Is |x-2|+|x+2|

Question

Is |x-2|+|x+2|<4?

1). x<0

2). x is within (-2, 2)

diegmat · Answer

Saying B here...

Statement 1. Could equal 4 or could equal less than 4 (plug in extreme numbers). INSUFF.

Statement 2. All instances equal 4. SUFF.

Fig · Answer

(D) for me

By observing the consrtuction of the function f(x)=|x-2|+|x+2|, we see that we remove 2 and add 2 to |x|. It preserves the symetry with the y-axes. The result is that:
> if |x| > 2 , |x-2|+|x+2| > 4
> if |x| =< 2 , |x-2|+|x+2| = 4

Thus, |x-2|+|x+2| is always >= 4.

baski6 · Answer

How could you say D?

Using 1)
Applying x= -1, -2 gives 4 
 x > 2 gives >4. 

So only B gives always 4 and so B is the answer

It's B.

Matrix02 · Answer

One more for D. 

Is |x-2|+|x+2|<4? 

Question is asking if |x-2|+|x+2|<4 so it doen't matter if it could be equal to 4 AND greater than 4. We can safely say that Statement 1 provides us with a enough information to say NO |x-2|+|x+2| will never be <4 BUT it could be 4 or greater. SUFFICIENT

Statement 2: Same deal - tells us that |x-2|+|x+2| will never be < 4. Sufficient. 

Correct me if I wrong but I think this DS is only asking if |x-2|+|x+2| <4. If GMAT wanted to know if it was less than or equal to they would have indicated so in the question.

anandsebastin · Answer

E 
A is clearly insufficient. 
B X = between -2 and 2. 
For all values except 2, and -2 value<4, but for X=2 or -2, value = 4. So, E.

anandsebastin · Answer

Oops! D it is!

amorica · Answer

How is A insufficient?... 

Even if you get 4, that is sufficient because you can answer the question.. 

X is not less than 4... its not less because its equal...

iced_tea · Answer

OA is D

in this particular DS, you don't need any stem - the question is answered by the info given in the question itself !

cicerone · Answer

Hey iced_tea, you are correct...........

Edited the post.........

I am taking the wrong inequality..........

Fig · Answer

Sorry cicerone, but i think that iced_tea is right

Actually, for all x real number, |x-2|+|x+2| >=4. The minimum is obtained when |x| =< 2 with |x-2|+|x+2| =4. o If 0 < x =< 2, |x-2| (>=0) = -(x-2) and |x+2| = x+2 thus, |x+2| + |x-2| = 2-x + x+2 = 4 o If -2 =< x < 0, |x-2| = (-x)+2 and |x+2| = x+2 thus, |x+2| + |x-2| = 2-x + x+2 = 4

quangviet512 · Answer

This's a bad quest indeed
What do u think if we change it in this way
Is lx-2l+lx+2l <= 4 (smaller or equal 4 )
1. x<0
2. x is within (-2,2)

Fig · Answer

It's (B) in this case

dipeshc4 · Answer

whats the correct answer, im confused.

Fig · Answer

The answer to the orginal problem is (D). quangviet512 adapted the orginal question : lx-2l+lx+2l < = 4 and asked the new answer, which is (B)

sm176811 · Answer

Agreed D for the reasons above!

Is |x-2|+|x+2|<4? 1). x<0 2). x is within (-2, 2

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