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If 3x + 1 < 2x < 9 - x, which of the following must be true? Updated on: 11 Feb 2014, 07:22
Originally posted by arunspanda on 11 Feb 2014, 07:08.
Last edited by Bunuel on 11 Feb 2014, 07:22, edited 1 time in total.
Renamed the topic and edited the question.
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Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!

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50% (01:41) correct 50% (02:05) wrong based on 18 sessions

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If 3x + 1 < 2x < 9 - x, which of the following must be true?

I. -1 < x < 3
II. x < -1
III. x < 3

(A) II only
(B) III only
(C) I and II only
(D) II and III only
(E) I, II and III

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A
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If 3x + 1 < 2x < 9 - x, which of the following must be true? 11 Feb 2014, 07:20
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Just try plugging in a number like 0 or 1, and you'll quickly find that the inequality doesn't hold.

So you can immediately cross out any answers with I or III, leaving just (A) II only.
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If 3x + 1 < 2x < 9 - x, which of the following must be true? 11 Feb 2014, 09:38
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There are two conditions.

3x +1 < 2x and 2x < 9-x
Or, 3x -2x < -1 and 3x < 9
Or, x < -1 and x < 3

Lower value of x satisfies both conditions. [Eliminate the less limiting inequality]

To check : 3x +1 < 2x < 9-x

x < -1 , let us choose x =-2 : -5 < -4 < 11 ....True
-1< x < 3, let us choose x=1: 4 < 2 < 8 ........False

Thus, x < -1 is the solution, which satisfies both conditions: 3x + 1 < 2x and 2x < 9-x

----------------------(-1)------------(3)-------------------------

Answer: (A)
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If 3x + 1 < 2x < 9 - x, which of the following must be true? 11 Feb 2014, 23:52
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arunspanda
If 3x + 1 < 2x < 9 - x, which of the following must be true?

I. -1 < x < 3
II. x < -1
III. x < 3

(A) II only
(B) III only
(C) I and II only
(D) II and III only
(E) I, II and III
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Technically, 'which of the following must be true?' implies that you are looking for a relation that must hold for every value that x can take. In that case, if (II) is correct, (III) is automatically correct. This means that if every value that x can take is less than -1, then every such value is obviously less than 3 too.

If the question is looking for the range in which x must lie, then the question must ask so.
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If 3x + 1 < 2x < 9 - x, which of the following must be true? 12 Feb 2014, 03:26
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arunspanda
If 3x + 1 < 2x < 9 - x, which of the following must be true?

I. -1 < x < 3
II. x < -1
III. x < 3

(A) II only
(B) III only
(C) I and II only
(D) II and III only
(E) I, II and III

Technically, 'which of the following must be true?' implies that you are looking for a relation that must hold for every value that x can take. In that case, if (II) is correct, (III) is automatically correct. This means that if every value that x can take is less than -1, then every such value is obviously less than 3 too.

If the question is looking for the range in which x must lie, then the question must ask so.
Show more


Kindly refer to the Q 156 of Quantitative Review, 2nd Edition, page 82.
The question in this post is very similar to the referred question in OG.
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If 3x + 1 < 2x < 9 - x, which of the following must be true? 13 Feb 2014, 01:34
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arunspanda
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arunspanda
If 3x + 1 < 2x < 9 - x, which of the following must be true?

I. -1 < x < 3
II. x < -1
III. x < 3

(A) II only
(B) III only
(C) I and II only
(D) II and III only
(E) I, II and III

Technically, 'which of the following must be true?' implies that you are looking for a relation that must hold for every value that x can take. In that case, if (II) is correct, (III) is automatically correct. This means that if every value that x can take is less than -1, then every such value is obviously less than 3 too.

If the question is looking for the range in which x must lie, then the question must ask so.


Kindly refer to the Q 156 of Quantitative Review, 2nd Edition, page 82.
The question in this post is very similar to the referred question in OG.
Show more

The difference is that the question from OG is correct and this one is not. The correct answer for this question must be D, not A.

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Still interested in this question? Check out the "Best Topics" block above for a better discussion on this exact question, as well as several more related questions.
Thank you for understanding, and happy exploring!
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