M39-57

Question

If  22 - |y + 14| = 20 , what is the sum of all possible values of  y ?

A.  -28 
B.  -16 
C.   -12 
D.  -4 
E.  4

Bunuel · Answer

Official Solution:

If  22 - |y + 14| = 20 , what is the sum of all possible values of  y ?

A.  -28 
B.  -16 
C.   -12 
D.  -4 
E.  4

22 - |y + 14| = 20 ;
 
 |y + 14| = 2 ;
 
 y + 14 = 2  or  y + 14 = -2 ;
 
 y = -12  or  y = -16 ;
 
Therefore, the sum of all possible values of  y  is  -12 + (-16) = -28.

Answer: A

MBAToronto2024 · Answer

KarishmaB 
Isn’t it mistake here?
If y>0, we’re getting y = -12. Which is not valid solution.

Bunuel · Answer

Where is it stated that y is positive? Why should it be positive? If you substitute y = −12 and y = −16, you'll see that both values satisfy 22 − |y + 14| = 20, so there is no mistake in the solution at all.

KarishmaB · Answer

The point of transition here is y = -14, not y = 0. We get y = -12 when y >= -14
Look at what Bunuel has done above.

|y+14| = 2

The two cases will be either y + 14 >= 0 or y + 14 < 0

Alternatively, y will take 2 values which are a distance of 2 away from -14. So y will be -16 and -12.

mexsolares · Answer

I like the solution - it’s helpful.

M39-57

Prep Toolkit

Top 5 GMAT Debrief Videos

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards