GMAT Question of the Day - Daily to your Mailbox; hard ones only

 It is currently 14 Oct 2019, 20:59

### 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

# Which of the options must be true if x satisfies the 2 inequalities gi

Author Message
TAGS:

### Hide Tags

Senior Manager
Joined: 25 Dec 2018
Posts: 484
Location: India
Concentration: General Management, Finance
GMAT Date: 02-18-2019
GPA: 3.4
WE: Engineering (Consulting)
Which of the options must be true if x satisfies the 2 inequalities gi  [#permalink]

### Show Tags

05 Mar 2019, 07:16
3
00:00

Difficulty:

95% (hard)

Question Stats:

30% (02:22) correct 70% (02:19) wrong based on 37 sessions

### HideShow timer Statistics

Which of the options must be true if x satisfies the 2 inequalities given below?

((5x−1)/(x+3))<1 and |2x − 5| ≤ 5?

x < 0
x > 0
x < 2
x > 2
None of the above
Intern
Joined: 26 Aug 2018
Posts: 3
Re: Which of the options must be true if x satisfies the 2 inequalities gi  [#permalink]

### Show Tags

05 Mar 2019, 09:20
1

Posted from my mobile device
Manager
Joined: 21 Feb 2019
Posts: 125
Location: Italy
Re: Which of the options must be true if x satisfies the 2 inequalities gi  [#permalink]

### Show Tags

05 Mar 2019, 10:21
3
The two inequalities must be verified at the same time. Let's take into account the first one:

$$\frac{5x - 1}{x + 3}< 1$$
$$\frac{5x - 1 - x - 3}{x + 3} < 0$$
$$\frac{4x - 4}{x + 3} < 0$$

$$Numerator: x ≥ 1$$
$$Denominator: x > - 3$$

So, it will be negative in the range $$(-3,1]$$

Let's consider the second one:

$$|2x - 5| ≤ 5$$
$$-5 ≤ 2x - 5 ≤ 5$$
$$0 ≤ x ≤ 5$$

So, the range is $$[0, 5]$$

Put these outputs together to assess the values for which $$x$$ is verified in both.

This happens when $$0 ≤ x ≤ 1$$

You reject all options except C.
_________________
If you like my post, Kudos are appreciated! Thank you.

MEMENTO AUDERE SEMPER
Manager
Joined: 05 Oct 2017
Posts: 79
Re: Which of the options must be true if x satisfies the 2 inequalities gi  [#permalink]

### Show Tags

22 May 2019, 06:03
1
lucajava wrote:
The two inequalities must be verified at the same time. Let's take into account the first one:

$$\frac{5x - 1}{x + 3}< 1$$
$$\frac{5x - 1 - x - 3}{x + 3} < 0$$
$$\frac{4x - 4}{x + 3} < 0$$

$$Numerator: x ≥ 1$$
$$Denominator: x > - 3$$

So, it will be negative in the range $$(-3,1]$$

Let's consider the second one:

$$|2x - 5| ≤ 5$$
$$-5 ≤ 2x - 5 ≤ 5$$
$$0 ≤ x ≤ 5$$

So, the range is $$[0, 5]$$

Put these outputs together to assess the values for which $$x$$ is verified in both.

This happens when $$0 ≤ x ≤ 1$$

You reject all options except C.

Hi,
how does option C x<2 satisfy our expected range of 0<=x<1?
As per x<2, x can be -1 which is not in our range.
Thanks!
_________________
Press Kudos if you liked my response!!!
Re: Which of the options must be true if x satisfies the 2 inequalities gi   [#permalink] 22 May 2019, 06:03
Display posts from previous: Sort by