GMAT Question of the Day: Daily via email | Daily via Instagram New to GMAT Club? Watch this Video

 It is currently 17 Feb 2020, 13:07

### 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

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

# If x < 3, is (x + 1)/(x - 3) > 1/3?

Author Message
TAGS:

### Hide Tags

GMAT Club Legend
Joined: 11 Sep 2015
Posts: 4320
If x < 3, is (x + 1)/(x - 3) > 1/3?  [#permalink]

### Show Tags

10 Feb 2017, 08:16
2
Top Contributor
12
00:00

Difficulty:

65% (hard)

Question Stats:

56% (01:55) correct 44% (02:04) wrong based on 162 sessions

### HideShow timer Statistics

If x < 3, is $$\frac{x + 1}{x - 3}$$ > 1/3?

(1) x < 2

(2) x > -1

*Kudos for all correct solutions

_________________
Test confidently with gmatprepnow.com
Marshall & McDonough Moderator
Joined: 13 Apr 2015
Posts: 1675
Location: India
Re: If x < 3, is (x + 1)/(x - 3) > 1/3?  [#permalink]

### Show Tags

Updated on: 10 Feb 2017, 10:23
2
(x + 1)/(x - 3) - 1/3 > 0?

2(x + 3)/3(x -3) > 0? --> We have to find out whether the expression (x + 3)/(x - 3) is positive.

St1: x < 2 --> The expression can be positive, negative or zero.
Insufficient.

St2: x > -1 --> -1 < x < 3 --> Numerator is always positive and denominator is always negative. So the expression is negative.
Sufficient.

Originally posted by Vyshak on 10 Feb 2017, 09:58.
Last edited by Vyshak on 10 Feb 2017, 10:23, edited 1 time in total.
Typo
GMAT Club Legend
Joined: 11 Sep 2015
Posts: 4320
Re: If x < 3, is (x + 1)/(x - 3) > 1/3?  [#permalink]

### Show Tags

10 Feb 2017, 10:08
Top Contributor
Vyshak wrote:
(x + 1)/(x - 1) - 1/3 > 0?

2(x + 3)/3(x -3) > 0? --> We have to find out whether the expression (x + 3)/(x - 3) is positive.

St1: x < 2 --> The expression can be positive, negative or zero.
Insufficient.

St2: x > -1 --> -1 < x < 3 --> Numerator is always positive and denominator is always negative. So the expression is negative.
Sufficient.

I think you may have incorrectly transcribed the question.
_________________
Test confidently with gmatprepnow.com
Marshall & McDonough Moderator
Joined: 13 Apr 2015
Posts: 1675
Location: India
Re: If x < 3, is (x + 1)/(x - 3) > 1/3?  [#permalink]

### Show Tags

10 Feb 2017, 10:24
GMATPrepNow wrote:
Vyshak wrote:
(x + 1)/(x - 1) - 1/3 > 0?

2(x + 3)/3(x -3) > 0? --> We have to find out whether the expression (x + 3)/(x - 3) is positive.

St1: x < 2 --> The expression can be positive, negative or zero.
Insufficient.

St2: x > -1 --> -1 < x < 3 --> Numerator is always positive and denominator is always negative. So the expression is negative.
Sufficient.

I think you may have incorrectly transcribed the question.

Thanks. I have corrected it now. But the steps seem to be fine.
GMAT Club Legend
Joined: 11 Sep 2015
Posts: 4320
Re: If x < 3, is (x + 1)/(x - 3) > 1/3?  [#permalink]

### Show Tags

10 Feb 2017, 11:54
Top Contributor
3
GMATPrepNow wrote:
If x < 3, is $$\frac{x + 1}{x - 3}$$ > 1/3?

(1) x < 2

(2) x > -1

Given: x < 3

Target question: Is (x + 1)/(x - 3) > 1/3?
This is a good candidate for rephrasing the target question.
Aside: See below for a video with tips on rephrasing the target question

Since x < 3, we know that (x - 3) will always be NEGATIVE.
So, let's take (x + 1)/(x - 3) > 1/3, and multiply both sides by (x - 3)
We get: x + 1 < (1/3)(x - 3) [ASIDE: since we multiplied both sides by a NEGATIVE value, we REVERSED the inequality sign]
Now take x + 1 < (1/3)(x - 3) and multiply both sides by 3 to get: 3(x + 1) < x - 3
Expand to get: 3x + 3 < x - 3
Subtract x from both sides: 2x + 3 < -3
Subtract 3 from both sides: 2x < -6
Divide both sides by 2 to get: x < -3

This equivalent inequality is much easier to work with. So, ....
REPHRASED target question: Is x < -3?

Statement 1: x < 2
There are several values of x that satisfy statement 1. Here are two:
Case a: x = -7, in which case x < -3
Case b: x = 0, in which case x > -3
Since we cannot answer the REPHRASED target question with certainty, statement 1 is NOT SUFFICIENT

Statement 2: x > -1
If x is greater than -1, then we can be 100% certain that x IS NOT less than -3
Since we can answer the REPHRASED target question with certainty, statement 2 is SUFFICIENT

RELATED VIDEOS FROM OUR COURSE

_________________
Test confidently with gmatprepnow.com
Current Student
Joined: 15 Oct 2014
Posts: 9
GMAT 1: 730 Q50 V38
GPA: 4
WE: Project Management (Energy and Utilities)
If x < 3, is (x + 1)/(x - 3) > 1/3?  [#permalink]

### Show Tags

22 Jun 2017, 02:20
Step 1-
(x-3)+4
X-3
gives
1+4/(x-3)>1/3
(2/(x-3))>-1/3
Now, option b , since x>-1 & <3,LHS can never be greater than -1/3
So B is sufficient
VP
Joined: 24 Nov 2016
Posts: 1200
Location: United States
If x < 3, is (x + 1)/(x - 3) > 1/3?  [#permalink]

### Show Tags

19 Nov 2019, 04:25
GMATPrepNow wrote:
If x < 3, is $$\frac{x + 1}{x - 3}$$ > 1/3?

(1) x < 2

(2) x > -1

$$\frac{x+1}{x-3}>1/3…\frac{(x+1)3-(x-3)1}{3(x-3)}>0…\frac{3x+3-x+3}{3x-9}>0…\frac{2(x+3)}{3(x-3)}>0$$
$$\frac{2(x+3)}{3(x-3)}>0…\frac{(x+3)}{x-3}>0…true:x<-3$$
$$(ie).x=-7:\frac{2(-7+3)}{3(-7-3)}>0…\frac{2(-4)}{3(-10)}>0…\frac{-8}{-30}>0$$

(1) x < 2 insufic

(2) x > -1 sufic

Ans (B)
If x < 3, is (x + 1)/(x - 3) > 1/3?   [#permalink] 19 Nov 2019, 04:25
Display posts from previous: Sort by