If x and y are positive numbers, is \(x<y\)?

[BTGmoderatorDC]

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

[Jay@ManhattanReview]

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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