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21 Feb 2012, 22:40
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E
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
35%
(medium)
Question Stats:
63% (01:05) correct
37%
(01:02)
wrong
based on 2331
sessions
History
Date
Time
Result
Not Attempted Yet
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
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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17 May 2025, 10:06
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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:
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
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.
• 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
General Discussion
30 Jun 2025, 19:46
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\((|p|!)^p = |p|!\) and we need to find which of the following could be true.
Let's substitute the values and check
I. \(p=-1\)
=> \((|-1|!)^{-1} = |-1|!\)
=> \((1!)^{-1} = 1!\)
=> \(1^{-1} = 1\)
=> 1 = 1
=> TRUE
II. \(p=0\)
=> \((|0|!)^{0} = |0|!\)
=> \((0!)^{0} = 0!\)
=> \(1^{0} = 1\)
=> 1 = 1
=> TRUE
III. \(p=1\)
=> \((|1|!)^{1} = |1|!\)
=> \((1!)^{1} = 1!\)
=> \(1^{1} = 1\)
=> 1 = 1
=> TRUE
=> All Options are true
So, Answer will be E
Hope it helps!
Watch the following video to MASTER Absolute Values
Let's substitute the values and check
I. \(p=-1\)
=> \((|-1|!)^{-1} = |-1|!\)
=> \((1!)^{-1} = 1!\)
=> \(1^{-1} = 1\)
=> 1 = 1
=> TRUE
II. \(p=0\)
=> \((|0|!)^{0} = |0|!\)
=> \((0!)^{0} = 0!\)
=> \(1^{0} = 1\)
=> 1 = 1
=> TRUE
III. \(p=1\)
=> \((|1|!)^{1} = |1|!\)
=> \((1!)^{1} = 1!\)
=> \(1^{1} = 1\)
=> 1 = 1
=> TRUE
=> All Options are true
So, Answer will be E
Hope it helps!
Watch the following video to MASTER Absolute Values
