 It is currently 22 May 2019, 01:45 ### GMAT Club Daily Prep

#### Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized
for You

we will pick new questions that match your level based on your Timer History

Track
Your Progress

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History

#### Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here. # xy is different form zero  Question banks Downloads My Bookmarks Reviews Important topics
Author Message
TAGS:
Founder  Joined: 18 Apr 2015
Posts: 6584
Followers: 107

Kudos [?]: 1258 , given: 5973

xy is different form zero [#permalink]
Expert's post 00:00

Question Stats: 77% (00:20) correct 22% (00:00) wrong based on 9 sessions
$$xy \neq 0$$

 Quantity A Quantity B $$\frac{x - y}{x}$$ $$\frac{x - y}{y}$$

A) Quantity A is greater.
B) Quantity B is greater.
C) The two quantities are equal.
D) The relationship cannot be determined from the information given.
[Reveal] Spoiler: OA

_________________ Manager Joined: 04 Feb 2019
Posts: 204
Followers: 4

Kudos [?]: 97  , given: 0

Re: xy is different form zero [#permalink]
1
This post received
KUDOS
Expert's post
This is one for picking numbers. But here's an easy answer. All we have to do is make y = x, then both quantities are 0 and are thus equal. But when they're different numbers, the two quantities will be different. That's enough to show that the answer is D.

If we pick two easy positive numbers, like x = 2 and y = 1, then Quantity A = $$\frac{1}{2}$$ and Quantity B = 1. So Quantity B is bigger.

But if we make one of them negative, like x = 2 and y = -1, then Quantity A = $$\frac{3}{2}$$ and Quantity B = -3. So Quantity A is bigger. GRE Instructor Joined: 10 Apr 2015
Posts: 1748
Followers: 58

Kudos [?]: 1668  , given: 8

Re: xy is different form zero [#permalink]
1
This post received
KUDOS
Expert's post
Carcass wrote:
$$xy \neq 0$$

 Quantity A Quantity B $$\frac{x - y}{x}$$ $$\frac{x - y}{y}$$

A) Quantity A is greater.
B) Quantity B is greater.
C) The two quantities are equal.
D) The relationship cannot be determined from the information given.

Here's an often-tested fraction property: $$\frac{a-b}{c}=\frac{a}{c}-\frac{b}{c}$$

So, when we apply the above property, we can rewrite each quantity as follows:
QUANTITY A: $$\frac{x}{x}-\frac{y}{x}$$
QUANTITY B: $$\frac{x}{y}-\frac{y}{y}$$

Simplify:
QUANTITY A: $$1-\frac{y}{x}$$
QUANTITY B: $$\frac{x}{y}-1$$

Add 1 to both quantities AND add y/x to both quantities to get:
QUANTITY A: $$1+1$$
QUANTITY B: $$\frac{x}{y}+\frac{y}{x}$$

Simplify:
QUANTITY A: $$2$$
QUANTITY B: $$\frac{x}{y}+\frac{y}{x}$$

At this point, we may be able to see that we can make the fractions as big as we want (e.g., x/y = 500/1) or we can make them as small as we want (e.g., x/y = -500/1)
So, Quantity B can be greater than 2 or less than 2.

Answer: D

If you're not convinced, let's test some values

case i: x = 100 and y = 1
We get:
QUANTITY A: $$2$$
QUANTITY B: $$\frac{100}{1}+\frac{1}{100}=100\frac{1}{100}$$
In this case, Quantity B is greater

case ii: x = -100 and y = 1
We get:
QUANTITY A: $$2$$
QUANTITY B: $$\frac{-100}{1}+\frac{1}{100}=-99\frac{99}{100}$$
In this case, Quantity A is greater

Answer: D

RELATED VIDEO FROM MY COURSE

_________________

Brent Hanneson – Creator of greenlighttestprep.com Sign up for my free GRE Question of the Day emails Re: xy is different form zero   [#permalink] 14 May 2019, 08:38
Display posts from previous: Sort by

# xy is different form zero  Question banks Downloads My Bookmarks Reviews Important topics Powered by phpBB © phpBB Group Kindly note that the GRE® test is a registered trademark of the Educational Testing Service®, and this site has neither been reviewed nor endorsed by ETS®.