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

Redeem

If y =|x|- x, is y> 0?

Expert replies
Source: — Data Sufficiency |

by GMATGuruNY » Fri Jan 13, 2017 8:04 am
NandishSS wrote:If y =|x|- x, is y> 0?
(1) x < 0
(2) y > 2
Statement 1:
Since y = |x| - x, we get:
y = |negative| - (negative) = positive + positive = positive.
Thus, y > 0.
SUFFICIENT.

Statement 2:
Since y > 2, it must be true that y > 0.
SUFFICIENT.

The correct answer is D.
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
Join the discussion

by [email protected] » Fri Jan 13, 2017 10:14 am
Hi NandishSS,

This question can be solved with Number Properties or by TESTing VALUES.

We're told that Y = |X| - X. We're asked if Y is greater than 0. This is a YES/NO question.

1) X < 0

IF...
X = -1
Y = |-1| - (-1) = 2 and the answer to the question is YES.

Notice how the math 'works' here: the absolute value of a negative (which is POSITIVE) minus a negative (which creates another POSITIVE)... means that Y will ALWAYS be positive when X is negative. Thus, the answer to the question would ALWAYS be YES.
Fact 1 is SUFFICIENT.

2) Y > 2

If Y is greater than 2, then the answer to the question is ALWAYS YES.
Fact 2 is SUFFICIENT.

Final Answer: D

GMAT assassins aren't born, they're made,
Rich
Contact Rich at [email protected]
Image
Join the discussion

by Jay@ManhattanReview » Sat Jan 14, 2017 11:58 pm
NandishSS wrote:If y =|x|- x, is y> 0?
(1) x < 0
(2) y > 2

OA:D

Source:Math Revolution
Hi Nandish,

y =|x|- x can rewritten as:

1. y =|x| - |x|, if x is positive
=> y = 0
=> y is not less than 0.

2. y =|x| - x = 0, if x = 0
=> y = 0
=> y is not less than 0.

3. y =|x| + |x|, if x is negative
=> y = 2*|x| = a positive quantity
=> y > 0.

Let us see each statement one by one.

S1: x < 0 => x is negative. This is case 3 scenerio. Suffcient.

S2: y > 2 itself answers the question. A number greater than 2 means that the number is greater than 0. Sufficient.

Answer: D

Hope this helps!

-Jay
_________________
Manhattan Review GMAT Prep

Locations: New York | New Delhi | Seoul | Cairo | and many more...

Schedule your free consultation with an experienced GMAT Prep Advisor! Click here.
Join the discussion