Is x 0 ? (1) x + 1 0 (2) |x + 4|

Question

Is  x>0 ?

(1)  x+1>0 
(2)  |x+4| < |x-2|

gmatophobia · Answer

Statement 1 (1) x+1>0 x > -1 The statement alone is not sufficient. If -1 < x \leq 0 ⇒ Is x>0 - No If x > 0 ⇒ Is x>0 - Yes We can eliminate A and D. Statement 2 (2) |x+4| < |x-2| Squaring both sides we get - x^2 + 16 + 8x < x^2 + 4 -4x 12x < -12 x < -1 We have a definite answer to the question "Is x>0 " - No Hence, the statement alone is sufficient. Option B

wminesh · Answer

Statement 1 was easy to comprehend.

x>-1 => clearly Statement 1 is Not Sufficient

Tried another way (brute force) of using statement 2:

|x+4| < |x-2| can be written out in 4 different ways:
1. x+4 < x-2 => 4<-2 || Not true
2. x+4 < 2-x => 2x<-2 => x<-1 || Not Suffcient
3. -x-4 < x-2 => -2<2x => -1<x || Not Suffcient
4. -x-4 < 2-x => -4<2 || True, does not give anything about x

Thus, Statement 2 is Not Sufficient.

Answer: E

Would want to hear any comments on the method for using Statement 2.

gmatophobia · Answer

wminesh My Two cents - 1) Whenever you're working with signs, you will have to consider the regions in which those signs hold true. For example In this case, you have assumed x + 4 > 0 ⇒ x > -4 x - 2 < 0 ⇒ x < 2 From the working, you arrived at x < -1, not sure why did you indicate the net result as "Not Sufficient" because all it tells us that between -4 and -1 the equation holds true. Hence, the values of x that satisfy the equation lie between -4 and -1. So ideally this part is sufficient because all such values are NOT greater than 0. Similarly - In this case, you have assumed x + 4 < 0 ⇒ x < -4 x + 2 > 0 ⇒ x > -2 The consideration itself is not valid as x cannot be less than -4 and greater than -2 at the same time. 2) You can form regions and evaluate the signs within that region - Screenshot 2023-03-30 135137.jpg Hope this clarifies.

Is x > 0 ? (1) x + 1 > 0 (2) |x + 4| < |x - 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

GMAT Data Sufficiency (DS) Questions