D01-16

Question

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

Bunuel · Answer

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

Ram1987 · Answer

1^-1 = 1 ? Please explain.

Bunuel · Answer

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

Van4ez · Answer

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

Bunuel · Answer

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.

Van4ez · Answer

Thank you, Bunuel, my fault. This is a good example why I couldn't reach my desired score:)

varundhanak · Answer

I think this is a  high-quality  question and I agree with explanation. Best question tests the concept of absolute value, exponents and factorials

coreyander · Answer

The explanation says   "any non-zero number to the power of 0 is 1."

So, is  0^0 
eq 1 ?

Bunuel · Answer

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.

Bunuel · Answer

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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D01-16

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