Max@Math Revolution wrote:[GMAT math practice question]
On the number line, 0 lies between x and y. Is x > y?
1) The distance between x and 0 is 2 times the distance between y and 0
2) x+y > 0
Since 0 lies between x and y, x and y have DIFFERENT SIGNS.
Statement 1: The distance between x and 0 is 2 times the distance between y and 0
Thus:
|x| = 2|y|
Case 1: y=1, implying that |x| = 2
Since x have must have different sign from y, x=-2.
In this case, x < y, so the answer to the question stem is NO.
Case 2: y=-1, implying that |x| = 2
Since x have must have different sign from y, x=2.
In this case, x > y, so the answer to the question stem is YES.
Since the answer is NO in Case 1 but YES in Case 2, INSUFFICIENT.
Statement 2: x + y > 0
Thus:
x > -y
Case 1: y=1, implying that x > -1
Since x must have a different sign from y, x must be a negative fraction.
In this case, then x < y, so the answer to the question stem is NO.
Case 2: y=-1, implying that x > 1
In this case, x > y, so the answer to the question stem is YES.
Since the answer is NO in Case 1 but YES in Case 2, INSUFFICIENT.
Statements combined:
Of the two cases that satisfy Statement 1, only Case 2 satisfies Statement 2.
Implication:
To satisfy both statements, y must be negative and x must be positive.
Thus, x > y, so the answer to the question stem is YES.
SUFFICIENT.
The correct answer is
C.
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