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Register now and save up to $200 Available with Beat the GMAT members only code • Most awarded test prep in the world Now free for 30 days 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 • Get 300+ Practice Questions 25 Video lessons and 6 Webinars for FREE 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 ## OG 13 - PS 158 tagged by: Brent@GMATPrepNow This topic has 4 expert replies and 3 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 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

### GMAT/MBA Expert

Jeff@TargetTestPrep GMAT Instructor
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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 + â€¦ + $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 Answer:C 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 ### GMAT/MBA Expert Rich.C@EMPOWERgmat.com Elite Legendary Member Joined 23 Jun 2013 Posted: 9172 messages Followed by: 472 members Upvotes: 2867 GMAT Score: 800 Sun May 04, 2014 11:24 am Hi gdshamain, This question describes a sequence of numbers: 1, 2, 3,â€¦..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 Final Answer: C 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: 11275 messages Followed by: 1225 members Upvotes: 5254 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.

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

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Rich.C@EMPOWERgmat.com Elite Legendary Member
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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
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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
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Mon May 05, 2014 10:05 pm
Thank you for the response.

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