Vincen wrote: ↑

Thu Jan 14, 2021 12:12 pm

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

Answer: C

Source: Official Guide

Solution:


We see that Nancy saved $1 in week 1, $2 in week 2, and so on. We see that this is an arithmetic progression of consecutive integers, with 52 terms. We can use the formula sum = average x number of terms to determine the total amount that she saved during the 52 weeks:

1 + 2 + 3 + … + 52 = (1 + 52) / 2 x 52 = 53 x 26 = $1,378

Answer: C

Vincen wrote: ↑

Thu Jan 14, 2021 12:12 pm

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

Answer: C

Source: Official Guide

Here's another approach (that doesn't require formulas).

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 is (26)(53)?
Fortunately, if we examine the answer choices, we see that we don't even 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 ends in 8, the correct answer must be C