Problem Solving

This kind of question is more interesting if we can see the answer choices. It obviously could involve a tedious calculation, so I'd at least glance at the answer choices to see if there are any shortcuts available. If the answers are far apart, we could do a rough estimate: if you add all the numbers between 500 and 800, you are summing roughly 300 numbers (301 to be precise, but we're estimating) which average to 650, so the sum would be approximately 300*650. We're only adding 1/3 of those numbers, since only 1/3 of the numbers in that range will be multiples of 3, so the sum should be very close to 300*650/3 = 65,000. That might be all you need to do if the answers are far apart (the exact answer turns out to be 64,950, so the estimate is good). We're also adding multiples of 3 here, so the answer must be a multiple of 3. So summing the digits of each answer choice might let you get to the right answer as well, if we're fortunate enough to find that only one answer is divisible by 3.

If the answers are close together, and if several of them are divisible by 3, then you would not have any alternative but to carry out the calculation as Mitch outlined above. But in my experience, it is very often possible to find a shortcut in most real GMAT questions that potentially involve lengthly calculations.

And just to finish up this trinity of expert advice pieces, I'll just put the evenly spaced set stuff right here:

Equation for Sum of an Evenly Spaced Set: Average * # of terms

Equation for Average of an Evenly Spaced Set: (First Term + Last Term) / 2

Equation for # of terms in an Evenly Spaced Set: ((Last Term - First Term) / Interval) + 1

So, in this case:

Average = 501 + 798 / 2 = (1299 / 2) = 649.5
# of terms = (( 798 - 501 ) / 3 + 1 = (297 / 3) + 1 = 99 + 1 = 100

Sum = Average * # 0f terms = 649.5 * 100 = 64950

Hope that helps!

-t