How many values of k satisfy k*|k| = 4?

Question

How many values of  k  satisfy  k*|k| = 4 ?

A. 0
B. 1
C. 2
D. 3
E. 4

Bunuel · Accepted Answer

Official Solution:

How many values of  k  satisfy  k*|k| = 4 ?

A. 0
B. 1
C. 2
D. 3
E. 4

Notice that  k  cannot be negative because in this case  k * |k| = (	ext{negative})(	ext{positive}) = 	ext{negative} 
eq 4 . Therefore,  k  must be positive. In this scenario,  |k| = k  and we'd have  k *k = 4 , which gives  k = 2  (remember  k  is positive so it cannot be  -2 ). Thus, only one value of  k  satisfies  k * |k| = 4 .

Answer: B

gmatophobia · Answer

|k| is a non-negative value. As the product,  k *|k|  is positive, we can infer that  k  is positive.

Hence, we can only have  1  value of  k, k = 2 .

Option B

BrushMyQuant · Answer

We need to find how many values of  k  satisfy  k*|k| = 4 ?

As we have |k| in the equation so we will have two cases 
 
   -   Case 1:  k ≥ 0 
=> |k| = k
=>  k*k = 4 
=>  k^2 = 4 
=> k = -2 or k = 2

But condition was k ≥ 0
=> k  = 2 is a  SOLUTION   
  -   Case 2:  k  ≤  0 
=> |k| = -k
=>  k * -k = 4 
=>  -k^2 = 4 
=>  k^2 = -4

But square of a number cannot be negative
=>   NO SOLUTION

So,  Answer will be B 
Hope it helps!

Watch the following video to MASTER Absolute Values

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

How many values of k satisfy k*|k| = 4?

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As we have \|k\| in the equation so we will have two cases
-Case 1: k ≥ 0 => \|k\| = k => \(k*k = 4\) => \(k^2 = 4\) => k = -2 or k = 2 But condition was k ≥ 0 => k = 2 is a SOLUTION	-Case 2: k ≤ 0 => \|k\| = -k => \(k * -k = 4\) => \(-k^2 = 4\) => \(k^2 = -4\) But square of a number cannot be negative => NO SOLUTION

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How many values of k satisfy k*|k| = 4?

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