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

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If (|p|!)^p = |p|!, which of the following could be [#permalink] New post 21 Feb 2012, 21:40
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59% (01:34) correct 41% (00:33) wrong based on 174 sessions
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
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Re: If (|p|!)^p = |p|!, which of the following could be [#permalink] New post 21 Feb 2012, 21:49
Expert's post
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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RESOURCES: [GMAT MATH BOOK]; 1. Triangles; 2. Polygons; 3. Coordinate Geometry; 4. Factorials; 5. Circles; 6. Number Theory; 7. Remainders; 8. Overlapping Sets; 9. PDF of Math Book; 10. Remainders; 11. GMAT Prep Software Analysis NEW!!!; 12. SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) NEW!!!; 12. Tricky questions from previous years. NEW!!!;

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Manager
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Status: Retaking next month
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Joined: 05 Mar 2011
Posts: 229
Location: India
Concentration: Marketing, Entrepreneurship
GMAT 1: 570 Q42 V27
GPA: 3.01
WE: Sales (Manufacturing)
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Kudos [?]: 21 [0], given: 32

Re: If (|p|!)^p = |p|!, which of the following could be [#permalink] New post 22 Feb 2012, 00:04
Sorry missed the "mod". Silly mistake :x
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Re: If (|p|!)^p = |p|!, which of the following could be [#permalink] New post 22 Feb 2012, 03:16
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
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Re: If (|p|!)^p = |p|!, which of the following could be [#permalink] New post 22 Feb 2012, 10:15
Isn't 0! equal to 1? I don't see where you see the 0^0.
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Re: If (|p|!)^p = |p|!, which of the following could be [#permalink] New post 22 Feb 2012, 10:24
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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NEW TO MATH FORUM? PLEASE READ THIS: ALL YOU NEED FOR QUANT!!!

PLEASE READ AND FOLLOW: 11 Rules for Posting!!!

RESOURCES: [GMAT MATH BOOK]; 1. Triangles; 2. Polygons; 3. Coordinate Geometry; 4. Factorials; 5. Circles; 6. Number Theory; 7. Remainders; 8. Overlapping Sets; 9. PDF of Math Book; 10. Remainders; 11. GMAT Prep Software Analysis NEW!!!; 12. SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) NEW!!!; 12. Tricky questions from previous years. NEW!!!;

COLLECTION OF QUESTIONS:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS ; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.


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Re: If (|p|!)^p = |p|!, which of the following could be [#permalink] New post 04 Dec 2012, 23:47
[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


Answer:E

I just learned that 0! = 1. Thanks!
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Re: If (|p|!)^p = |p|!, which of the following could be [#permalink] New post 04 Jul 2014, 10:19
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Re: If (|p|!)^p = |p|!, which of the following could be   [#permalink] 04 Jul 2014, 10:19
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