• Get 300+ Practice Questions

Available with Beat the GMAT members only code

• 5 Day FREE Trial
Study Smarter, Not Harder

Available with Beat the GMAT members only code

• Free Practice Test & Review
How would you score if you took the GMAT

Available with Beat the GMAT members only code

• 1 Hour Free
BEAT THE GMAT EXCLUSIVE

Available with Beat the GMAT members only code

• Free Trial & Practice Exam
BEAT THE GMAT EXCLUSIVE

Available with Beat the GMAT members only code

• Free Veritas GMAT Class
Experience Lesson 1 Live Free

Available with Beat the GMAT members only code

• Award-winning private GMAT tutoring
Register now and save up to $200 Available with Beat the GMAT members only code • 5-Day Free Trial 5-day free, full-access trial TTP Quant Available with Beat the GMAT members only code • Magoosh Study with Magoosh GMAT prep Available with Beat the GMAT members only code ## OG 13 - PS 158 tagged by: Brent@GMATPrepNow This topic has 2 expert replies and 5 member replies gdshamain Senior | Next Rank: 100 Posts Joined 09 Jan 2014 Posted: 41 messages #### OG 13 - PS 158 Sun May 04, 2014 10:45 am Elapsed Time: 00:00 • Lap #[LAPCOUNT] ([LAPTIME]) 158. 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

Need free GMAT or MBA advice from an expert? Register for Beat The GMAT now and post your question in these forums!

### GMAT/MBA Expert

Rich.C@EMPOWERgmat.com Elite Legendary Member
Joined
23 Jun 2013
Posted:
8699 messages
Followed by:
460 members
Thanked:
2729 times
GMAT Score:
800
Sun May 04, 2014 11:24 am
Hi gdshamain,

This question describes a sequence of numbers: 1, 2, 3,…..52 and asks you to add them all up.

Adding the numbers up in order would take way too much time to be practical. There are actually a couple of ways to quickly add up these terms; here's one way called "bunching":

When adding up a group of numbers, the order of the numbers does not matter. I can group the numbers into consistent sub-groups:

1+52 = 53
2+51 = 53
3+50 = 53
4+49 = 53
etc.

So every group of 2 terms sums to 53. There are 52 total terms, so that means that there are 26 sets of 2 terms.

26(53) = 1378

GMAT assassins aren't born, they're made,
Rich

_________________
Contact Rich at Rich.C@empowergmat.com

### GMAT/MBA Expert

Brent@GMATPrepNow GMAT Instructor
Joined
08 Dec 2008
Posted:
10760 messages
Followed by:
1212 members
Thanked:
5144 times
GMAT Score:
770
Sun May 04, 2014 11:30 am
Quote:
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 a similar 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 _________________ Brent Hanneson – Founder of GMATPrepNow.com Use our video course along with Check out the online reviews of our course Come see all of our free resources GMAT Prep Now's comprehensive video course can be used in conjunction with Beat The GMAT’s FREE 60-Day Study Guide and reach your target score in 2 months! ### GMAT/MBA Expert Rich.C@EMPOWERgmat.com Elite Legendary Member Joined 23 Jun 2013 Posted: 8699 messages Followed by: 460 members Thanked: 2729 times GMAT Score: 800 Sun May 04, 2014 12:09 pm Hi gdshamain, There's also a more-formal arithmetic approach for sequences that are made up of evenly-spaced terms: 1) Take the average of the smallest and largest terms: (1+52)/2 = 26.5 2) Count up the total numbers of terms: 52 3) Multiply the two values: (26.5)(52) You'll end up with the exact same answer: C GMAT assassins aren't born, they're made, Rich _________________ Contact Rich at Rich.C@empowergmat.com confused13 Senior | Next Rank: 100 Posts Joined 17 Dec 2013 Posted: 97 messages Followed by: 2 members Thanked: 8 times Sun May 04, 2014 12:27 pm Last edited by confused13 on Sun May 11, 2014 11:17 pm; edited 1 time in total gdshamain Senior | Next Rank: 100 Posts Joined 09 Jan 2014 Posted: 41 messages Mon May 05, 2014 10:05 pm Thank you for the response. ### GMAT/MBA Expert Jeff@TargetTestPrep GMAT Instructor Joined 09 Apr 2015 Posted: 323 messages Followed by: 6 members Thanked: 30 times Tue Jul 07, 2015 3:37 am gdshamain wrote: 158. 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
Solution:

Let's first set up the pattern of Nancy's savings. The first week she saved $1, the second week she saved$2, the third week she saved $3, and so forth. Therefore, the total amount of money she will have saved at the end of 52 weeks will be:$1 + $2 +$3 + $4 + … +$52. The pattern is obvious, but the arithmetic looks daunting because we need to add 52 consecutive integers. To shorten this task, we can use the formula: sum = average x quantity.

We know that Nancy saved money over the course of 52 weeks, so our quantity is 52.

To determine the average, we add together the first amount saved and the last amount saved and then divide by 2. Remember, this technique only works when we have an evenly spaced set.

The first quantity is $1 and the last is$52. Thus, we know:

average = (1 + 52)/2 = 53/2

Now we can determine the sum.

sum = average x quantity

sum = (53/2) x 52

sum = 53 x 26 = 1,378

Note: If we did not want to actually multiply out 26 x 53, we could have focused on units digits in the answer choices. We know that 26 x 53 will produce a units digit of 8 (because 6 x 3 = 18), and the only answer choice that has a units digit of 8 is answer choice C.

_________________
Jeffrey Miller Head of GMAT Instruction

seandcarey Newbie | Next Rank: 10 Posts
Joined
07 Jul 2015
Posted:
6 messages
Tue Jul 07, 2015 5:57 pm
Another way to do it is

N*(N+1)/2

In this case N is equal to 52.

(52*53)/2 = 1378

If it were 100
100 * 101 / 2 = 5050

It is very useful for expected value questions also. For example, what is the EV of the roll of a single die.

EV = Sum of outcomes / # of outcomes
6*7 = 42/2 = 21. 21/6 = 3.5

### Best Conversation Starters

1 Vincen 180 topics
2 lheiannie07 61 topics
3 Roland2rule 54 topics
4 ardz24 44 topics
5 VJesus12 14 topics
See More Top Beat The GMAT Members...

### Most Active Experts

1 Brent@GMATPrepNow

GMAT Prep Now Teacher

155 posts
2 Rich.C@EMPOWERgma...

EMPOWERgmat

105 posts
3 GMATGuruNY

The Princeton Review Teacher

101 posts
4 Jay@ManhattanReview

Manhattan Review

82 posts
5 Matt@VeritasPrep

Veritas Prep

80 posts
See More Top Beat The GMAT Experts