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Bunuel
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What is the value of x? (1) |x| = x (2) |x|^2 = x^2 22 Feb 2021, 01:15
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B
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Difficulty:

45% (medium)

Question Stats:

58% (01:10) correct 42% (01:07) wrong based on 139 sessions

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What is the value of x?

(1) \(|x| = −x\)

(2) \(|x|^2 = −x^2\)
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B
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What is the value of x? (1) |x| = x (2) |x|^2 = x^2 23 Feb 2021, 01:30
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Bunuel
What is the value of x?

(1) \(|x| = −x\)

(2) \(|x|^2 = −x^2\)
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What is the value of x?

(1) |x| = −x. This implies that x is less than or equal to zero. Not sufficient.

(2) \(|x|^2= -x^2\) --> \(x^2=-x^2\) --> \(2x^2=0\) --> \(x=0\). Sufficient.

Answer: B.
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What is the value of x? (1) |x| = x (2) |x|^2 = x^2 22 Feb 2021, 01:28
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Bunuel
What is the value of x?

(1) \(|x| = −x\)

(2) \(|x|^2 = −x^2\)
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Question: x = ?

Statement 1: \(|x| = −x\)

i.e. x is non-positive
i.e.x may be be {0, -1, -2, -3...}

NOT SUFFICIENT

Statement 2: \(|x|^2 = −x^2\)

|x|^2 can NOT be Negative
−x^2 can NOT be Positive

i.e. for \(|x|^2 = −x^2\), x must be zero


i.e. x = 0

SUFFICIENT

Answer: Option B
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What is the value of x? (1) |x| = x (2) |x|^2 = x^2 Updated on: 23 Feb 2021, 04:20
Originally posted by JoeAl on 22 Feb 2021, 02:02.
Last edited by JoeAl on 23 Feb 2021, 04:20, edited 1 time in total.
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Statement1:
X <=0

Statement 2:
x^2 + |x|^2 = 0

Only value that satisfies is 0
Hence B.

Posted from my mobile device
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What is the value of x? (1) |x| = x (2) |x|^2 = x^2 22 Feb 2021, 10:12
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What is the value of x?

Stat1: |x|=−x. so can be any value x= 0, -1, -2...So, Not sufficient.

Stat2: |x|^2=−x^2, which is only possible at x = 0, Sufficient.

So, I think B. :)
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What is the value of x? (1) |x| = x (2) |x|^2 = x^2 25 Feb 2021, 02:36
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(1) |x| = -x

This states that x <= 0

Remember that for data sufficiency questions we must have ONE UNIQUE ANSWER

INSUFFICIENT

(2) (|x|)^2 = -x^2

The expression of an absolute value can never be less than 0. This expression only holds true when x=0

SUFFICIENT.

The answer is B
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What is the value of x? (1) |x| = x (2) |x|^2 = x^2 28 Feb 2021, 02:52
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Solution



Given
In this question stem, we are given no information.

To find
We need to determine
    The value of x

Approach and Working out

Statement 1:
    |x| = -x
      Since |x| ≥ 0, we have that -x ≥ 0
      Thus, x ≤ 0.
      But this gives us no value of x.
    Statement 1 is insufficient alone.

Statement 2:
    \(|x|^2 = -x^2\)
      Since \(|x|^2 ≥ 0\), we have that \(-x^2 ≥ 0\)
      Thus, \(x^2 ≤ 0\).
      This is only possible if x = 0. (since, \(x^2 ≥ 0\))
    Statement 2 is sufficient alone.



Thus, option B is the correct answer.
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What is the value of x? (1) |x| = x (2) |x|^2 = x^2 16 Apr 2023, 06:38
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