If x + y 0, is 1/(x + y)

Question

If x + y ≠ 0, is 1/(x + y) < 2?

(1) x^3 = y^3
(2) 1/x < 2

GMATinsight · Answer

Question: is 1/(x + y) < 2? Statement 1 : x^3 = y^3 i.e. x = y (But they can be integers or fractions both) Case 1: x = y = 1, 1/(x + y) < 2 Case 2: x = y = 0.1, 1/(x + y) > 2 NOT SUFFICIENT Statement 2 : 1/x < 2 no information about y and x may be an integer or a non-integer both (also they could be +ve and -ve both) hence NOT SUFFICIENT Combining the statements i.e. x = y (But they can be integers or fractions both) but from statement-2, we get that x must be greater than 0.5 if x >0 Also, Case 1: if x and y are negative then 1/(x + y) < 2 Case 2: if x = y > 0.5, (x + y) > 1 and 1/(x + y) < 2 SUFFICIENT Answer: Option C

gmatophobia · Answer

IMO C

Bunuel · Answer

Official Solution:

If  x + y ≠ 0 , is  \frac{1}{x + y} < 2 ? 
 
(1)  x^3 = y^3 
 
Taking the cube root of the above gives  x = y . However, this is not sufficient to determine whether  \frac{1}{x + y} < 2 . For instance, consider  x = y = 1  and  x = y = \frac{1}{2} .
 
(2)  \frac{1}{x} < 2 
 
This statement is clearly insufficient, since no information about  y  is provided.
 
(1)+(2) From (1), since  x = y , the question becomes: is  \frac{1}{2x} < 2 ? This can be further rewritten as: is  \frac{1}{x} < 4 ? Since (2) states that  \frac{1}{x} < 2 , it follows that  \frac{1}{x}  must also be less than 4.Sufficient.

Answer: C

Bunuel · Answer

Practice harder version of this question  HERE .

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 + y 0, is 1/(x + y) < 2? (1) x^3 = y^3 (2) 1/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