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# GMAT Diagnostic Test Question 16

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GMAT Diagnostic Test Question 16 [#permalink]

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06 Jun 2009, 22:31
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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, 21:28, edited 3 times in total.
Updated
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Re: GMAT Diagnostic Test Question 15 [#permalink]

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01 Jul 2009, 11:28
3
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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.

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Last edited by bb on 28 Sep 2013, 12:56, edited 1 time in total.
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Re: GMAT Diagnostic Test Question 15 [#permalink]

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07 Aug 2009, 00:43
2
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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]

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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]

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02 Apr 2010, 11:36
1
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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]

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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]

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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]

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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.cfm

Thanks for the feedback!
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]

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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]

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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]

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02 Jun 2010, 02:04
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]

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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]

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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]

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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]

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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]

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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]

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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]

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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.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]

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19 Dec 2010, 16:35
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]

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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   [#permalink] 03 Apr 2011, 14:40

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# GMAT Diagnostic Test Question 16

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