BTGModeratorVI wrote: ↑Thu Mar 19, 2020 5:21 am
If x and y are positive numbers, is (x+1)/(y+1) > x/y?
(1) x > 1
(2) x < y
Answer:
B
Source: Official Guide
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/y
Since 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 + x
Subtract xy from both sides to get:
y > x
So, 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 > x
Since 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
