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GMAT Diagnostic Test Question 16

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GMAT Diagnostic Test Question 16 [#permalink] New post 06 Jun 2009, 21:31
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GMAT Diagnostic Test Question 16
Field: Modules, Powers
Difficulty: 750


If (|p|!)^p = |p|!, which of the following could be true?

I. p=-1
II. p=0
III. p=1

A. I only
B. II only
C. III only
D. II and III only
E. I, II and III
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Last edited by bb on 28 Sep 2013, 20:28, edited 3 times in total.
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Re: GMAT Diagnostic Test Question 15 [#permalink] New post 01 Jul 2009, 10:28
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Explanation:

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.

Answer: E.
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Last edited by bb on 28 Sep 2013, 11:56, edited 1 time in total.
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Re: GMAT Diagnostic Test Question 15 [#permalink] New post 06 Aug 2009, 23:43
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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} = 1

p=0:

(|0|!)^{0} = |0|!
(0!)^{0} = 0!
1^{0} = 1
1 = 1

p=1:

(|1|!)^{1} = |1|!
(1!)^{1} = 1!
1^{1} = 1
1 = 1

Hope 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] New post 01 Apr 2010, 04:19
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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] New post 06 Aug 2009, 21:23
can someone illustrate this using a #?
If (|p|!)^p = |p|!
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Re: GMAT Diagnostic Test Question 15 [#permalink] New post 19 Dec 2009, 13:55
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] New post 01 Apr 2010, 05:10
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.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

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Re: GMAT Diagnostic Test Question 15 [#permalink] New post 02 Apr 2010, 10:36
bb wrote:
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
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Re: GMAT Diagnostic Test Question 15 [#permalink] New post 01 Jun 2010, 14:28
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] New post 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.
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Re: GMAT Diagnostic Test Question 15 [#permalink] New post 02 Jun 2010, 01:04
sheetalsanjana, valencia:

Statement 2 holds for both 2 and 1:

2^2 = 2^2 = 4

1^1 = 1^2 = 1

Remember 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] New post 18 Jul 2010, 12:52
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] New post 18 Jul 2010, 14:04
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] New post 03 Sep 2010, 19:19
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] New post 03 Sep 2010, 22:06
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] New post 04 Dec 2010, 07:34
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] New post 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.
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Re: GMAT Diagnostic Test Question 15 [#permalink] New post 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.
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Re: GMAT Diagnostic Test Question 15 [#permalink] New post 19 Dec 2010, 15:35
Thanks a lot Bunuel ! That makes a lot of sense and ver helpful. Faith in GMAT restored ;).

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Re: GMAT Diagnostic Test Question 15 [#permalink] New post 03 Apr 2011, 13:40
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   [#permalink] 03 Apr 2011, 13:40
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