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

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by M7MBA » Wed Jun 24, 2020 6:04 am
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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

[spoiler]OA=E[/spoiler]

Source: GMAT Club Tests
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Re: If \((|p|!)^p=|p|!,\) which of the following could be the value(s) of \(p?\)

by Jay@ManhattanReview » Thu Jun 25, 2020 4:29 am
M7MBA wrote: ↑
Wed Jun 24, 2020 6:04 am
 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

[spoiler]OA=E[/spoiler]

Source: GMAT Club Tests
Looking at the options, we see that we have to deal with three probable values of p. So, let's test these values from options.

(1) p = –1:

\((|-1|!)^{(-1)}=|-1|!\)
\((1!)^{(-1)}=1!\)
\(1=1\). This is the correct value of p.

(2) p = 0:

\((|0|!)^{(0)}=|0|!\)
\((1)^{(0)}=1\)
\(1=1\). This is the correct value of p.

The correct answer is E.

Though we got the answer, let's test p = 1, too.

(1) p = 1:

\((|1|!)^{(1)}=|1|!\)
\((1!)^{(1)}=1!\)
\(1=1\). This is the correct value of p.

Correct answer: E

Hope this helps!

-Jay
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