Summer is Coming! Join the Game of Timers Competition to Win Epic Prizes. Registration is Open. Game starts Mon July 1st.

It is currently 17 Jul 2019, 19:45

Close

GMAT Club Daily Prep

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.

Close

Request Expert Reply

Confirm Cancel

What is the value of 38^2 + 39^2 + 40^2 + 41^2 + 42^2 ?

  new topic post reply Question banks Downloads My Bookmarks Reviews Important topics  
Author Message
TAGS:

Hide Tags

Find Similar Topics 
VP
VP
User avatar
D
Joined: 31 Oct 2013
Posts: 1392
Concentration: Accounting, Finance
GPA: 3.68
WE: Analyst (Accounting)
What is the value of 38^2 + 39^2 + 40^2 + 41^2 + 42^2 ?  [#permalink]

Show Tags

New post Updated on: 09 Apr 2018, 07:08
15
00:00
A
B
C
D
E

Difficulty:

  35% (medium)

Question Stats:

75% (02:14) correct 25% (02:24) wrong based on 135 sessions

HideShow timer Statistics


What is the value of \(38^2 + 39^2 + 40^2 + 41^2 + 42^2\) ?

A. 7950
B. 7990
C. 8010
D. 8050
E. 8070

Originally posted by KSBGC on 09 Apr 2018, 06:55.
Last edited by Bunuel on 09 Apr 2018, 07:08, edited 1 time in total.
Renamed the topic and edited the question.
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 56277
Re: What is the value of 38^2 + 39^2 + 40^2 + 41^2 + 42^2 ?  [#permalink]

Show Tags

New post 09 Apr 2018, 07:06
CEO
CEO
User avatar
V
Joined: 12 Sep 2015
Posts: 3848
Location: Canada
Re: What is the value of 38^2 + 39^2 + 40^2 + 41^2 + 42^2 ?  [#permalink]

Show Tags

New post 09 Apr 2018, 07:48
3
Top Contributor
selim wrote:
What is the value of \(38^2 + 39^2 + 40^2 + 41^2 + 42^2\) ?

A. 7950
B. 7990
C. 8010
D. 8050
E. 8070


I love this question (and all of the replicas :-) )!!

First notice that 38² + 39² + 40² + 41² + 42² = (40 - 2)² + (40 - 1)² + 40² + (40 + 1)² + (40 + 2)²

Now notice that (40 - 2)² + (40 - 1)² + 40² + (40 + 1)² + (40 + 2)² has the form (x - 2)² + (x - 1)² + x² + (x + 1)² + (x + 2)²
So, let's expand and simplify (x - 2)² + (x - 1)² + x² + (x + 1)² + (x + 2)² and see what we get.

(x - 2)² + (x - 1)² + x² + (x + 1)² + (x + 2)² = [x² - 4x + 4] + [x² - 2x + 1] + [x²] + [x² + 2x + 1] + [x² + 4x + 4] [lots of canceling to do here...]
= 5x² + 10

So, if (x - 2)² + (x - 1)² + x² + (x + 1)² + (x + 2)² simplifies to become 5x² + 10...
...then (40 - 2)² + (40 - 1)² + 40² + (40 + 1)² + (40 + 2)² must simplify to become 5(40²) + 10

5(40²) + 10 = 5(1600) + 10
= 8000 + 10
= 8010

Answer: C

Cheers,
Brent
_________________
Test confidently with gmatprepnow.com
Image
Math Expert
User avatar
V
Joined: 02 Aug 2009
Posts: 7764
What is the value of 38^2 + 39^2 + 40^2 + 41^2 + 42^2 ?  [#permalink]

Show Tags

New post 09 Apr 2018, 08:43
selim wrote:
What is the value of \(38^2 + 39^2 + 40^2 + 41^2 + 42^2\) ?

A. 7950
B. 7990
C. 8010
D. 8050
E. 8070


It is always good to know the formula for SUM of square of first n natural numbers.. \(\frac{n(n+1)(2n+1)}{6}\)..

so \(38^2 + 39^2 + 40^2 + 41^2 + 42^2\) = (\(1^2+2^2+............. 41^2 + 42^2\))-(\(1^2 + 2^2 + 3^2 +...........+ 36^2 + 37^2\))..

\(\frac{42(42+1)(2*42+1)}{6}-\frac{37(37+1)(2*37+1)}{6}=7*43*85-37*19*25=8010\)
_________________
Intern
Intern
avatar
B
Joined: 26 Mar 2018
Posts: 12
Re: What is the value of 38^2 + 39^2 + 40^2 + 41^2 + 42^2 ?  [#permalink]

Show Tags

New post 09 Apr 2018, 09:02
2
My method:

(30+8) + (30+9) + (30+10) + (30+11) + 30+12) . I just did 8^2+9^2+10^2+11^2+12^2 = ...10, so the number should end with 10. The answer is C.

Posted from my mobile device
Retired Moderator
User avatar
V
Joined: 27 Oct 2017
Posts: 1229
Location: India
Concentration: International Business, General Management
GPA: 3.64
WE: Business Development (Energy and Utilities)
Re: What is the value of 38^2 + 39^2 + 40^2 + 41^2 + 42^2 ?  [#permalink]

Show Tags

New post 09 Apr 2018, 09:20
I don't think this is right approach, this approach could have worked if we want to eliminate some options which do
not end with 0. here all the options end with 0. so this approach might not work.

Experts view needed Bunuel, @chetan4u

Iamnowjust wrote:
My method:

(30+8) + (30+9) + (30+10) + (30+11) + 30+12) . I just did 8^2+9^2+10^2+11^2+12^2 = ...10, so the number should end with 10. The answer is C.

Posted from my mobile device

_________________
Retired Moderator
User avatar
V
Joined: 27 Oct 2017
Posts: 1229
Location: India
Concentration: International Business, General Management
GPA: 3.64
WE: Business Development (Energy and Utilities)
Re: What is the value of 38^2 + 39^2 + 40^2 + 41^2 + 42^2 ?  [#permalink]

Show Tags

New post 09 Apr 2018, 09:24
I really like your approach using this formula.
In fact I want to add 2 more fundamental formula for summation:

1) \(1+2+3+...+n = n(n+1)/2\) - Sum of first n natural numbers.
2) \(1^3+2^3+...+n^3 = (n(n+1)/2)^2\) - Sum of cube of first n natural numbers.


chetan2u wrote:
selim wrote:
What is the value of \(38^2 + 39^2 + 40^2 + 41^2 + 42^2\) ?

A. 7950
B. 7990
C. 8010
D. 8050
E. 8070


It is always good to know the formula for SUM of square of first n natural numbers.. \(\frac{n(n+1)(2n+1)}{6}\)..

so \(38^2 + 39^2 + 40^2 + 41^2 + 42^2\) = \(1^2+2^2+.......38^2 + 39^2 + 40^2 + 41^2 + 42^2\)-(\(1^2 + 2^2 + 3^2 +...........+ 36^2 + 37^2\)..

\(\frac{42(42+1)(2*42+1)}{6}-\frac{37(37+1)(2*37+1)}{6}=7*43*85-37*19*25=8010\)

_________________
Math Expert
User avatar
V
Joined: 02 Aug 2009
Posts: 7764
Re: What is the value of 38^2 + 39^2 + 40^2 + 41^2 + 42^2 ?  [#permalink]

Show Tags

New post 09 Apr 2018, 09:45
Iamnowjust wrote:
My method:

(30+8) + (30+9) + (30+10) + (30+11) + 30+12) . I just did 8^2+9^2+10^2+11^2+12^2 = ...10, so the number should end with 10. The answer is C.

Posted from my mobile device



You are lucky to have got the correct answer..

There is no logic behind this..
example 38^2+39^2=2965, ...so __65
8^2+9^2=145

so you can just talk of UNITS digit and NOT tens digit
_________________
Manager
Manager
avatar
B
Joined: 08 Sep 2016
Posts: 110
Re: What is the value of 38^2 + 39^2 + 40^2 + 41^2 + 42^2 ?  [#permalink]

Show Tags

New post 09 Apr 2018, 10:28
(40-2)^2 + (40-1)^2 + 40^2 + (40+1)^2 + (40+2)^2

You can foil each expression for the answer. A quick way to the answer is to focus on the last multiplication when you foil for each expression.

You will get 4+1+4+1 = 10

Check out the link that Bunuel provided. His/her approach to this problem is really good.
https://gmatclub.com/forum/36-126078.html
Non-Human User
User avatar
Joined: 09 Sep 2013
Posts: 11666
Re: What is the value of 38^2 + 39^2 + 40^2 + 41^2 + 42^2 ?  [#permalink]

Show Tags

New post 13 Apr 2019, 22:15
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.
_________________
GMAT Club Bot
Re: What is the value of 38^2 + 39^2 + 40^2 + 41^2 + 42^2 ?   [#permalink] 13 Apr 2019, 22:15
Display posts from previous: Sort by

What is the value of 38^2 + 39^2 + 40^2 + 41^2 + 42^2 ?

  new topic post reply Question banks Downloads My Bookmarks Reviews Important topics  





Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne