GMAT Question of the Day - Daily to your Mailbox; hard ones only

 It is currently 16 Jan 2019, 00:27

### 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

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

## Events & Promotions

###### Events & Promotions in January
PrevNext
SuMoTuWeThFrSa
303112345
6789101112
13141516171819
20212223242526
272829303112
Open Detailed Calendar
• ### The winning strategy for a high GRE score

January 17, 2019

January 17, 2019

08:00 AM PST

09:00 AM PST

Learn the winning strategy for a high GRE score — what do people who reach a high score do differently? We're going to share insights, tips and strategies from data we've collected from over 50,000 students who used examPAL.
• ### Free GMAT Strategy Webinar

January 19, 2019

January 19, 2019

07:00 AM PST

09:00 AM PST

Aiming to score 760+? Attend this FREE session to learn how to Define your GMAT Strategy, Create your Study Plan and Master the Core Skills to excel on the GMAT.

# M30-08

Author Message
TAGS:

### Hide Tags

Math Expert
Joined: 02 Sep 2009
Posts: 52120

### Show Tags

16 Sep 2014, 00:45
00:00

Difficulty:

45% (medium)

Question Stats:

57% (01:14) correct 43% (01:14) wrong based on 110 sessions

### HideShow timer Statistics

What is the value of $$x$$?

(1) $$|x|=-\frac{4}{x}$$

(2) $$x=-|\frac{4}{x}|$$

_________________
Math Expert
Joined: 02 Sep 2009
Posts: 52120

### Show Tags

16 Sep 2014, 00:45
Official Solution:

(1) $$|x|=-\frac{4}{x}$$.

The left-hand side of the equation is an absolute value, so it must be non-negative, thus the right-hand side must also be non-negative: $$-\frac{4}{x}\geq{0}$$, thus $$x\leq{0}$$ but since $$x$$ is in denominator it cannot be zero, hence $$x < 0$$.

Next, $$x < 0$$ means that $$|x|=-x$$, so $$|x|=-\frac{4}{x}$$ becomes $$-x=-\frac{4}{x}$$. From this it follows that $$x^2=4$$, so $$x=2$$ or $$x=-2$$. Discard the positive root because we know that $$x$$ must be negative and we are left with $$x=-2$$. Sufficient.

(2) $$x=-|\frac{4}{x}|$$. Re-arrange: $$|\frac{4}{x}|=-x$$.

Basically the same here: the left-hand side of the equation is an absolute value, so it must be non-negative, thus the right-hand side must also be non-negative: $$-x\geq{0}$$. Re-arrange: $$x\leq{0}$$ but since $$x$$ is in denominator it cannot be zero, hence $$x < 0$$.

Next, $$x < 0$$ means that $$|x|=-x$$, so $$|\frac{4}{x}|=-x$$ becomes $$\frac{4}{-x}=-x$$. Simplify: $$x^2=4$$, so $$x=2$$ or $$x=-2$$. Discard the positive root because we know that $$x$$ must be negative and we are left with $$x=-2$$. Sufficient.

_________________
Senior Manager
Joined: 31 Mar 2016
Posts: 384
Location: India
Concentration: Operations, Finance
GMAT 1: 670 Q48 V34
GPA: 3.8
WE: Operations (Commercial Banking)

### Show Tags

01 Aug 2016, 02:01
I think this is a high-quality question and I agree with explanation. Great question but must be classified as 700 not 600
Intern
Joined: 10 Jun 2017
Posts: 23

### Show Tags

23 Apr 2018, 03:05
definitely 700 question...
Re: M30-08 &nbs [#permalink] 23 Apr 2018, 03:05
Display posts from previous: Sort by

# M30-08

Moderators: chetan2u, Bunuel

 Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne Kindly note that the GMAT® test is a registered trademark of the Graduate Management Admission Council®, and this site has neither been reviewed nor endorsed by GMAC®.