Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized for You

we will pick new questions that match your level based on your Timer History

Track Your Progress

every week, we’ll send you an estimated GMAT score based on your performance

Practice Pays

we will pick new questions that match your level based on your Timer History

Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.

It appears that you are browsing the GMAT Club forum unregistered!

Signing up is free, quick, and confidential.
Join other 500,000 members and get the full benefits of GMAT Club

Registration gives you:

Tests

Take 11 tests and quizzes from GMAT Club and leading GMAT prep companies such as Manhattan GMAT,
Knewton, and others. All are free for GMAT Club members.

Applicant Stats

View detailed applicant stats such as GPA, GMAT score, work experience, location, application
status, and more

Books/Downloads

Download thousands of study notes,
question collections, GMAT Club’s
Grammar and Math books.
All are free!

Thank you for using the timer!
We noticed you are actually not timing your practice. Click the START button first next time you use the timer.
There are many benefits to timing your practice, including:

In the first week of the Year, Nancy saved $1. [#permalink]

Show Tags

11 Nov 2012, 19:35

4

This post received KUDOS

16

This post was BOOKMARKED

00:00

A

B

C

D

E

Difficulty:

25% (medium)

Question Stats:

69% (02:20) correct
31% (01:42) wrong based on 905 sessions

HideShow timer Statistics

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?

Re: In the first week of the Year, Nancy saved $1. [#permalink]

Show Tags

11 Nov 2012, 19:48

13

This post received KUDOS

Expert's post

4

This post was BOOKMARKED

Bigred2008 wrote:

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

Does anyone have a better way to do this?

The total amount of money will be 1 + 2 + 3 + 4 + ... + 52 (in the 52nd week, she will save $52)

Sum of first n consecutive positive integers = n*(n+1)/2 Sum = 52*53/2 = 26*53 The product will end with 8 since 6*3 = 18 so answer must be (C) _________________

Re: In the first week of the Year, Nancy saved $1. [#permalink]

Show Tags

19 May 2013, 10:00

2

This post received KUDOS

For an even list of consecutive numbers where a = the first number and z = the last number and (in this case) a total of 52 consecutive numbers-- (a+z)(.5*number of consecutive integers)---> (1+52)*26=1378 _________________

Re: In the first week of the Year, Nancy saved $1. [#permalink]

Show Tags

03 Jun 2014, 07:14

How did you know about that formula (n(n+1))/2 ? I've read through the GMAT Official Guide Math Review but don't recall learning that. It seems if you know that formula the question is very easy, but if you don't the problem can be a big time drain. Do you recommend other guides I should be reading to study up on tips and formulas for problems like these?

Re: In the first week of the Year, Nancy saved $1. [#permalink]

Show Tags

03 Jun 2014, 21:08

1

This post received KUDOS

Expert's post

2

This post was BOOKMARKED

momentofzen wrote:

How did you know about that formula (n(n+1))/2 ? I've read through the GMAT Official Guide Math Review but don't recall learning that. It seems if you know that formula the question is very easy, but if you don't the problem can be a big time drain. Do you recommend other guides I should be reading to study up on tips and formulas for problems like these?

The sum of first n consecutive positive integers is given by the formula n(n+1)/2. For GMAT, it is a good idea to know this formula. It could simplify many calculations. Test prep companies discuss all such useful formulas in their curriculum. The Official Guides only give practice questions.

You should also know the more generic formula of sum of an Arithmetic Progression. From that you can easily derive this formula.

Sum of an Arithmetic Progression will be n*Average where n is the number of terms in the AP and Average will be the average value of the terms. The average value can be found as (First term + Last term)/2

If first term is a, last term is a + (n-1)*d where d is the common difference.

Average = (a + a + (n-1)*d)/2

Sum = n*(a + a + (n-1)*d)/2 = n/2(2a + (n-1)*d)

In case of consecutive integers starting from 1, a = 1 and d = 1

Re: In the first week of the Year, Nancy saved $1. [#permalink]

Show Tags

03 Jun 2014, 23:47

4

This post received KUDOS

momentofzen wrote:

How did you know about that formula (n(n+1))/2 ? I've read through the GMAT Official Guide Math Review but don't recall learning that. It seems if you know that formula the question is very easy, but if you don't the problem can be a big time drain. Do you recommend other guides I should be reading to study up on tips and formulas for problems like these?

If you don't recall the formula, there is one method:

Re: In the first week of the Year, Nancy saved $1. [#permalink]

Show Tags

04 Jun 2014, 12:08

PareshGmat wrote:

momentofzen wrote:

How did you know about that formula (n(n+1))/2 ? I've read through the GMAT Official Guide Math Review but don't recall learning that. It seems if you know that formula the question is very easy, but if you don't the problem can be a big time drain. Do you recommend other guides I should be reading to study up on tips and formulas for problems like these?

If you don't recall the formula, there is one method:

Sum of 3rd & 3rd last digit = 3 + 50 = 53 . . . . This is repeated 26 times

So, 26 * 53 = 1378

Answer = C

Yes! Definitely better/easier/faster to apply logic than to memorize another formula. This way, you can use the logic even if you don't start at one. Or if you are counting by 2's or 3's. For example, what if Nancy saved $51 the first week of the year, and increased her savings by $1 each week after that.

Start at $51. Know that there are 52 weeks in a year, so the last week she will save 102. So the sequence will be 51, 52, 53... 100, 101, 102. See how adding the first and last is the same as adding the second and the second-to-last, and the same as the third and third-to-last? All like pairs are $153. If there are 52 items, then there are 26 pairs. $153 x 26 = $3978

Counting by 3's: First week is $51. Last week will be (52 - 1) x 3 = 153 more, or 51+153=204. So: 51, 54, 57... 198, 201, 204. First + last: 51 + 204 = $255. Times 26 pairs: $255 x 26 = $6630

Counting by 3's, odd number of weeks: Let's say Nancy only saved for 51 weeks, because she bought holiday presents for everyone in the last week. First week is $51. Last week will be (51 - 1) x 3 = 150 more, or 51+150=201. So: 51, 54, 57... 195, 198, 201. First + last: $51 + $201 = $252. Now, there are 25 pairs + 1. The one is in the very middle. So $252 x 25 = $6300. Still have to add that last number that wasn't part of a pair. What was it? Nancy saved for 51 weeks, so that's 25 weeks on one side, 25 on the other, the middle is the 26th week. 26th week is (26 - 1) x $3 = $75 more than week 1, or 51 + 75 = 126. $6300 + $126 = $6426

Re: In the first week of the Year, Nancy saved $1. [#permalink]

Show Tags

04 Jun 2014, 20:04

Expert's post

Puzzler wrote:

Yes! Definitely better/easier/faster to apply logic than to memorize another formula. This way, you can use the logic even if you don't start at one. Or if you are counting by 2's or 3's. For example, what if Nancy saved $51 the first week of the year, and increased her savings by $1 each week after that.

It's certainly better to apply logic than just learn up formulas for specific situation because you may find you have no formula for a given situation in the question. Also, you need to know exactly when the formula is applicable for example here you must know that the formula is applicable for first n positive integers only.

That said, n(n+1)/2 is a very basic and useful formula. You should know it for GMAT, not because you may not be able to do a question without it but because you may spend unnecessary amount of time on a question when other people will be able to run away on it with the formula. _________________

Re: In the first week of the Year, Nancy saved $1. [#permalink]

Show Tags

15 Feb 2016, 00:58

Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email. _________________

Re: In the first week of the Year, Nancy saved $1. [#permalink]

Show Tags

23 Jun 2016, 09:27

Bigred2008 wrote:

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

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

Answer is 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 Scott Woodbury-Stewart Founder and CEO

Re: In the first week of the Year, Nancy saved $1. [#permalink]

Show Tags

28 Jul 2016, 07:24

Top Contributor

Bigred2008 wrote:

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 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

Brent Hanneson - Founder of GMAT Prep Now, a free & comprehensive GMAT course with: - over 500 videos (35 hours of instruction) - over 1800 practice questions - 2 full-length practice tests and other bonus offers - http://www.gmatprepnow.com/ Brent also tutors students for the GMAT

gmatclubot

Re: In the first week of the Year, Nancy saved $1.
[#permalink]
28 Jul 2016, 07:24

Excellent posts dLo saw your blog too..!! Man .. you have got some writing skills. And Just to make an argument = You had such an amazing resume ; i am glad...

So Much $$$ Business school costs a lot. This is obvious, whether you are a full-ride scholarship student or are paying fully out-of-pocket. Aside from the (constantly rising)...