If x and y lie on the number line shown above, which of the following

Question

https://gmatclub.com/forum/download/file.php?id=36215 If x and y lie on the number line shown above, which of the following statements must be true? (A) 1/y > 2 (B) 1/x < 2 (C) 1/x < 1/y (D) x + y < 1 (E) xy < 1/2 2017-07-12_1229.png

jedit · Answer

It should be E.

A- 1/y would be greater than 2 if y was less than 0.5 but this is not the case since 1/2 < y < 1.

B- Conversely 1/x would be less than 2 if x was greater than 0.5 which is not the case.

C- 1/x would be less than 1/y if x > y but we know x is actually less than y. flipping fraction for x and y would flip the inequality between them.

D- We cannot be certain about this. If x = 3/10 and y = 9/10, x+y would be greater than 1 while both still satisfy the conditions.

E- Say we assume y as close to 1 as possible. 99/100 or 0.99, x cannot be greater than 0.5 or 1/2. so xy has to be less than half of y since multiple x is less than half. 1/2 of y is of course less than 1/2 since y < 1.

Mo2men · Answer

I will try to DISPROVE each statement by plugging numbers

Let x = 1/4 & y =3/4

(A) 1/y = 4/3 Not greater than 2B) 1/x < 2 ........... Eliminate

B) 1/x = 4 Not less than 2 B) 1/x < 2 ........... Eliminate

(C) 1/x < 1/y...... 4 < 4/3 ........... Eliminate

(D) x + y < 1...1/4 + 3/4 = 1....... ........... Eliminate

(E) xy < 1/2................No need to test

Answer: E

sarathyishere · Answer

Based on the figure given and fractions, A) 1/y > 2 - 1/Y is always less than 2 because y>1/2 - Incorrect B) 1/X <2 - 1/X is always greater than 2 because X<1/2 - Incorrect C) 1/X < 1/Y - incorrect because it implies Y

sergioas22 · Answer

I've just made the inequalities look more comfortable and picked up numbers for x and y (x=1/4 ; y=3/4) (A) 1/y >2 --- 1>2y -- 1>2*3/4 -- 1>3/2? -- Clearly false. (B) 1/x <2 --- 1<2x -- 1<2*1/4 -- 1<1/2? -- False. (C) 1/x < 1/y --- y

FB2017 · Answer

Using x=1/4 and y=3/4
only xy < 1/2 this inequality is satisfied. So answer is E

vineet6316 · Answer

If x coincided with 1/2 and y coincided with 1, xy would have been 1/2. But, we know that both variables are on the left hand side of the assumption.

Hence E is the right choice!

ScottTargetTestPrep · Answer

We see that 0 < x < 1/2 and 1/2 < y < 1. Thus, 1/x > 2 and 1 < 1/y < 2. Therefore, answer choices A, B, and C are wrong. Answer choice D is not correct either, since if x = 2/5 and y = 4/5, then x + y = 6/5 > 1. Thus, answer choice E must be correct. In fact, since x is a positive number less than 1/2 and y is a positive number less than 1, the product of x and y must be less than 1/2 * 1 = 1/2. Answer: E

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 and y lie on the number line shown above, which of the following

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 and y lie on the number line shown above, which of the following

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