If x y 0, is y

Question

If  x>y>0 , is  y<2 ?

(1)  \frac{1}{x} = \frac{1}{2}

(2)  (\frac{1}{x})+(\frac{1}{y}) =1

gmatophobia · Answer

x>y>0 On a number line, y lies to the left of x ------- 0 ------------ y ----------- x -------- Statement 1 (1) \frac{1}{x} = \frac{1}{2} x = 2 As y lies to the left of x on the number line, we can infer that y < 2 . The statement alone is sufficient. Statement 2 (2) (\frac{1}{x})+(\frac{1}{y}) =1 Assume, x = y. If that were the case, x = y = 2 would satisfy this equation. However, x > y . Let's assume that x < 2 the value of \frac{1}{x} will be greater than \frac{1}{2} as y is less than x , the value of \frac{1}{y} will be greater than the value of \frac{1}{x} This situation will result in the sum of \frac{1}{y} and \frac{1}{x} greater than 1 (\frac{1}{x})+(\frac{1}{y}) > 1 However, the statement states that (\frac{1}{x})+(\frac{1}{y}) =1 . Therefore the value of x must be greater than 2. In such a case, the value of \frac{1}{x} will be less than \frac{1}{2} . To compensate for the decrease in the value of \frac{1}{x } and to maintain the sum of (\frac{1}{x})+(\frac{1}{y}) =1 , the value of y must now be less than 2 , making \frac{1}{y} > \frac{1}{x} . Hence, we can conclude that y < 2 The statement is also sufficient. Option D

If x > y > 0, is y < 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