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:

Guys this is how I am trying to solve this. But after doing it for 15 minutes I gave up and think to post. No idea where I am getting this wrong and i don't have an OA either.

Now the (1) can be simplified into 1296 {1+74+149+226+.................+641} ==> 1296*2805 => This doesn't give me any of the above choices. Any idea guys where I am getting it wrong?

Guys this is how I am trying to solve this. But after doing it for 15 minutes I gave up and think to post. No idea where I am getting this wrong and i don't have an OA either.

Now the (1) can be simplified into 1296 {1+74+149+226+.................+641} ==> 1296*2805 => This doesn't give me any of the above choices. Any idea guys where I am getting it wrong?

Ans is C

Take the middle number here it is 40 now 36 = (40-4), 37 = (40-3) and so on

on squaring this (40-4)^2 = 1600+16-320 and (40+4)^2 = 1600+16+320

on adding these two we get 2*1600+2*16

similarly we solve for all the above and finally we get => 8*1600+1600+2*(16+9+4+1) = 14460 (C)

We have 9 terms, middle term is 40^2. Express all other terms as 40-x: \(36^2+37^2+38^2+39^2+40^2+41^2+42^2+43^2+44^2=\) \(=(40-4)^2+(40-3)^2+(40-2)^2+(40-1)^2+40^2+(40+1)^2+(40+2)^2+(40+3)^2+(40+4)^2\). Now, when you expand these expressions applying \((x-y)^2=x^2-2x+y^2\) and \((x+y)^2=x^2+2x+y^2\) you'll see that \(-2xy\) and \(2xy\) cancel out and we'll get:

Approach #2: The sum of the squares of the first n positive integers is given by: \(1^2+2^2+...+n^2=\frac{n(n+1)(2n+1)}{6}\) (note that it's highly unlikely that you'll need it on the real GMAT test). For example the sum of the first 3 positive integers: \(1^2+2^2+3^3=\frac{3(3+1)(2*3+1)}{6}=14\).

Now, we can calculate the sum of the squares of the first 44 positive integers and subtract from it the sum of the squares of the first 35 positive integers to get the answer: \(36^2+37^2+38^2+39^2+40^2+41^2+42^2+43^2+44^2=\frac{44(44+1)(2*44+1)}{6}-\frac{35(35+1)(2*35+1)}{6}=14,460\).

We have 9 terms, middle term is 40^2. Express all other terms as 40-x: \(36^2+37^2+38^2+39^2+40^2+41^2+42^2+43^2+44^2=\) \(=(40-4)^2+(40-3)^2+(40-2)^2+(40-1)^2+40^2+(40+1)^2+(40+1)^2+(40+3)^2+(40+4)^2\). Now, when you expand these expressions applying \((x-y)^2=x^2-2x+y^2\) and \((x+y)^2=x^2+2x+y^2\) you'll see that \(-2xy\) and \(2xy\) cancel out and we'll get:

hm, before looking to ur solution, I solved the q. in this way- let a =36^2 then we have a+(a+1)+(a+2) (a+3) (a+4) (a+5) (a+6) (a+7) (a+8)

I feel that it is just an arithmetic progression with mean=median

so the sum of these numbers are 9*(a+4)=9*40^2=14400

later I saw ur solution -=9*40^2+2*(4^2+3^2+2^2+1^2)=14,400+60=14,460 we seem to be in the same way, but using my method how to come to +2*(4^2+3^2+2^2+1^2)?
_________________

Happy are those who dream dreams and are ready to pay the price to make them come true

I am still on all gmat forums. msg me if you want to ask me smth

We have 9 terms, middle term is 40^2. Express all other terms as 40-x: \(36^2+37^2+38^2+39^2+40^2+41^2+42^2+43^2+44^2=\) \(=(40-4)^2+(40-3)^2+(40-2)^2+(40-1)^2+40^2+(40+1)^2+(40+1)^2+(40+3)^2+(40+4)^2\). Now, when you expand these expressions applying \((x-y)^2=x^2-2x+y^2\) and \((x+y)^2=x^2+2x+y^2\) you'll see that \(-2xy\) and \(2xy\) cancel out and we'll get:

hm, before looking to ur solution, I solved the q. in this way- let a =36^2 then we have a+(a+1)+(a+2) (a+3) (a+4) (a+5) (a+6) (a+7) (a+8)

I feel that it is just an arithmetic progression with mean=median

so the sum of these numbers are 9*(a+4)=9*40^2=14400

later I saw ur solution -=9*40^2+2*(4^2+3^2+2^2+1^2)=14,400+60=14,460 we seem to be in the same way, but using my method how to come to +2*(4^2+3^2+2^2+1^2)?

The problem is that 36^2, 37^2, 38^2, 39^2, 40^2, 41^2, 42^2, 43^2, and 44^2 DOES NOT form an AP. You assumed that \(a+1=36^2+1=37^2\), \(a+2=36^2+2=38^2\), ... but that's not correct: \(37^2\neq{36^2+1}\), \(38^2\neq{36^2+2}\), ... .

I feel that it is just an arithmetic progression with mean=median

It is not an arithmetic progression, so if you assume that it is, you will get the wrong answer. An arithmetic progression is 'equally spaced'. If you just look at the smallest perfect squares, you can see that they are not equally spaced: 1, 4, 9, 16, 25... In fact the spacing gets larger the further you get into this list.

You can use the spacing of perfect squares to answer this question. From the difference of squares, we have that

41^2 - 40^2 = (41 + 40)(41 - 40) = 81

So 41^2 = 40^2 + 81. Similarly, 42^2 = 41^2 + 83, and 39^2 = 40^2 - 79, and so on. Listing all of the values we need to sum:

Now adding these in columns, we get (9)(40^2) + 4(81-79) + 3(83 - 77) + 2(85 - 75) + (87 - 73) = 9*1600 + 4*2 + 3*6 + 2*10 + 14 = 14,400 + 8 + 18 + 20 + 14 = 14,460

I'd still probably use the first method outlined in Bunuel's post above, but you can use the spacing of squares to get the answer if you look at the problem in the right way.
_________________

GMAT Tutor in Toronto

If you are looking for online GMAT math tutoring, or if you are interested in buying my advanced Quant books and problem sets, please contact me at ianstewartgmat at gmail.com

I feel that it is just an arithmetic progression with mean=median

It is not an arithmetic progression, so if you assume that it is, you will get the wrong answer. An arithmetic progression is 'equally spaced'. If you just look at the smallest perfect squares, you can see that they are not equally spaced: 1, 4, 9, 16, 25... In fact the spacing gets larger the further you get into this list.

You can use the spacing of perfect squares to answer this question. From the difference of squares, we have that

41^2 - 40^2 = (41 + 40)(41 - 40) = 81

So 41^2 = 40^2 + 81. Similarly, 42^2 = 41^2 + 83, and 39^2 = 40^2 - 79, and so on. Listing all of the values we need to sum:

Now adding these in columns, we get (9)(40^2) + 4(81-79) + 3(83 - 77) + 2(85 - 75) + (87 - 73) = 9*1600 + 4*2 + 3*6 + 2*10 + 14 = 14,400 + 8 + 18 + 20 + 14 = 14,460

I'd still probably use the first method outlined in Bunuel's post above, but you can use the spacing of squares to get the answer if you look at the problem in the right way.

I also used this approach, but it's really calculation intensive.

Option C. Using the formula for calculating sum of squares of n natural nos.:[n(n+1)(2n+1)]/6 First calculate for n=44 then for n=35 And subtract second from first to get the answer.

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.
_________________

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.
_________________

Since my last post, I’ve got the interview decisions for the other two business schools I applied to: Denied by Wharton and Invited to Interview with Stanford. It all...

[rss2posts title=The MBA Manual title_url=https://mbamanual.com/2016/11/22/mba-vs-mim-guest-post/ sub_title=MBA vs. MiM :3qa61fk6]Hey, guys! We have a great guest post by Abhyank Srinet of MiM-Essay . In a quick post and an...

Marketing is one of those functions, that if done successfully, requires a little bit of everything. In other words, it is highly cross-functional and requires a lot of different...