First note the following about the sequence from -93 to 252:

-93,-92,-91,-90,.......-1,0,1,....90,91,92,93,.....251,252

So when we're summing our multiples of 3, we can exclude the sequence {-93,93}, since those will add up to 0.

Our new sequence is {94,252}.

\(252 - 94 + 1 = 159\)

There are 159 terms in the sequence. Dividing this number by 3 will give us the number of multiples of 3 in the sequence.

\(\frac{159}{3} = 53\)

So there are 53 multiples of 3 in the sequence. We want to use the Gaussian trick and make pairs out of the multiples, so we'll pull out 96 from the sequence and we'll be left with 52 multiples of 3 in order to divide by 2. (Keep that 96 in mind, we'll need it later).

Using the Gaussian trick to sum numbers in a sequence:

\(252 + 99 = 351\)
\(249 + 102 = 351\)
\(246 + 105 = 351\)
.
.
.

Since there are 52 multiples, there are 26 pairs of multiples of 3 that we can arrange in the way we did above which sum to 351. Since we pulled out the 96 from before, we need to add that back in as well.

This can all be written as:

\(26*(351) + 96 = 9222\)


Therefore A is greater.