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

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Manager
Joined: 25 Dec 2018
Posts: 131
Location: India
Concentration: General Management, Finance
GMAT 1: 590 Q48 V23
GPA: 3.4
WE: Engineering (Consulting)
Which of the options must be true if x satisfies the 2 inequalities gi  [#permalink]

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05 Mar 2019, 07:16
1
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Difficulty:

75% (hard)

Question Stats:

33% (02:08) correct 67% (01:46) wrong based on 18 sessions

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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: 1
Re: Which of the options must be true if x satisfies the 2 inequalities gi  [#permalink]

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05 Mar 2019, 09:20

Posted from my mobile device
Intern
Joined: 21 Feb 2019
Posts: 36
Re: Which of the options must be true if x satisfies the 2 inequalities gi  [#permalink]

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05 Mar 2019, 10:21
1
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.
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Re: Which of the options must be true if x satisfies the 2 inequalities gi   [#permalink] 05 Mar 2019, 10:21
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