GMAT Changed on April 16th - Read about the latest changes here

It is currently 23 Apr 2018, 06:29

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

Events & Promotions

Events & Promotions in June
Open Detailed Calendar

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

Manager
Manager
avatar
B
Joined: 31 Oct 2013
Posts: 106
Concentration: Accounting, Finance
GPA: 3.68
WE: Analyst (Accounting)
CAT Tests
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
4
This post was
BOOKMARKED
00:00
A
B
C
D
E

Difficulty:

  25% (medium)

Question Stats:

70% (01:59) correct 30% (01:39) wrong based on 44 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
[Reveal] Spoiler: OA

Originally posted by selim 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.
Expert Post
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 44635
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
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


This is a copy of this question: https://gmatclub.com/forum/36-126078.html and this one: https://gmatclub.com/forum/what-is-the- ... 98546.html
_________________

New to the Math Forum?
Please read this: Ultimate GMAT Quantitative Megathread | All You Need for Quant | PLEASE READ AND FOLLOW: 12 Rules for Posting!!!

Resources:
GMAT Math Book | Triangles | Polygons | Coordinate Geometry | Factorials | Circles | Number Theory | Remainders; 8. Overlapping Sets | PDF of Math Book; 10. Remainders | GMAT Prep Software Analysis | SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) | Tricky questions from previous years.

Collection of Questions:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.


What are GMAT Club Tests?
Extra-hard Quant Tests with Brilliant Analytics

Expert Post
Top Contributor
1 KUDOS received
SVP
SVP
User avatar
P
Joined: 12 Sep 2015
Posts: 2298
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
1
This post received
KUDOS
Expert's post
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
_________________

Brent Hanneson – Founder of gmatprepnow.com

Image

Expert Post
Math Expert
User avatar
V
Joined: 02 Aug 2009
Posts: 5777
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 \(38^2 + 39^2 + 40^2 + 41^2 + 42^2\) = (\(1^2+2^2+............. 41^2 + 42^2\))-(\(1^2 + 2^2 + 3^2 +...........+ 36^2 + 37^2\))..

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

Absolute modulus :http://gmatclub.com/forum/absolute-modulus-a-better-understanding-210849.html#p1622372
Combination of similar and dissimilar things : http://gmatclub.com/forum/topic215915.html


GMAT online Tutor

Intern
Intern
avatar
B
Joined: 26 Mar 2018
Posts: 4
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
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
Senior Manager
Senior Manager
User avatar
G
Joined: 27 Oct 2017
Posts: 314
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

_________________

SC: Confusable words
All you need for Quant, GMAT PS Question Directory,GMAT DS Question Directory
Error log/Key Concepts

Appreciate my post by giving kudos .

Senior Manager
Senior Manager
User avatar
G
Joined: 27 Oct 2017
Posts: 314
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 \(38^2 + 39^2 + 40^2 + 41^2 + 42^2\) = \(1^2+2^2+.......38^2 + 39^2 + 40^2 + 41^2 + 42^2\)-(\(1^2 + 2^2 + 3^2 +...........+ 36^2 + 37^2\)..

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

_________________

SC: Confusable words
All you need for Quant, GMAT PS Question Directory,GMAT DS Question Directory
Error log/Key Concepts

Appreciate my post by giving kudos .

Expert Post
Math Expert
User avatar
V
Joined: 02 Aug 2009
Posts: 5777
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
_________________

Absolute modulus :http://gmatclub.com/forum/absolute-modulus-a-better-understanding-210849.html#p1622372
Combination of similar and dissimilar things : http://gmatclub.com/forum/topic215915.html


GMAT online Tutor

Manager
Manager
avatar
B
Joined: 08 Sep 2016
Posts: 62
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
Re: What is the value of 38^2 + 39^2 + 40^2 + 41^2 + 42^2 ?   [#permalink] 09 Apr 2018, 10:28
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  


GMAT Club MBA Forum Home| About| Terms and Conditions| GMAT Club Rules| Contact| Sitemap

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

Kindly note that the GMAT® test is a registered trademark of the Graduate Management Admission Council®, and this site has neither been reviewed nor endorsed by GMAC®.