Find all School-related info fast with the new School-Specific MBA Forum

It is currently 30 Aug 2015, 02:31
GMAT Club Tests

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.

Events & Promotions

Events & Promotions in June
Open Detailed Calendar

Tough and tricky: The sum of the even numbers.

  Question banks Downloads My Bookmarks Reviews Important topics  
Author Message
TAGS:
Expert Post
1 KUDOS received
Math Expert
User avatar
Joined: 02 Sep 2009
Posts: 29110
Followers: 4726

Kudos [?]: 49770 [1] , given: 7403

Tough and tricky: The sum of the even numbers. [#permalink] New post 11 Oct 2009, 16:11
1
This post received
KUDOS
Expert's post
4
This post was
BOOKMARKED
00:00
A
B
C
D
E

Difficulty:

(N/A)

Question Stats:

67% (02:31) correct 33% (00:41) wrong based on 35 sessions
I found a doc of quant problems, regarded as tough and tricky.

I'm starting posting most interesting of them. Maybe some of them were already posted here but still it would be useful to discuss once more.

They all have the answers but some of them are really doubtful so I'll try to avoid such ones or correct them. Also I'll provide the solutions given, with additional comments when necessary.

First one:

1. The sum of the even numbers between 1 and k is 79*80, where k is an odd number, then k=?

(A) 79
(B) 80
(C) 81
(D) 157
(E) 159
_________________

NEW TO MATH FORUM? PLEASE READ THIS: ALL YOU NEED FOR QUANT!!!

PLEASE READ AND FOLLOW: 12 Rules for Posting!!!

RESOURCES: [GMAT MATH BOOK]; 1. Triangles; 2. Polygons; 3. Coordinate Geometry; 4. Factorials; 5. Circles; 6. Number Theory; 7. Remainders; 8. Overlapping Sets; 9. PDF of Math Book; 10. Remainders; 11. GMAT Prep Software Analysis ; 12. SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) ; 12. 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?
25 extra-hard Quant Tests

GMAT Club Premium Membership - big benefits and savings

Manager
Manager
avatar
Joined: 11 Sep 2009
Posts: 129
Followers: 5

Kudos [?]: 241 [0], given: 6

Re: Tough and tricky: The sum of the even numbers. [#permalink] New post 11 Oct 2009, 17:02
We're looking at the sum of even numbers between 1 and k, with k being an odd number. So essentially, we're looking for the sum of even numbers between 2 and (k-1).

Sum (in consecutive series) = Average * Number of Elements in Subset

Average \(= \frac{2 + (k-1)}{2}\)

Number of Elements in Subset\(= \frac{k-1}{2}\)

Sum \(= [\frac{2 + (k-1)}{2}][\frac{(k-1)}{2}]\)

\(= [\frac{(k+1)}{2}][\frac{(k-1)}{2}]\)

\(= [\frac{(k+1)}{2}][\frac{(k+1)}{2} - 1]\)

It's easy to see that these two terms are consecutive digits. We know that the sum is equal to 79*80, and therefore we can solve for k.

\(80 = \frac{k+1}{2}\)

\(160 = k + 1\)

\(k = 159\)

Therefore, the correct answer is E:159.
Senior Manager
Senior Manager
avatar
Joined: 18 Aug 2009
Posts: 328
Followers: 8

Kudos [?]: 220 [0], given: 13

Re: Tough and tricky: The sum of the even numbers. [#permalink] New post 11 Oct 2009, 18:13
\((K-1)*(K+1)/4 = 79*80\)
\((K-1)*(K+1) = 158*160\)
So K = 159.
Expert Post
Math Expert
User avatar
Joined: 02 Sep 2009
Posts: 29110
Followers: 4726

Kudos [?]: 49770 [0], given: 7403

Re: Tough and tricky: The sum of the even numbers. [#permalink] New post 12 Oct 2009, 08:38
Expert's post
VP
VP
avatar
Status: There is always something new !!
Affiliations: PMI,QAI Global,eXampleCG
Joined: 08 May 2009
Posts: 1356
Followers: 14

Kudos [?]: 177 [0], given: 10

Re: Tough and tricky: The sum of the even numbers. [#permalink] New post 03 May 2011, 23:05
(k+1) * (k-1) = 79 *80 * 4

for k = 157, LHS/4 = 78 * 79
for k = 159, LHS/4 = 79 * 80 Hence E.
_________________

Visit -- http://www.sustainable-sphere.com/
Promote Green Business,Sustainable Living and Green Earth !!

Manager
Manager
avatar
Joined: 29 Sep 2013
Posts: 52
Followers: 0

Kudos [?]: 18 [0], given: 46

Re: Tough and tricky: The sum of the even numbers. [#permalink] New post 06 Nov 2013, 18:41
The Above are some very good explanations. But I approached the problem in another way.

Notice a general pattern.
2+4 = 6 which is also 2*3=6
2+4+6=12 which is also 3*4=12
2+4+6+8=20 which is also 4*5=20
2+4+6+8+10=30 which is also 5*6=30

(So the sum of a series of positive even integers starting from 2, is equal to the number of integers "n" multiplied by "n+1")

The question tells us that the sum is equal to 79*80 meaning that its the sum of the first 79 even integers.
79*2=158
the only answer choice that encompasses this figure is 159. So the answer is E.
GMAT Club Legend
GMAT Club Legend
User avatar
Joined: 09 Sep 2013
Posts: 6108
Followers: 340

Kudos [?]: 69 [0], given: 0

Premium Member
Re: Tough and tricky: The sum of the even numbers. [#permalink] New post 17 May 2015, 04:53
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 Books | GMAT Club Tests | Best Prices on GMAT Courses | GMAT Mobile App | Math Resources | Verbal Resources

Manager
Manager
User avatar
Joined: 21 Jan 2015
Posts: 140
Location: India
Concentration: Strategy, Marketing
GMAT 1: 620 Q48 V28
WE: Marketing (Other)
Followers: 0

Kudos [?]: 33 [0], given: 22

GMAT ToolKit User CAT Tests
Tough and tricky: The sum of the even numbers. [#permalink] New post 17 May 2015, 21:08
Bunuel wrote:
1. The sum of the even numbers between 1 and k is 79*80, where k is an odd number, then k=?

(A) 79
(B) 80
(C) 81
(D) 157
(E) 159



Ans: E

sum of n consecutive numbers= [n(n+1)]/2 = S
sum of only even or only odd numbers = S/2
now by putting the value we know: n= 158
so the value of k is 159
_________________

--------------------------------------------------------------------
The Mind is Everything, What we Think we Become.
Kudos will encourage many others, like me.
Please Give Kudos Image !!
Thanks :-)

Tough and tricky: The sum of the even numbers.   [#permalink] 17 May 2015, 21:08
    Similar topics Author Replies Last post
Similar
Topics:
Experts publish their posts in the topic Tough and tricky 6: Probability of drawing Bunuel 5 11 Oct 2009, 17:17
Experts publish their posts in the topic Tough and tricky 5: Race Bunuel 5 11 Oct 2009, 17:14
5 Experts publish their posts in the topic Tough and tricky 4: addition problem Bunuel 9 11 Oct 2009, 16:42
Experts publish their posts in the topic Tough and tricky 3: leap year Bunuel 5 11 Oct 2009, 16:25
Experts publish their posts in the topic Tough and tricky 2: Bunuel 4 11 Oct 2009, 16:17
Display posts from previous: Sort by

Tough and tricky: The sum of the even numbers.

  Question banks Downloads My Bookmarks Reviews Important topics  


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

Powered by phpBB © phpBB Group and phpBB SEO

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®.