfmThe 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.
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Re: GMAT Diagnostic Test Question 15 [#permalink]
19 Dec 2010, 16:35
Thanks a lot Bunuel ! That makes a lot of sense and ver helpful. Faith in GMAT restored  . Posted from my mobile device 
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Re: GMAT Diagnostic Test Question 15 [#permalink]
03 Apr 2011, 14:40
Gentlemen, 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 I will go with answer A. Any takers? Regards Rahul
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Re: GMAT Diagnostic Test Question 15
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03 Apr 2011, 14:40
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