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D01-16

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Bunuel
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D01-16 [#permalink] New post  16 Sep 2014, 00:12
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74% (01:03) correct 26% (01:03) wrong based on 142 sessions
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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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Bunuel
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Re D01-16 [#permalink] New post  16 Sep 2014, 00:12
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Official Solution:


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


Two important properties:

• \(0!=1\).

• Any non-zero number raised 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.


Answer: E
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Ram1987
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Re: D01-16 [#permalink] New post  11 Dec 2014, 06:11
1^-1 = 1 ? Please explain.
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Bunuel
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Re: D01-16 [#permalink] New post  11 Dec 2014, 06:30
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Ram1987 wrote:
1^-1 = 1 ? Please explain.


Negative powers:
\(a^{-n}=\frac{1}{a^n}\), hence \(1^{(-1)}=\frac{1}{1^1}=1\).

Theory on Exponents: math-number-theory-88376.html
Tips on Exponents: exponents-and-roots-on-the-gmat-tips-and-hints-174993.html

All DS Exponents questions to practice: search.php?search_id=tag&tag_id=39
All PS Exponents questions to practice: search.php?search_id=tag&tag_id=60

Tough and tricky DS exponents and roots questions with detailed solutions: tough-and-tricky-exponents-and-roots-questions-125967.html
Tough and tricky PS exponents and roots questions with detailed solutions: tough-and-tricky-exponents-and-roots-questions-125956.html

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Re: D01-16 [#permalink] New post  11 Dec 2014, 09:00
It seems I have missed some basics of factorials. I was surprised to find out that (-1)!=-1. I was thinking it is undefined.
If (-1)!=-1 is it correct to assume the following:
(-2)! = 2 = -1 X -2
(-3)! = -6 = -1 X -2 X -3
(-4)! = 24 = -1 X -2 X -3 X -4
(-5)! = -120 = -1 X -2 X -3 X -4 X -5
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Bunuel
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Re: D01-16 [#permalink] New post  11 Dec 2014, 10:23
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Van4ez wrote:
It seems I have missed some basics of factorials. I was surprised to find out that (-1)!=-1. I was thinking it is undefined.
If (-1)!=-1 is it correct to assume the following:
(-2)! = 2 = -1 X -2
(-3)! = -6 = -1 X -2 X -3
(-4)! = 24 = -1 X -2 X -3 X -4
(-5)! = -120 = -1 X -2 X -3 X -4 X -5


No, that;s not correct at all. Factorial is defined only for non-negative integers: the factorial of a non-negative integer n, denoted by n!, is the product of all positive integers less than or equal to n.

In the original question we don't have (-1)! (which would be undefined), we have (|-1|)!. Notice that -1 there is in modulus sign: (|-1|)! = (1)! = 1.

Hope it's clear.
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Re: D01-16 [#permalink] New post  11 Dec 2014, 10:29
Thank you, Bunuel, my fault. This is a good example why I couldn't reach my desired score:)
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varundhanak
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Re: D01-16 [#permalink] New post  21 Sep 2018, 07:28
I think this is a high-quality question and I agree with explanation. Best question tests the concept of absolute value, exponents and factorials
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Re: D01-16 [#permalink] New post  10 Jul 2020, 05:06
The explanation says "any non-zero number to the power of 0 is 1."

So, is \(0^0 \neq 1\)?
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Bunuel
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Re: D01-16 [#permalink] New post  10 Jul 2020, 05:09
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coreyander wrote:
The explanation says "any non-zero number to the power of 0 is 1."

So, is \(0^0 \neq 1\)?


0^0, in some sources equals to 1, some mathematicians say it's undefined. But you won't need this for the GMAT because the case of 0^0 is not tested on the GMAT.
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Re: D01-16 [#permalink] New post  24 Sep 2023, 10:04
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I have edited the question and the solution by adding more details to enhance its clarity. I hope it is now easier to understand.
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Re: D01-16 [#permalink]
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