I agree with Rich - this seems way too computation-heavy for a GMAT problem. Vipugoyal's solution is correct, but it's important to understand how we got there.
If we have 4 consecutive multiples of 16, then the first term is going to be 16 times some number, the second term will be 16 times the next biggest number, and so on.
16x + 16(x + 1) + 16(x + 2) + 16(x + 3)
We're told that the sum of these terms is equal to 2048 more than the second number (a real GMAT question would use "term" instead of "number"). Since the second term was 16(x + 1), we can say:
16x + 16(x + 1) + 16(x + 2) + 16(x + 3) = 2048 + 16(x + 1)
Subtract that 16(x + 1) from both sides, and simplify.
Now at this point, you'll have to do way more math than you'd ever do on a real GMAT problem to solve. I'd disregard this question... and other questions from whatever source it came from.
Just make sure you understand consecutive integer setup!
Ceilidh Erickson
EdM in Mind, Brain, and Education
Harvard Graduate School of Education
