BrentGMATPrepNow wrote:
Is |x + 3| < 3?
(1) x is negative
(2) x < -6
Target question: Is |x + 3| < 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
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So, we'll take the inequality: |x + 3| < 3
And apply
Rule #1 to get: -3 < x + 3 < 3
Subtract 3 from all sides to get: to get:
-6 < x < 0 We can now rephrase the target question as follows:
REPHRASED target question: Is -6 < x < 0?Aside: the video below has tips on rephrasing the target question Statement 1: x is negative There are infinitely many values of x that satisfy statement 1. Here are two:
Case a: x = -1. In this case, the answer to the REPHRASED target question is
YES, it's true that -6 < x < 0Case b: x = -7. In this case, the answer to the REPHRASED target question is
NO, it's not true that -6 < x < 0Since we can’t answer the
REPHRASED target question with certainty, statement 1 is NOT SUFFICIENT
Statement 2: x < -6For all values of x that are less than -6, the answer to the REPHRASED target question is always the same:
NO, it's not true that -6 < x < 0Since we can answer the
REPHRASED target question with certainty, statement 2 is SUFFICIENT
Answer: B
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