GMATBusters
Is |x + 2| < 3?
(1) x < 1
(2) x > -5
Target question: Is |x + 2| < 3?This is a good candidate for
rephrasing the target question. -------------ASIDE-------------
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 < -kNote: these rules assume that k is positive------------------------------------
So, we can take the target question
Is |x + 2| < 3?....
and rewrite it as
Is -3 < x + 2 < 3?To make things more clear, let's subtract 2 from all three parts of the inequality to get: and rewrite it as
Is -5 < x < 1? REPHRASED target question: Is -5 < x < 1? Statement 1: x < 1 There are infinitely many values of x that satisfy statement 1. Here are two:
Case a: x = 0, in which case the answer to the REPHRASED target question is
YES, it's true that -5 < x < 1Case b: x = -10, in which case the answer to the REPHRASED target question is
NO, it's not true that -5 < x < 1Since we can’t answer the
REPHRASED target question with certainty, statement 1 is NOT SUFFICIENT
Statement 2: x > -5There are infinitely many values of x that satisfy statement 2. Here are two:
Case a: x = 0, in which case the answer to the REPHRASED target question is
YES, it's true that -5 < x < 1Case b: x = 10, in which case the answer to the REPHRASED target question is
NO, it's not true that -5 < x < 1Since we can’t answer the
REPHRASED target question with certainty, statement 2 is NOT SUFFICIENT
Statements 1 and 2 combined Statement 1 tells us that x < 1
Statement 2 tells us that x > -5
We combine the two inequalities we get
-5 < x < 1, which means the answer to the REPHRASED target question is
YES, it's true that -5 < x < 1Since we can answer the
target question with certainty, the combined statements are SUFFICIENT
Answer: C
VIDEO ON REPHRASING THE TARGET QUESTION: