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

Redeem

Equation

Expert replies
by [email protected] » Sun Dec 08, 2013 3:15 am
The answer is B but im not clear cox if we test value for x-1 for example if X is -8 then -8-1 is a perfect square but does that prove that X is positive?

Please explain-Thanks
Attachments
Algebra.jpg
Join the discussion
Source: — Data Sufficiency |

by GMATGuruNY » Sun Dec 08, 2013 5:13 am
Statement 1: 1/(x+1) < 1
It's possible that x=1, since 1/(1+1) = 1/2, which is less than 1.
In this case, x is positive.
It's possible that x=-2, since 1/(-2+1) = -1, which is less than 1.
In this case, x is negative.
INSUFFICIENT.

Statement 2: x-1 is a perfect square
A perfect square is the square of an integer:
0² = 0
1² = 1
2² = 4
3² = 9
And so on.
In the list above, the least possible option for x-1 is 0:
x-1 = 0
x = 1.
Since the least possible option for x is 1, we know that x must be positive.
SUFFICIENT.

The correct answer is B.
[email protected] wrote:The answer is B but im not clear cox if we test value for x-1 for example if X is -8 then -8-1 is a perfect square but does that prove that X is positive?

Please explain-Thanks
-8-1 = -9 is not the square of an integer and thus is NOT a perfect square.
As shown by the list above, the smallest perfect square is 0.
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