Troube with Inequality... PLz help...

Expert replies

Viren1808: Junior | Next Rank: 30 Posts; Posts: 16; Joined: Sun Oct 16, 2011 10:08 am

by Viren1808 » Mon Nov 14, 2011 4:12 am

Q. Is (x+1)/(x-3) < 0 ?
(1) -1 < x < 1
(2) x^2 - 4 < 0

Request you to kindly provide some trick to tackle such problems during the test in fastest possible ways.

Like this post

Source: Beat The GMAT — Data Sufficiency | Mon Nov 14, 2011 4:12 am

shankar.ashwin: Legendary Member; Posts: 966; Joined: Sat Jan 02, 2010 8:06 amFollowed by: 21 members; Thanked: 230 times

by shankar.ashwin » Mon Nov 14, 2011 4:20 am

Find values in each statement, substitute in the question and find a pattern.

Statement 1:

Given x= 0.

We can find the expression becomes -1/3 < 0. Sufficient.

Statement 2:

-2<x<2

or x = (-1,0,1)

Substitute x = -1, expression becomes 0 (Numerator becomes 0)

We have already checked for x=0. So 2 contradicting answers. Insufficient.

A IMO

Like this post

rijul007: Legendary Member; Posts: 588; Joined: Sun Oct 16, 2011 9:42 amFollowed by: 9 members; Location: New Delhi, India; Thanked: 130 times; GMAT Score:720

by rijul007 » Mon Nov 14, 2011 4:23 am

Is (x+1)/(x-3) < 0 ?
(1) -1 < x < 1
(2) x^2 - 4 < 0

(x+1)/(x-3) < 0

Case 1- [x > 3]

(x+1)/(x-3) will be positive

Case 2- [ -1 < x < 3]

(x+1)/(x-3) will be negative

Case 3 - [x < -1]

(x+1)/(x-3) positive

Statement 1
-1 < x < 1
this satisifies case 2

Sufficient

Statement 2
x^2 - 4 < 0
(x+2)(x-2) < 0
-2 < x < 2

values of the expression in this range can either be -ve or +ve

Insufficient

Option A

Like this post

GMATGuruNY: GMAT Instructor; Posts: 15539; Joined: Tue May 25, 2010 12:04 pmFollowed by: 1906 members; Location: New York, NY; Thanked: 13060 times; GMAT Score:790

by GMATGuruNY » Mon Nov 14, 2011 5:45 am

Viren1808 wrote:Q. Is (x+1)/(x-3) < 0 ?
(1) -1 < x < 1
(2) x^2 - 4 < 0

Request you to kindly provide some trick to tackle such problems during the test in fastest possible ways.

Determine the critical points: the values of x that will make the numerator or the denominator equal to 0.
The critical points here are x=-1 and x=3.
These are the only values of x where (x+1)/(x-3) is equal to 0 or is undefined.
Thus, when x is any other value, (x+1)/(x-3) will be either greater than or less than 0.
To determine the range of x, test one value to the left and right of each critical point.

x < -1.
If x=-2, we get:
(-2+1)/(-2-3) < 0.
1/5 < 0.
Doesn't work.
x < -1 is not part of the range.

-1 < x < 3.
If x=0, we get:
(0+1)/(0-3) < 0.
-1/3 < 0.
This works.
-1<x<3 is part of the range.

x > 3.
If x=4, we get:
(4+1)/(4-3) < 0.
5 < 0.
Doesn't work.
x > 3 is not part of the range.

Question rephrased: Is -1 < x < 3?

Statement 1: -1 < x < 1.
Thus, x must be between -1 and 3.
SUFFICIENT.

Statement 2: xÂ²<4.
Since it's possible that x = 0 (which is between -1 and 3) or that x = -3/2 (which is not between -1 and 3), INSUFFICIENT.

The correct answer is A.

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

Like this post

kevincanspain: GMAT Instructor; Posts: 613; Joined: Thu Mar 22, 2007 6:17 amFollowed by: 64 members; Location: madrid; Thanked: 171 times; GMAT Score:790

by kevincanspain » Mon Nov 14, 2011 7:24 am

Viren1808 wrote:Q. Is (x+1)/(x-3) < 0 ?
(1) -1 < x < 1
(2) x^2 - 4 < 0

Request you to kindly provide some trick to tackle such problems during the test in fastest possible ways.

I believe that it is usually worthwhile to simplify the question:

Note that a fraction is negative if and only if the numerator and denominator have opposite signs: in this case, because x+1 > x-3 , the answer will be yes if and only if x+1 > 0
and x - 3 < 0
i.e. -1 < x < 3.

Kevin Armstrong
GMAT Instructor
Gmatclasses
Madrid

Like this post

Post new topic Post Reply

• Page 1 of 1

GMAT Course Reviews

560 reviews

1168 reviews

431 reviews

359 reviews

147 reviews

5/5

5 Star (560 Reviews)

"Target Test Prep is the closest to the official version of the GMAT exam, about 99% accuracy in terms of the quality and quantity of information. The course has excellently created singular sets of focused lessons and tests for every possible topic that one could come across in the official GMAT exam."

"The TTP course maximizes the efficiency of the time you spend studying. It will take time and effort but I could almost guarantee that if you complete the course exactly as it is laid out you will get an amazing score. They also have a very responsive team willing to help with any questions you might have."

"TTP has two things that I think no other test prep company offers: A teaching approach that reinforces understanding and an attitude that will give you the mental preparedness needed to succeed on the test. TTP gives you a deep understanding of the concept you need to know while teaching you how to think."

Write a Review