Is x positive? (1) |x + 6| 6 (2) |x - 6| 6

Question

Is x positive?

(1) |x + 6| > 6

(2) |x - 6| > 6

BrentGMATPrepNow · Accepted Answer

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 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 positive Case 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 positive Since we cannot answer the target question with certainty, statement 1 is NOT SUFFICIENT Statement 2 : |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 add 6 to both side to get x > 12. In this case, the answer to the target question is YES, x IS positive Case 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 positive Since 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 positive Case b : x = -15. In this case, the answer to the target question is NO, x is NOT positive Since we cannot answer the target question with certainty, the combined statements are NOT SUFFICIENT Answer: E Cheers, Brent

SatyamOP · Answer

Solution: Pre Analysis: We are asked if x is positive or not This is a YES-NO question Statement 1: |x + 6| > 6 We know that if we have |x±a|>d , then the range of x will be x±a>d and x±a<-d Therefore, if |x + 6| > 6 , then we can say x+6>6 and x+6<-6 Or x>0 and x<-12 So, the value of x can be, for example, 2 (positive) and also -13 (negative) Thus, statement 1 alone is not sufficient and we can eliminate options A and D Statement 2: |x - 6| > 6 We know that if we have |x±a|>d , then the range of x will be x±a>d and x±a<-d Therefore, if |x - 6| > 6 , then we can say x-6>6 and x-6<-6 Or x>12 and x<0 So, the value of x can be, for example, 13 (positive) and also -1 (negative) Thus, statement 2 alone is also not sufficient Combining: Upon combining, the range that we get is x>12 and x<-12 And we still cannot say if x is positive or not Hence the right answer is Option E

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Is x positive? (1) |x + 6| > 6 (2) |x - 6| > 6

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