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 350,000 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:

Answer D. Let x=54,820 and y = 54,822 = x + 2. Then average is (x^2 + y^2) / 2 = [(x^2) + (x + 2)^2] / 2 = (x^2 + x^2 + 4x + 4) /2 = x^2 +2x + 2 = (x + 1)^2 + 1 Now, sub into original numbers the average is (54,820 + 1)^2 + 1 = 54,821^2 = 1.

Re: PS: Manhattan Gmat Math [#permalink]
07 May 2011, 08:34

3

This post received KUDOS

1

This post was BOOKMARKED

One can try plugging numbers and see the pattern:

Take 2 and 4: average= 3 Now, for \(2^2\) and \(4^2\), \(average = 10 =3^2 +1\)

Take 4 and 6: average= 5 Now, for \(4^2\) and \(6^2\): \(average= 26= 5^2+1\)

We can quickly realize that average of 54820 and 54822= 54821 So, as per the pattern derived above, average of \(54820^2\) and \(54822^2\)= \(54821^2 +1\)

If I come across this question in a test, I would just take some small values to convince myself. Say \(\frac{(2^2 + 4^2)}{2} = 10\) which can also be represented as \(3^2 + 1\) A couple more such examples and the pattern would be convincing. Say \(\frac{(4^2 + 6^2)}{2} =\frac{(16 + 36)}{2} = 26\) \(5^2 + 1 = 26\)

If you insist of using algebra, average of \((a - 1)^2\) and \((a+1)^2\) = \(\frac{[(a-1)^2 + (a+1)^2]}{2} = a^2 + 1\) Hence answer (D) _________________

Re: The average of (54,820)^2and (54,822)^2 = [#permalink]
14 Sep 2013, 10:18

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. _________________

Test some small numbers: \(\frac{2^2+4^2}{2}=10=3^2+1\) or: \(\frac{4^2+6^2}{2}=26=5^2+1\).

APPROACH #2:

Say \(54,821=x\), then \(\frac{54,820^2+54,822^2}{2}=\frac{(x-1)^2+(x+1)^2}{2}=x^2+1=54,821^2+1\).

APPROACH #3:

The units digit of \(54,820^2+54,822^2\) is \(0+2=4\). Now, since \(54,820^2+54,822^2\) must be a multiple of 4, then \(\frac{54,820^2+54,822^2}{2}\) must have the units digit of 2. Only answer choice D fits.

Hello everyone! Researching, networking, and understanding the “feel” for a school are all part of the essential journey to a top MBA. Wouldn’t it be great... ...

Are you interested in applying to business school? If you are seeking advice about the admissions process, such as how to select your targeted schools, then send your questions...