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:
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.
As I’m halfway through my second year now, graduation is now rapidly approaching. I’ve neglected this blog in the last year, mainly because I felt I didn’...
Perhaps known best for its men’s basketball team – winners of five national championships, including last year’s – Duke University is also home to an elite full-time MBA...
Hilary Term has only started and we can feel the heat already. The two weeks have been packed with activities and submissions, giving a peek into what will follow...