In the first week of the Year, Nancy saved $1. In each of the next 51

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BTGModeratorVI: Legendary Member; Posts: 1223; Joined: Sat Feb 15, 2020 2:23 pm; Followed by:1 members

In the first week of the Year, Nancy saved $1. In each of the next 51

by BTGModeratorVI » Sat Aug 08, 2020 7:00 am

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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

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Source: Beat The GMAT — Problem Solving | Sat Aug 08, 2020 7:00 am

GMAT/MBA Expert

Brent@GMATPrepNow: GMAT Instructor; Posts: 16207; Joined: Mon Dec 08, 2008 6:26 pm; Location: Vancouver, BC; Thanked: 5254 times; Followed by:1268 members; GMAT Score:770

Re: In the first week of the Year, Nancy saved $1. In each of the next 51

by Brent@GMATPrepNow » Mon Aug 10, 2020 4:46 am

BTGModeratorVI wrote: ↑
Sat Aug 08, 2020 7:00 am
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 any 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

Brent Hanneson - Creator of GMATPrepNow.com

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GMAT/MBA Expert

Scott@TargetTestPrep: GMAT Instructor; Posts: 8086; Joined: Sat Apr 25, 2015 10:56 am; Location: Los Angeles, CA; Thanked: 43 times; Followed by:29 members

Re: In the first week of the Year, Nancy saved $1. In each of the next 51

by Scott@TargetTestPrep » Wed Aug 12, 2020 2:21 pm

BTGModeratorVI wrote: ↑
Sat Aug 08, 2020 7:00 am
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. The total amount of money Nancy saved during the 52 weeks was:

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

Answer: C

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