## If |x| > 3, which of the following must be true?

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### If |x| > 3, which of the following must be true?

by AAPL » Mon Aug 23, 2021 5:18 am

00:00

A

B

C

D

E

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If |x| > 3, which of the following must be true?

I. x > 3
II. x^2 > 9
III. |x - 1| > 2

A. I only
B. II only
C. I and II only
D. II and III only
E. I, II, and III

OA D

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### Re: If |x| > 3, which of the following must be true?

by [email protected] » Mon Aug 23, 2021 3:44 pm
AAPL wrote:
Mon Aug 23, 2021 5:18 am
GMAT Prep

If |x| > 3, which of the following must be true?

I. x > 3
II. x^2 > 9
III. |x - 1| > 2

A. I only
B. II only
C. I and II only
D. II and III only
E. I, II, and III

OA D
If |x| > 3, then it must be true that EITHER x > 3 OR x < -3

(1) x > 3
This need not be true, since it's also possible that x < -3.
For example, x COULD equal -5
So, statement I need not be true.
ELIMINATE answer choice A, C and E

Important: The remaining two answer choices (B and D) both state that statement II is true.
So, we need not analyze statement II, since we already know it must be true.
That said, let's analyze it for "fun"
(2) x² > 9
This means that EITHER x > 3 OR x < -3
Perfect - this matches our original conclusion that EITHER x > 3 OR x < -3

(3) |x-1| > 2
Let's solve this further.
We get two cases:
case a) x - 1 > 2, which means x > 3 PERFECT
or
case b) x - 1 < -2, which means x < -1
Must it be true that x < -1?
YES.
We already learned that EITHER x > 3 OR x < -3
If x < -3, then we can be certain that x < -1
For example, if I tell you that the temperature is less than -3 degrees Celsius, can we be certain that the temperature is less than -1 degrees? Yes.
So, statement 3 must also be true.