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Is |x| + x < 2? (1) x > -1 (2) x < 0

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Bunuel
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Is |x| + x < 2? (1) x > -1 (2) x < 0 [#permalink] New post   31 Mar 2023, 08:45
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A
B
C
D
E

Difficulty:

15% (low)

Question Stats:

78% (01:16) correct 22% (01:28) wrong based on 59 sessions
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Is \(|x|+x <2\) ?

(1) \(x>-1\)
(2) \(x<0\)
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B
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gmatophobia
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Re: Is |x| + x < 2? (1) x > -1 (2) x < 0 [#permalink] New post   31 Mar 2023, 09:03
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Bunuel wrote:
Is \(|x|+x <2\) ?

(1) \(x>-1\)
(2) \(x<0\)


Statement 1

(1) \(x>-1\)

x = 0 ; |x| + x < 2 -- Yes !

x = 1 ; |x| + x < 2 -- No!

As we have two contradicting answers to the question, the statement alone is not sufficient.

We can eliminate A and D.

Statement 2

(2) \(x<0\)

When x < 0, |x| = -x

-x + x = 0

Is \(|x|+x <2\) -- Yes !

The statement is sufficient to answer the question.

Option B
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GMATGuruNY
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Re: Is |x| + x < 2? (1) x > -1 (2) x < 0 [#permalink] New post   31 Mar 2023, 10:46
Expert Reply
Bunuel wrote:
Is \(|x|+x <2\) ?

(1) \(x>-1\)
(2) \(x<0\)


Question stem, rephrased:
Is |x| < 2-x ?

Statement 1: x>-1
If x=0, then |x|=0 and 2-x=2, so the answer to the rephrased question stem is YES.
If x=1, then |x|=1 and 2-x=1, so the answer to the rephrased question stem is NO.
INSUFFICIENT.

Note:
|x| = the distance between x and 0
|x-y| = the distance between x and y

Statement 2: x<0
Here, 2-x is POSITIVE, with the result that 2-x = |2-x|=|x-2|.
Question stem, rephrased:
Is |x| < |x-2|?
In words:
Is x closer to 0 than to 2?
Since x is negative, the answer is YES.
SUFFICIENT.

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sanjayparihar16
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Re: Is |x| + x < 2? (1) x > -1 (2) x < 0 [#permalink] New post   01 Apr 2023, 17:13
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Rule of operating the mod ->

|x|
When assuming x>=0, |x| translates into x
When assuming x<0, |x| translates into -x
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Re: Is |x| + x < 2? (1) x > -1 (2) x < 0 [#permalink]
01 Apr 2023, 17:13
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Bunuel
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