Problem Solving

In the first week of the year, Nancy saved $1. In each of the next 51 weeks, she saved $1 more than she had saved in the previous week. What was the total amount that Nancy saved during the 52 weeks?

A. $1,326
B. $1,352
C. $1,378
D. $2,652
E. $2,756

Here's one approach with a slight TWIST at the end.

We want to add 1+2+3+4+...+51+52
So, let's add them in pairs, starting from the outside and working in.
1+2+3+4+...+51+52 = (1+52) + (2+51) + (3+50) + . . .
= 53 + 53 + 53 + ....

How many 53's are there in our new sum?
Well, there are 52 numbers in the sum 1+2+3+..+52, so there must be 26 pairs, which means there are 26 values in our new sum of 53 + 53 + 53 + ....

So, what does (26)(53) equal?
Fortunately, if we examine the answer choices, we see that we don't need to calculate (26)(53)

Why not?
Notice that when we multiply (26)(53), the units digit in the product will be 8 (since 6 times 3 equals 18).

Since only 1 answer choice (C) ends in 8, the correct answer must be C

Cheers,
Brent