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21 Feb 2017, 18:21
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A
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
45%
(medium)
Question Stats:
59% (01:08) correct
41%
(01:06)
wrong
based on 362
sessions
History
Date
Time
Result
Not Attempted Yet
22 Feb 2017, 09:22
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chetan2u
Great question, chetan2u!
Target question: Is x < |x|?
This is a great candidate for rephrasing the target question.
To see what I mean, let's examine 3 possible scenarios: x is negative, x is positive and x is zero
Scenario #1: x is negative
If x is negative, then |x| is positive. So, we get x < |x|, since x is negative and |x| is positive.
For example, if x = -2, then we have -2 < |-2|
Scenario #2: x is positive
If x is positive, then x and |x| are BOTH positive. In fact, x = |x|
For example, if x = 3, then we have 3 = |3|
Scenario #3: x is zero
Since |0| = 0, then we have the case where x = |x|
So, the ONLY time that x < |x| is when x is negative.
So, asking Is x < |x|? is the SAME as asking, Is x negative?
This means we can REPHRASE the target question....
REPHRASED target question: Is x negative?
Now onto the statements.....
Statement 1: x > 2x
Subtract x from both sides to get: 0 > x
In other words, x is negative. PERFECT!
Since we can answer the REPHRASED target question with certainty, statement 1 is SUFFICIENT
Statement 2: x is non-positive integer
If x is NOT POSITIVE, then x can be negative OR x can equal 0
In other words, x may or may not be negative.
Since we cannot answer the REPHRASED target question with certainty, statement 2 is NOT SUFFICIENT
Answer: A
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General Discussion
22 Feb 2017, 07:05
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Option A
Statement 1 : this will be true only when x is negative
Statement 2 : x could be zero or negative. not sufficient
Statement 1 : this will be true only when x is negative
Statement 2 : x could be zero or negative. not sufficient
