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If (|x| - 2)(x + 5) < 0, then which of the following must be true?

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Brian_1

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11 Sep 2025, 01:36

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Erm, conversely x can be -10 and then option B will not be valid ?

Bunuel

You are wrong. It's the other way around. Again, we have \(x < -5\) or \(-2 < x < 2\). ANY \(x\) from these possible ranges will for sure be less than 2 (option B). E, x < -5, on the other hand, is NOT always true, because x can be say 0, and in this case x < -5 will not be true.

To understand the underline concept better practice other Trickiest Inequality Questions Type: Confusing Ranges.

Bunuel

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11 Sep 2025, 01:40

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Brian_1

Erm, conversely x can be -10 and then option B will not be valid ?

Yes, x can be -10 as it is in the valid range (\(x < -5\) or \(-2 < x < 2\)). But in this case how is B (x < 2) not correct? Isn't -10 less than 2? Please invest more time in the question and the discussion. Follow the links to the similar questions for more.

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11 Sep 2025, 01:45

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Sorry.

Help me understand, I am new to GMAT.

If x = -2, then it doesn't satisfy the given inequality. As, Mod(-2) - 2 will result in 0. And 0 is not less than 0 ? Hence, B cannot be the answer for sure.

Thoughts ??

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11 Sep 2025, 01:51

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Brian_1

The valid ranges for x are \(x < -5\) or \(-2 < x < 2\). So, x CANNOT be -2! Please, invest time and study the discussion carefully!

Brian_1

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11 Sep 2025, 01:57

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Nvm, I understood.

X can take a lot of values and it has to less than 2. Gotcha. I got caught up with the option choices. Thanks

Bunuel

The valid ranges for x are \(x < -5\) or \(-2 < x < 2\). So, x CANNOT be -2! Please, invest time and study the discussion carefully!

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25 Nov 2025, 23:39

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If (|x| - 2)(x + 5) < 0, then which of the following must be true?

Case 1: |x| - 2 < 0 & x + 5>0
|x| < 2; -2 < x < 2
x > -5

-2 < x < 2 (1)

Case 2: |x| - 2 > 0 & x + 5 < 0
x < -5
x < -2 or x > 2

x < -5 (2)

Combining (1) & (2)

-2 < x < 2 or
x < -5

x < 2 must be TRUE

IMO B

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24 Apr 2026, 22:54

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For the first factor, mod(x) = 2 is the critical point.
-2 to 2 gives negative values for mod(x)-2 expression.

Now for each of this range from -2 to 2 we see that second factor is always positive.
So it remains negative through and satisfies.

Between -2 to 5 we see it is positive.

For making second factor to be less than 0 we need x<-5.
And for each of these values first expression remains positive and satisfies expression.

So basically all values x<2 satisfies except -2 to 5 range and x<2 is a guarantee this way.
If x>2 then both equations become positive, this not valid.

Answer: Option B

Bunuel

If (|x| - 2)(x + 5) < 0, then which of the following must be true?

A. x > 2
B. x < 2
C. -2 < x < 2
D. -5 < x < 2
E. x < -5

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24 Apr 2026, 23:24

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Official question???

Bunuel

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24 Apr 2026, 23:42

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Official question???

This is a GMAT Club Tests questions. One of the most trickiest and hardest for the students.

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25 Apr 2026, 01:58

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Bunuel
Option B also includes values like -3 & -4. At these values of x the inequality becomes positive. Does anyone can explain why B is answer?

Bunuel

If (|x| - 2)(x + 5) < 0, then which of the following must be true?

A. x > 2
B. x < 2
C. -2 < x < 2
D. -5 < x < 2
E. x < -5

Option B also includes values like -3 & -4. At these values of x the inequality becomes positive. Does anyone can explain why B is answer?

Bunuel

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25 Apr 2026, 04:37

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rgv143

Bunuel
Option B also includes values like -3 & -4. At these values of x the inequality becomes positive. Does anyone can explain why B is answer?

Your doubt is addressed in the thread. Please review.

To understand the underline concept better practice other Trickiest Inequality Questions Type: Confusing Ranges.

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