chetan2u wrote:
Is x < |x|?
(1) x > 2x
(2) x is non-positive integer
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 0In 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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