GMATsid2016 wrote:If |x|>3, which of the following must be true?
1) x>3
2) x^2>9
3) |x-1|>2
A) 1 only
B) 2 only
C) 1 and 2 only
D) 2 and 3 only
E) 1,2, and 3
When solving inequalities involving ABSOLUTE VALUE, there are 2 things you need to know:
Rule #1: If |something| < k, then -k < something < k
Rule #2: If |something| > k, then EITHER something > k OR something < -k
Note: these rules assume that k is positive
Given: |x| > 3
Applying Rule #2, we get:
EITHER x > 3 OR x < -3
Now check the statements...
1) x > 3
This ignores the possibility that x < -3
For example, x could equal -4, in which case
statement 1 is NOT TRUE
ELIMINATE answer choices A, C and E
Important: Check out the two remaining answer choices: B) 2 only and D) 2 and 3 only
Since both remaining answer choices tell us that
statement 2 is true, we need not check statement 2.
So, we need only check statement 3...
3) |x-1|>2
Applying Rule #2, we get:
EITHER x - 1 > 2 OR x - 1 < -2
Consider both cases:
case a) x - 1 > 2
Add 1 to both sides to get
x > 3
case b) x - 1 < -2
Add 1 to both sides to get
x < -1
So...
EITHER x > 3 OR x < -1
Well, the first part,
x > 3, matches the one part of the conclusion we reached from the given information.
But what about
x < -1?
Well, if we already know from the given information that
x < -3, then we can be certain that
x < -1.
So,
statement 3 must be TRUE
Answer:
D
RELATED VIDEO
- Inequalities and absolute value:
https://www.gmatprepnow.com/module/gmat ... /video/985
