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

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Manager
Status: Retaking next month
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GPA: 3.01
WE: Sales (Manufacturing)
If (|p|!)^p = |p|!, which of the following could be [#permalink]

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21 Feb 2012, 22:40
2
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46
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Difficulty:

25% (medium)

Question Stats:

62% (00:45) correct 38% (00:42) wrong based on 1054 sessions

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

A. -1
B. 0
C. 1
D. -1 and 1
E. -1, 0, and 1

How is OA E . factorials are not even defined for - numbers. Pls clarify.

Q 15 Diagnostic test
[Reveal] Spoiler: OA
Math Expert
Joined: 02 Sep 2009
Posts: 44401
Re: If (|p|!)^p = |p|!, which of the following could be [#permalink]

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21 Feb 2012, 22:49
Expert's post
2
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GMATPASSION wrote:
If $$(|p|!)^p = |p|!$$, which of the following could be the value(s) of $$p$$ ?

A. -1
B. 0
C. 1
D. -1 and 1
E. -1, 0, and 1

How is OA E . factorials are not even defined for - numbers. Pls clarify.

Q 15 Diagnostic test

You are right factorial of negative number is undefined. But it's not the case here since we have |p|!, so it's factorial of absolute value of p.

Hope it's clear.
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Manager
Status: Retaking next month
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Location: India
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GMAT 1: 570 Q42 V27
GPA: 3.01
WE: Sales (Manufacturing)
Re: If (|p|!)^p = |p|!, which of the following could be [#permalink]

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22 Feb 2012, 01:04
Sorry missed the "mod". Silly mistake
Manager
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Re: If (|p|!)^p = |p|!, which of the following could be [#permalink]

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22 Feb 2012, 04:16
I would go with D rather than E as 0^0 is not defined for GMAT

D. -1 and 1

(|p|!)^p = |p|! = |-1|!)^-1 = 1^-1 = 1
(|p|!)^p = |p|! = |1|!)^1 = 1^1 = 1
Manager
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Re: If (|p|!)^p = |p|!, which of the following could be [#permalink]

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22 Feb 2012, 11:15
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Isn't 0! equal to 1? I don't see where you see the 0^0.
Math Expert
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Posts: 44401
Re: If (|p|!)^p = |p|!, which of the following could be [#permalink]

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22 Feb 2012, 11:24
1
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Expert's post
You are right: 0^0 is not possible for LHS.

My copy of this question has (|p|!)^p=|p^p|!, so either it's some other question or it has already been revised. In its current form p=0 is a valid solution.
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Senior Manager
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Concentration: Marketing, Finance
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Re: If (|p|!)^p = |p|!, which of the following could be [#permalink]

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05 Dec 2012, 00:47
2
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[quote="GMATPASSION"]If $$(|p|!)^p = |p|!$$, which of the following could be the value(s) of $$p$$ ?

Test Values
A. -1 ==> $$|-1|^-1$$=$$|-||!$$ ==> $$\frac{1}{1}=1$$ ==> -1 is valid
B. 0 ==> $$|0|!^0=|0|!$$ ==> $$1^0=1$$ ==> $$1=1$$ ==> 0 is valid
C. 1 ==> $$1^1=1$$ ==> 1 is valid
D. -1 and 1
E. -1, 0, and 1

I just learned that 0! = 1. Thanks!
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Re: If (|p|!)^p = |p|!, which of the following could be [#permalink]

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25 Oct 2014, 18:02
2
KUDOS
I haven't touched math for quite sometime since I chose to get a PhD in molecular genetics, and even though I'm having a blast on this site "learning" how to solve problems, some things just make no sense.

How can 0!=1?
who made up that rule? were they doing meth?

so if I have zero eggs then I can arrange them 0!=1 ways in my fridge
which is awesome for two main reasons.
a) I can put my zero eggs in the fridge one way without caring if I have or not space for eggs.
b) If I don't buy eggs then I'm burning one egg-arranging calorie quantum constantly so I'll be skinny in no time. Just don't buy eggs.

Man I love math, too bad I'll fail on the GMAT test.
Math Expert
Joined: 02 Sep 2009
Posts: 44401
If (|p|!)^p = |p|!, which of the following could be [#permalink]

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26 Oct 2014, 05:47
1
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Expert's post
3
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quijotes wrote:
I haven't touched math for quite sometime since I chose to get a PhD in molecular genetics, and even though I'm having a blast on this site "learning" how to solve problems, some things just make no sense.

How can 0!=1?
who made up that rule? were they doing meth?

so if I have zero eggs then I can arrange them 0!=1 ways in my fridge
which is awesome for two main reasons.
a) I can put my zero eggs in the fridge one way without caring if I have or not space for eggs.
b) If I don't buy eggs then I'm burning one egg-arranging calorie quantum constantly so I'll be skinny in no time. Just don't buy eggs.

Man I love math, too bad I'll fail on the GMAT test.

Why does 0! = 1?

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Re: If (|p|!)^p = |p|!, which of the following could be [#permalink]

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26 Oct 2014, 06:46
The GMAT has not tested the fact 0!=1, and I highly doubt that they would test if students know 0!=1.

Dabral
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Joined: 02 Mar 2015
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Re: If (|p|!)^p = |p|!, which of the following could be [#permalink]

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21 Mar 2016, 21:17
If (|p|!)p=|p|!(|p|!)p=|p|!, which of the following could be the value(s) of pp ?

A. -1
B. 0
C. 1
D. -1 and 1
E. -1, 0, and 1

How is OA E . factorials are not even defined for - numbers. Pls clarify.

Q 15 Diagnostic test

OA is E.

0! = 1(as studied in school books in India)
one can solve for all the values -1 , 0 , 1.

Thanks!
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Joined: 12 Aug 2015
Posts: 2508
GRE 1: 323 Q169 V154
Re: If (|p|!)^p = |p|!, which of the following could be [#permalink]

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23 Mar 2016, 08:58
Here We can test to see that all the values are possible.
Also we knoew he negative factorials are not defined but due to mod all the values are positive.
hence E
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Director
Joined: 04 Jun 2016
Posts: 638
GMAT 1: 750 Q49 V43
Re: If (|p|!)^p = |p|!, which of the following could be [#permalink]

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25 Jul 2016, 03:58
1
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GMATPASSION wrote:
If $$(|p|!)^p = |p|!$$, which of the following could be the value(s) of $$p$$ ?

A. -1
B. 0
C. 1
D. -1 and 1
E. -1, 0, and 1

How is OA E . factorials are not even defined for - numbers. Pls clarify.

Q 15 Diagnostic test

The only factorial that are perfect squares are 0! and 1!

-1, 0 , 1 all three are possible
since |-1|= 1

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Manager
Joined: 07 Jun 2017
Posts: 108
Re: If (|p|!)^p = |p|!, which of the following could be [#permalink]

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06 Aug 2017, 03:05
how is -1 valid? I still do not get it
Intern
Joined: 18 Aug 2017
Posts: 30
GMAT 1: 670 Q49 V33
Re: If (|p|!)^p = |p|!, which of the following could be [#permalink]

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22 Aug 2017, 07:56
1
KUDOS
pclawong wrote:
how is -1 valid? I still do not get it

The absolute value sign.

(|-1|!)^ (-1) = 1/(1!) = 1.
Manager
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Location: United States
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Re: If (|p|!)^p = |p|!, which of the following could be [#permalink]

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13 Nov 2017, 13:05
0! = 1 because an empty set can only be ordered in 1 way.
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Re: If (|p|!)^p = |p|!, which of the following could be   [#permalink] 13 Nov 2017, 13:05
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