CAMANISHPARMAR wrote:
Is x positive?
(1) |x + 6| > 6
(2) |x - 6| > 6
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
Target question: Is x positive? Statement 1: |x + 6| > 6 Applying Rule #2, we can conclude that EITHER x + 6 > 6 OR x + 6 < -6
Let's examine each possible case:
Case a: If x + 6 > 6, then we can subtract 6 from both side to get x > 0. In this case, the answer to the target question is
YES, x IS positiveCase b: If x + 6 < -6, then we can subtract 6 from both side to get x < -12. In this case, the answer to the target question is
NO, x is NOT positiveSince we cannot answer the
target question with certainty, statement 1 is NOT SUFFICIENT
Statement 2: |x - 6| > 6Applying Rule #2, we can conclude that EITHER x - 6 > 6 OR x - 6 < -6
Let's examine each possible case:
Case a: If x - 6 > 6, then we can add 6 to both side to get x > 12. In this case, the answer to the target question is
YES, x IS positiveCase b: If x - 6 < -6, then we can add 6 to both side to get x < 0. In this case, the answer to the target question is
NO, x is NOT positiveSince we cannot answer the
target question with certainty, statement 2 is NOT SUFFICIENT
Statements 1 and 2 combined Statement 1 indirectly tells us that EITHER x > 0 OR x < -12
Statement 2 indirectly tells us that EITHER x > 12 OR x < 0
Since both statements are true, we should look for values of x that satisfy BOTH statements.
There are several values of x that satisfy BOTH statements. Here are two:
Case a: x = 15. In this case, the answer to the target question is
YES, x IS positiveCase b: x = -15. In this case, the answer to the target question is
NO, x is NOT positiveSince we cannot answer the
target question with certainty, the combined statements are NOT SUFFICIENT
Answer: E
Cheers,
Brent