Data Sufficiency

If x and y are positive, is y<2?
(1)x>2y
(2)x<y+2

Don't have an OA for this one. Here is my take on it though.

(1)x-2y>0

x=7 and y=1 then x-2y>0 is satisfied and y<2 is satisfied
x=7 and y=3 then x-2y>0 is satisfied but y<2 is not satisfied. Hence Insufficient.

(2)x-y<2

x=7 and y=6 then x-y<2 is satisfied but y<2 is not satisfied
x=2 and y=1 then x-y<2 is satisfied and y<2 is satisfied. Hence Insufficient

Combining both we have...x-2y>0 and x-y<2 multiplying the second statement by -1 we have -x+y>-2 and adding this to the 1st statement we have y<2. Hence C. Hoping to clarify if my logic is correct. Thanks

Seems right to me. answer should be C

plugging numbers in might have been the long route on this one.

neither 1 nor 2 are sufficient alone.
you can actually plug 2 into 1 yielding:
x>2y & x<y+2 = y+2>2y

subtracting a y from either side we're left with:
2>y.

Answer is C

knight247 wrote:If x and y are positive, is y<2?
(1)x>2y
(2)x<y+2

Don't have an OA for this one. Here is my take on it though.

(1)x-2y>0

x=7 and y=1 then x-2y>0 is satisfied and y<2 is satisfied
x=7 and y=3 then x-2y>0 is satisfied but y<2 is not satisfied. Hence Insufficient.

(2)x-y<2

x=7 and y=6 then x-y<2 is satisfied but y<2 is not satisfied
x=2 and y=1 then x-y<2 is satisfied and y<2 is satisfied. Hence Insufficient

Combining both we have...x-2y>0 and x-y<2 multiplying the second statement by -1 we have -x+y>-2 and adding this to the 1st statement we have y<2. Hence C. Hoping to clarify if my logic is correct. Thanks