BREAKING: Target Test Prep releases Brand New 2026 On Demand GMAT prep course

Redeem

Manhattan CAT

This topic has expert replies
Post new topic Post Reply
Previous Topic Next Topic
Senior | Next Rank: 100 Posts
Posts: 84
Joined: Sat Jun 18, 2011 9:50 pm
Location: New Delhi
Thanked: 35 times
Followed by:3 members
GMAT Score:800

Manhattan CAT

by CSASHISHPANDAY » Sat Jun 29, 2013 11:18 pm
What is the value of y?

(1) 3|x^2 - 4| = y - 2

(2) |3 - y| = 11

Ans C

Somehow I can reach on right ans but want to know that in choice (1) how one can say that

absolute value expression |x^2 - 4| must be greater than or equal to 0.
If you find one of my posts helpful, please take a moment to click on the "Thank" icon.
Contact me for free GMAT Learning!
Top
Source: — Data Sufficiency |
User avatar
GMAT Instructor
Posts: 15539
Joined: Tue May 25, 2010 12:04 pm
Location: New York, NY
Thanked: 13060 times
Followed by:1906 members
GMAT Score:790

by GMATGuruNY » Sun Jun 30, 2013 2:17 am
CSASHISHPANDAY wrote:What is the value of y?

(1) 3|x^2 - 4| = y - 2

(2) |3 - y| = 11

Ans C

Somehow I can reach on right ans but want to know that in choice (1) how one can say that

absolute value expression |x^2 - 4| must be greater than or equal to 0.
|a-b| = the DISTANCE between a and b.
Thus, |x²-4| = the distance between x² and 4.
The distance between two values must be NONNEGATIVE.
Thus, |x²-4| ≥ 0.

Statement 1: 3|x^2 - 4| = y - 2
|x²-4| = (y-2)/3.
Since |x²-4| ≥ 0, it must also be true that (y-2)/3 ≥ 0.
Thus:
(y-2)/3 ≥ 0
y-2 ≥ 0
y ≥ 2.
No way to determine the value of y.
INSUFFICIENT.

Statement 2: |3 - y| = 11
Case 1: 3-y = 11
-y = 8
y = -8.

Case 2: -3+y = 11
y = 14.

Since it's possible that y=-8 or y=14, INSUFFICIENT.

Statements combined:
Only y=14 satisfies both statements.
SUFFICIENT.

The correct answer is C.
Private tutor exclusively for the GMAT and GRE, with over 20 years of experience.
Followed here and elsewhere by over 1900 test-takers.
I have worked with students based in the US, Australia, Taiwan, China, Tajikistan, Kuwait, Saudi Arabia -- a long list of countries.
My students have been admitted to HBS, CBS, Tuck, Yale, Stern, Fuqua -- a long list of top programs.

As a tutor, I don't simply teach you how I would approach problems.
I unlock the best way for YOU to solve problems.

For more information, please email me (Mitch Hunt) at [email protected].
Student Review #1
Student Review #2
Student Review #3
Top
Senior | Next Rank: 100 Posts
Posts: 84
Joined: Sat Jun 18, 2011 9:50 pm
Location: New Delhi
Thanked: 35 times
Followed by:3 members
GMAT Score:800

by CSASHISHPANDAY » Sun Jun 30, 2013 3:15 am
can u plz explain the concept in detail
If you find one of my posts helpful, please take a moment to click on the "Thank" icon.
Contact me for free GMAT Learning!
Top
Post new topic Post Reply
• Page 1 of 1