If n is not 0, for how many integers is |n|^n = n * n

Question

If n is not 0, for how many integers is |n|^n = n * n (A) 0 (B) 1 (C) 2 (D) 3 (E) more than 3 Similar Question: https://gmatclub.com/forum/for-how-many ... 26963.html

zamis · Accepted Answer

In case someone dumb like me, who initially didn't understand, why not -2 other than 1, -1 & 2

|-2|^-2=-2*-2
=> 1/4#4

chetan2u · Answer

|n|^n = n * n 
 |n|^n = n ^2 
Surely one value is when n=2.
The other values are possible when both sides are 1, and n^2=1, when n is 2 or -2
So three values :
1) 1 :  |1|^1=1^2......1=1 
2) -1 :  |-1|^{-1}=(-1)^2......1=1 
3) 2 :  |2|^2=2^2......4=4

D

philipssonicare · Answer

Incase you're an idiot like me and forgot to note that n≠0

0^2=0 
 0^0  is  undefined .

So it can't work anyway

BrushMyQuant · Answer

Given that n is not 0 and we need to find for how many integers is  |n|^n = n*n

We can solve this by   Substitution

|n|^n = n*n  =  n^2

Definitely 1 and 2   are two possible choices

Case n = 1 or n = 2

-  n = 1 
=>  |1|^1 = 1^2 
=> 1 = 1
=>  n = 1 is  SOLUTION

-  n = 2 
=>  |2|^2 = 2^2 
=> 4 = 4
=>  n = 2 is  SOLUTION

As we have Absolute value on left side and square on right side so let's try with -1 and -2 also

Case n = -1 or n = -2

-  n = -1 
=>  |-1|^{-1} = (-1)^2 
=> 1 = 1
=>  n = -1 is  SOLUTION

-  n = -2 
=>  |-2|^{-2} = (-2)^2 
=>  1/4  ≠ 4
=>  n = -1 is  NOT a SOLUTION

Now, there will be no other integer for which we will have  |n|^n = n^2 
As, n raised to its own power will always be greater or smaller than n to the power of 2

So,  Answer will be D 
Hope it helps!

Watch the following video to learn the Basics of Absolute Values

https://www.youtube.com/watch?v=huFiBk8PaGY

Praful_0810 · Answer

1] |1| ^ 1 = 1 x 1
2] |-1|^ (-1) = (-1)^2
 1^(-1)
 1/1 = 1 = 1
3] |2|^2 = 2 x 2
 4 = 4

So correct answer is option D

Posted from my mobile device

bumpbot · Answer

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If n is not 0, for how many integers is |n|^n = n * n

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Case n = 1 or n = 2
-n = 1 => \(\|1\|^1 = 1^2\) => 1 = 1 => n = 1 is SOLUTION	-n = 2 => \(\|2\|^2 = 2^2\) => 4 = 4 => n = 2 is SOLUTION

Case n = -1 or n = -2
-n = -1 => \(\|-1\|^{-1} = (-1)^2\) => 1 = 1 => n = -1 is SOLUTION	-n = -2 => \(\|-2\|^{-2} = (-2)^2\) => \(1/4\) ≠ 4 => n = -1 is NOT a SOLUTION

GMAT Problem Solving (PS) Questions

If n is not 0, for how many integers is |n|^n = n * n

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