Question: If x = - |x|, then which one of the following statements could be true?

1. x = 0
2. x < 0
3. x > 0

(A) None
(B) I only
(C) III only
(D) I and II
(E) II and III

Correct Answer: (D)

Solution and Explanation:

Approach Solution 1:

The problem statement implies that

Given:

• x = - |x|

Asked:

• To find out which of the following statements could be true that is

1. x = 0
2. x < 0
3. x > 0

The equation x = - |x| indicates that:

1. x can be zero.
2. x can be any negative integer.

Now, let’s verify each of the options

1. x = 0 => True since it depends on point (1)
2. x < 0 => True since it depends on point (2)
3. x > 0 => False, since the value of x should be either zero or less than 0.

Approach Solution 2:

The problem statement cites an equation x = - |x|

Find Out:

• Which of the following statements could be true

1. x = 0
2. x < 0
3. x > 0

The equation as stated in the question is x = - |x|
We can rewrite the equation as |x| is greater than or equal to 0
Hence, -|x| is less than or equal to 0
Therefore, x must be 0 or less than 0.

Approach Solution 3:

The problem statement informs that:

Given: x = - |x|

Find Out: Which of the following statements could be true:

1. x = 0
2. x < 0
3. x > 0

We can solve the problem by using the trial and error process.

1. x = 0, therefore, we can say,
   0= -|0| = 0 — YES.
2. x < 0, therefore by substituting we get,
   -1= -|1|
   -1= -1 — YES.

3.  x > 0, therefore by substituting we get,
   2= -|2|
   2 = -2 — NO.

“If x = - |x|, then which one of the following statements”- is a topic of the GMAT Quantitative reasoning section of the GMAT exam. This question has been taken from GMAT Official Guide Quantitative Review 2021. GMAT Problem Solving questions test the logical thinking capacity of candidates in order to solve quantitative problems. GMAT Quant practice papers comprise miscellaneous kinds of questions that enable candidates to boost their mathematical knowledge.

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