j_shreyans wrote:Is |x−6| > 5 ?
(1) x is an integer
(2) x² < 1
OAB
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
Target question: Is |x−6| > 5?
This is a great candidate for rephrasing the target question.
Aside: We have a free video with tips on rephrasing the target question: https://www.gmatprepnow.com/module/gmat- ... cy?id=1100
We'll apply rule #2 (above). If |x−6| > 5, then EITHER x−6 > 5 OR x-6 < -5
Simplify to conclude that EITHER x > 11 OR x < 1
So, we can REPHRASE the target question as....
REPHRASED target question: Is EITHER x > 11 OR x < 1? (this is a YES/NO question)
Statement 1: x is an integer
There are several values of x that satisfy this condition. Here are two:
Case a: x = 7, in which case the answer to the REPHRASED target question is NO,
x is not either greater than 11 OR less than 1
Case b: x = 20, in which case the answer to the REPHRASED target question is YES,
x is either greater than 11 OR less than 1
Since we cannot answer the
REPHRASED target question with certainty, statement 1 is NOT SUFFICIENT
Statement 2: x² < 1
This tells us that -1 < x < 1
This means that
x is definitely less than 1.
So, the answer to the REPHRASED target question is YES,
x is either greater than 11 or less than 1
Since we can answer the
REPHRASED target question with certainty, statement 2 is SUFFICIENT
Answer =
B
Cheers,
Brent
For even more information on rephrasing the target question, you can read this article I wrote for BTG:
https://www.beatthegmat.com/mba/2014/06/ ... t-question
