BTGmoderatorDC wrote:If x and y are positive numbers, is \(x<y\)?
1. \(\frac{(x+1)}{(y+1)}>\frac{x}{y}\)
2. \(\frac{(x-1)}{(y-1)} < \frac{(x+1)}{(y+1)}\)
OA D
Source: e-GMAT
Given: x and y are positive numbers
We have to determine whether \(x<y\).
Let's take each statement one by one.
1. \(\frac{(x+1)}{(y+1)}>\frac{x}{y}\)
We have (x + 1) / (y + 1) > x / y
(x + 1) / (y + 1) - x / y > 0
=> (y - x) / y(y + 1) > 0
=> (y - x) > 0*[ y(y + 1)]
=> (y - x) > 0
=> y > x
The answer is no. A unique answer. Sufficient.
2. \(\frac{(x-1)}{(y-1)} < \frac{(x+1)}{(y+1)}\)
On similar, we can conclude that y > x. Sufficient.
The correct answer:
D
Hope this helps!
-Jay
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