If x is a non-negative integer and |6 - |x + 2|| = 10, then find the n

Question

If x is a non-negative integer and |6 - |x + 2|| = 10, then find the number of values of x that satisfy the given absolute value inequality?

a. 0
b. 1
c. 2
d. 3
e. 4

i did as follows: |6-x-2|=10 (x+2 will be +ve since x is a non neg integer) => |4-x|=10 (again 4-x should be +ve since x is a non neg integer) 4-x=10 => -6=x hence there should be zero values that satisfy the inequality as x has to be a non neg integer. could someone help pls?

GMATinsight · Accepted Answer

Let's solve it this way

|6 - |x + 2|| = 10

i.e. 6 - |x + 2| =  + 10

6 - |x + 2| = 10

i.e. |x + 2| = -4 NOT POSSIBLE because absolute values of any function is non-negative

6 - |x + 2| = -10
i.e. |x + 2| = 16

i.e. x + 2 = 16 or x + 2 = -16

i.e. x = 14 or x = -18

Since x is non-negative so x can only be 14 and can NOT be -18

Answer: Option B

Bunuel · Answer

For |6 - |x + 2|| = 10 to hold |x + 2| must be 16. (|x + 2| obviously cannot be -4)

|x + 2| = 16.
x = 14 or x = -18. Since given that x is a non-negative integer, discard x = -18.

Answer: B.

MathRevolution · Answer

|6 - |x + 2|| = 10

| - 10| = 10 and |10| = 10. So we need 6 - |x + 2| = 10 or -10.

=> 6 - |x + 2| = 10 for this 6 - 10 = -4 = |x + 2| (Not possible)

=> 6 - |x + 2| = -10 for this 6 + 10 = 16 = |x + 2|

=> x + 2 = 16 and x = 14 and x + 2 = -16 and x = -18

'x' is a non-negative and hence x = 14 is the value considered.

Answer B

Crytiocanalyst · Answer

The question simply asks us to find whether |x+2| = 16

=>which is possible in two scenarios that being at x=14 since it's positive it can take this posiibilities

next we have x=-18 which it cannot be included since we require only positive values

Therefore IMO only value satisfies 
Hence B

4ce5 · Answer

When should we be solving it the way described in the explanations vs substituting | x+ 2 | with a and solving based on that? Would that even work? Why or why not?

I tried it and got the right answer.. but I think I stumbled onto it through luck

Can,Will · Answer

egmat   KarishmaB   gmatophobia  Can you please check whether my approach is correct ?

KarishmaB · Answer

|6 - |x + 2|| = 10 Since x is non negative, (x+2) will always be positive. So |x + 2| = (x + 2) |6 - x - 2| = 10 which is equivalent to: |x - 4| = 10 x is a point at a distance 10 away from 4. There are only 2 such points: -6 and 14 Answer (C) Absolute values as distances is discussed here: https://youtu.be/oqVfKQBcnrs

KarishmaB · Answer

It is correct though too many unnecessary calculations.

Can,Will · Answer

KarishmaB  
 If p is a non-positive number, then for what value of p does the expression |77 – 6p| holds the minimum value?

A. 77/12
 B. 77/6
 C. 12
 D. 0
 E. -77/6

in this problem can we say that since p is a non positive I77-6pI is negative i.e -77+6p

KarishmaB · Answer

|77 - 6p| = |6p - 77| gives two cases: 6p - 77 >= 0 which means p >= 77/6 (Not possible because p is not positive) OR 6p - 77 < 0 which means p < 77/6 (which includes 0 and all negative values) So |6p - 77| = - (6p - 77) You should check out this post: https://anaprep.com/algebra-the-why-beh ... questions/ This is how you will arrive at the answer here though: p is non positive (though this term isn't really used) means p can be 0 or negative. If p = 0, |77 – 6p| = 77 If p is negative, – 6p becomes positive and when added to 77 is gives us something more than 77. So the minimum value of |77 – 6p| happens when p = 0.

Bunuel · Answer

This question is discussed here: https://gmatclub.com/forum/if-x-is-a-no ... l#p3389087

bumpbot · Answer

Automated notice from GMAT Club BumpBot: 

A member just gave Kudos to this thread, showing it’s still useful. I’ve bumped it to the top so more people can benefit. Feel free to add your own questions or solutions.

 This post was generated automatically.

If x is a non-negative integer and |6 - |x + 2|| = 10, then find the n

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

GMAT Problem Solving (PS) Questions

If x is a non-negative integer and |6 - |x + 2|| = 10, then find the n

Prep Toolkit

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