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

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

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21 Feb 2012, 21:40
2
48
00:00

Difficulty:

35% (medium)

Question Stats:

63% (01:04) correct 37% (01:02) wrong based on 1130 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: 431
Concentration: Marketing, Finance
GPA: 3.23
Re: If (|p|!)^p = |p|!, which of the following could be  [#permalink]

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04 Dec 2012, 23:47
3
3
[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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##### General Discussion
Math Expert
Joined: 02 Sep 2009
Posts: 50580
Re: If (|p|!)^p = |p|!, which of the following could be  [#permalink]

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21 Feb 2012, 21:49
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  [#permalink]

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22 Feb 2012, 00:04
Sorry missed the "mod". Silly mistake
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Re: If (|p|!)^p = |p|!, which of the following could be  [#permalink]

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22 Feb 2012, 03:16
1
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
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Re: If (|p|!)^p = |p|!, which of the following could be  [#permalink]

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22 Feb 2012, 10:15
1
Isn't 0! equal to 1? I don't see where you see the 0^0.
Math Expert
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Re: If (|p|!)^p = |p|!, which of the following could be  [#permalink]

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22 Feb 2012, 10:24
1
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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Re: If (|p|!)^p = |p|!, which of the following could be  [#permalink]

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25 Oct 2014, 17:02
2
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: 50580
If (|p|!)^p = |p|!, which of the following could be  [#permalink]

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26 Oct 2014, 04:47
2
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  [#permalink]

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26 Oct 2014, 05:46
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, 20:17
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!
Current Student
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Posts: 2633
Schools: Boston U '20 (M)
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Re: If (|p|!)^p = |p|!, which of the following could be  [#permalink]

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23 Mar 2016, 07:58
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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Re: If (|p|!)^p = |p|!, which of the following could be  [#permalink]

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25 Jul 2016, 02:58
1
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: 103
Re: If (|p|!)^p = |p|!, which of the following could be  [#permalink]

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06 Aug 2017, 02:05
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, 06:56
1
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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Re: If (|p|!)^p = |p|!, which of the following could be  [#permalink]

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13 Nov 2017, 12:05
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 &nbs [#permalink] 13 Nov 2017, 12:05
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