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Manager  Status: Retaking next month
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Concentration: Marketing, Entrepreneurship
GMAT 1: 570 Q42 V27 GPA: 3.01
WE: Sales (Manufacturing)
If (|p|!)^p = |p|!, which of the following could be the value(s) of p?  [#permalink]

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Question Stats: 60% (01:04) correct 40% (01:01) wrong based on 1440 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
Senior Manager  Joined: 13 Aug 2012
Posts: 401
Concentration: Marketing, Finance
GPA: 3.23
Re: If (|p|!)^p = |p|!, which of the following could be the value(s) of p?  [#permalink]

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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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Math Expert V
Joined: 02 Sep 2009
Posts: 58381
Re: If (|p|!)^p = |p|!, which of the following could be the value(s) of p?  [#permalink]

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

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Sorry missed the "mod". Silly mistake Manager  Joined: 10 Jan 2010
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Re: If (|p|!)^p = |p|!, which of the following could be the value(s) of p?  [#permalink]

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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  Joined: 12 Oct 2011
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GMAT 1: 700 Q48 V37 GMAT 2: 720 Q48 V40 Re: If (|p|!)^p = |p|!, which of the following could be the value(s) of p?  [#permalink]

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Isn't 0! equal to 1? I don't see where you see the 0^0.
Math Expert V
Joined: 02 Sep 2009
Posts: 58381
Re: If (|p|!)^p = |p|!, which of the following could be the value(s) of p?  [#permalink]

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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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GMAT 1: 660 Q47 V34 Re: If (|p|!)^p = |p|!, which of the following could be the value(s) of p?  [#permalink]

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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 V
Joined: 02 Sep 2009
Posts: 58381
Re: If (|p|!)^p = |p|!, which of the following could be the value(s) of p?  [#permalink]

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2
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 the value(s) of p?  [#permalink]

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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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Posts: 24
Re: If (|p|!)^p = |p|!, which of the following could be the value(s) of p?  [#permalink]

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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
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Schools: Boston U '20 (M)
GRE 1: Q169 V154 Re: If (|p|!)^p = |p|!, which of the following could be the value(s) of p?  [#permalink]

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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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GMAT 1: 750 Q49 V43 Re: If (|p|!)^p = |p|!, which of the following could be the value(s) of p?  [#permalink]

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

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

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pclawong wrote:
how is -1 valid? I still do not get it

The absolute value sign.

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

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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 the value(s) of p?  [#permalink]

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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

Dear Moderator,
Can we remove the answer which is outside the spoiler, so that we can get the joy of arriving at the answer ourselves. Thank you.
_________________
- Stne
Math Expert V
Joined: 02 Sep 2009
Posts: 58381
Re: If (|p|!)^p = |p|!, which of the following could be the value(s) of p?  [#permalink]

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stne wrote:
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

Dear Moderator,
Can we remove the answer which is outside the spoiler, so that we can get the joy of arriving at the answer ourselves. Thank you.

_________________
Done. Thank you.
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Intern  B
Joined: 12 Oct 2018
Posts: 33
Location: India
Re: If (|p|!)^p = |p|!, which of the following could be the value(s) of p?  [#permalink]

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Hi Bunuel can you please provide the answer to the above question. I was not able to understand it from the above discussion. Thank you! Re: If (|p|!)^p = |p|!, which of the following could be the value(s) of p?   [#permalink] 24 Dec 2018, 07:02
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