If x and y are positive, is xy > x + y? GMAT Data Sufficiency

Solving the question using a variable approach method in which we have to remember that equal numbers of variables and independent equations ensure a solution.

xy > x + y
⇔ xy - x - y > 0
⇔ xy - x - y + 1 > 1
⇔ (x-1)(y-1) > 1

S1: x < ;
Put x = 1/2, y = 2; 1 > 2.5; Answer is NO
Put x = 3, y = 4; 12 > 7; Answer is YES

Not sufficient

S2: 2 < x
x = 3, y = 4: Yes
x = 3, y = 1/2: No

Not sufficient

Correct option: C

xy > x + y
⇔ xy - x - y > 0
⇔ xy - x - y + 1 > 1
⇔ (x-1)(y-1) > 1
Since we have 2 variables (x and y) and 0 equations,C is most likely to be the answer.

Statement 1:
x = 2, y = 3: Yes
x = 1/2, y = 1: No

The statement 1 is not sufficient.

Statement 2:
x = 3, y = 4: Yes
x = 3, y = 1/2: No

The statement 2 is not sufficient.

Correct option: C

xy > x + y
xy - x - y > 0
Adding 1 on both sides
xy - x - y + z > 1
(x - 1)(y - 1) > 1
So either
x - 1 > 1 more so x > 2
or y - 1 > 1 more so y > 2
So the question is x>2 and y>2. We can answer our question if we know about x and y.

Statement 1:
x < y
We know that x > 0 and y > 0, but we don't know if x > 2 and y > 2

Insufficient.

Statement 2:
2 < x
We know that x > 0, so x > 2 but don't have any information about y

Insufficient

Now combining S1 and S2, we have:
2 < x < y
So, we have x > 2 and y > 2

Correct option: C