Hi abhasjha,

Rahul has correctly answered this question. I'm going to add a few more details to the explanation.

We're told that each of the variables is either 0 or 1, which really limits the possibilities. We're asked for the value of W+X+Y+Z.

Fact 1: W/2 + X/4 + Y/8 + Z/16 = 11/16

A little algebra gives us:

8W/16 + 4X/16 + 2Y/16 + Z/16 = 11/16

Then....

8W + 4X + 2Y + Z = 11

With the limitation that each variable is either 0 or 1, we'd have these possibilities:

8W = 0 or 8
4X = 0 or 4
2Y = 0 or 2
Z = 0 or 1

With these options, the ONLY way to get to 11 is 8+0+2+1

So W = 1, X = 0, Y = 1 and Z = 1

With just one possibility, Fact 1 is SUFFICIENT (the answer to the prompt is 1+0+1+1 = 3, but you don't need to do THAT math).

Fact 2: Involves math that is similar to Fact 1, but the fractions and common-denominator are different.

We'd end up with:

27W + 9X + 3Y = Z = 31

27W = 0 or 27
9X = 0 or 9
3Y = 0 or 3
Z = 0 or 1

Here, the ONLY way to get to 31 is 27+0+3+1.

Fact 2 is also SUFFICIENT.

Final Answer: D

GMAT assassins aren't born, they're made,
Rich