GMAT Changed on April 16th - Read about the latest changes here

 It is currently 25 Apr 2018, 14:57

### 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

# Events & Promotions

###### Events & Promotions in June
Open Detailed Calendar

# What is the value of |x|? (1) The average (arithmetic mean) of x^2 and

 new topic post reply Question banks Downloads My Bookmarks Reviews Important topics
Author Message
TAGS:

### Hide Tags

Math Expert
Joined: 02 Sep 2009
Posts: 44656
What is the value of |x|? (1) The average (arithmetic mean) of x^2 and [#permalink]

### Show Tags

26 Dec 2017, 00:12
2
This post received
KUDOS
Expert's post
1
This post was
BOOKMARKED
00:00

Difficulty:

25% (medium)

Question Stats:

72% (00:30) correct 28% (00:41) wrong based on 86 sessions

### HideShow timer Statistics

What is the value of |x|?

(1) The average (arithmetic mean) of x^2 and 16 is 12.5
(2) x = –|x|
[Reveal] Spoiler: OA

_________________
examPAL Representative
Joined: 07 Dec 2017
Posts: 305
Re: What is the value of |x|? (1) The average (arithmetic mean) of x^2 and [#permalink]

### Show Tags

26 Dec 2017, 01:05
Bunuel wrote:
What is the value of |x|?

(1) The average (arithmetic mean) of x^2 and 16 is 12.5
(2) x = –|x|

We'll solve this question by relying on properties of the absolute value (without calculation).
This is a Logical approach.

Simplifying (1) gives us a quadratic equation x^2 = some number.
Then the two values of x are the positive and negative roots of the same number so they share the same absolute value.
Therefore there is only one solution for |x|.
Sufficient!

(2) Any negative number (or 0) can fulfill this property (try and see!).
Insufficient.

Our answer is (A)
_________________

David
Senior tutor at examPAL
Signup for a free GMAT course

We won some awards:

Join our next webinar (free)
Save up to \$250 on examPAL packages (special for GMAT Club members)

Manager
Joined: 24 Nov 2016
Posts: 148
Re: What is the value of |x|? (1) The average (arithmetic mean) of x^2 and [#permalink]

### Show Tags

26 Dec 2017, 17:55
1
This post received
KUDOS
Bunuel wrote:
What is the value of |x|?

(1) The average (arithmetic mean) of x^2 and 16 is 12.5
(2) x = –|x|

What is the absolute value of $$x$$?
(1) The average (arithmetic mean) of x^2 and 16 is 12.5 So, $$\frac{x^2+16}{2}=12.5$$ then, $$x^2 = 25-16 = 9$$, $$x = 3, or -3$$; absolute value of $$|x|=3$$; sufficient.

(2) x = –|x|. Then, $$x$$ is less than or equal to $$0$$; could be 0 or any negative..; insufficient.

(A) is the answer.
Re: What is the value of |x|? (1) The average (arithmetic mean) of x^2 and   [#permalink] 26 Dec 2017, 17:55
Display posts from previous: Sort by

# What is the value of |x|? (1) The average (arithmetic mean) of x^2 and

 new topic post reply Question banks Downloads My Bookmarks Reviews Important topics

 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®.