Bunuel wrote:
If x and y are positive numbers, is \(\frac{x + 1}{y + 1} > \frac{x}{y}\)?
(1) x > 1
(2) x < y
Target question: Is (x + 1)/(y + 1) > x/y ? Given: x and y are positive numbers This is a great candidate for
rephrasing the target question.
We have the inequality:
(x + 1)/(y + 1) > x/ySince y is positive, we can multiply both sides of the inequality by y
Likewise, since y is positive, we know that y+1 is positive, which means we can multiply both sides of the inequality by (y+1)
When perform both of these multiplications we get:
(x + 1)(y) > (x)(y + 1)Expand to get:
xy + y > xy + xSubtract xy from both sides to get:
y > xSo, we can now ask...
REPHRASED target question: Is y > x ? Statement 1: x > 1 There's no information about y, so there's no way to determine whether or not
y > xSince we cannot answer the
REPHRASED target question with certainty, statement 1 is NOT SUFFICIENT
Statement 2: x < y Perfect!!!
Since we can answer the
REPHRASED target question with certainty, statement 2 is SUFFICIENT
Answer: B
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Brent Hanneson – Creator of gmatprepnow.com
