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

It is currently 27 Aug 2016, 20:26
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

If the sum of the first four numbers in a list of six consecutive even

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

Hide Tags

Director
Director
avatar
Joined: 21 Dec 2009
Posts: 591
Concentration: Entrepreneurship, Finance
Followers: 18

Kudos [?]: 611 [0], given: 20

If the sum of the first four numbers in a list of six consecutive even [#permalink]

Show Tags

New post 04 Aug 2010, 11:03
1
This post was
BOOKMARKED
00:00
A
B
C
D
E

Difficulty:

  45% (medium)

Question Stats:

69% (02:44) correct 31% (02:09) wrong based on 129 sessions

HideShow timer Statistics

If the sum of the first four numbers in a list of six consecutive even numbers is 908, what is the sum of the last four numbers in the list?

A. 912
B. 914
C. 916
D. 920
E. 924

[Reveal] Spoiler:
I tried it, but got screwed up:
let 2x be one of the numbers;
list: 2x-4, 2x-2, 2x, 2x+2, 2x+4, 2x+6
sum of the first four: (2x-4) + (2x-2) + (2x) + 2x+2)
--> 4x-4=908
x=228

sum of last four: 2x + (2x+2) + (2x+4) + (2x+6)
= 8x+12
=8(228) + 12
=1836...... non of the answers

Please what is the correct approach?
[Reveal] Spoiler: OA

_________________

KUDOS me if you feel my contribution has helped you.

Expert Post
3 KUDOS received
Math Expert
User avatar
Joined: 02 Sep 2009
Posts: 34457
Followers: 6279

Kudos [?]: 79682 [3] , given: 10022

Re: If the sum of the first four numbers in a list of six consecutive even [#permalink]

Show Tags

New post 04 Aug 2010, 11:31
3
This post received
KUDOS
Expert's post
gmatbull wrote:
If the sum of the first four numbers in a list of six consecutive even numbers is 908,
what is the sum of the last four numbers in the list?
A. 912
B. 914
C. 916
D. 920
E. 924

I tried it, but got screwed up:
let 2x be one of the numbers;
list: 2x-4, 2x-2, 2x, 2x+2, 2x+4, 2x+6
sum of the first four: (2x-4) + (2x-2) + (2x) + 2x+2)
--> 4x-4=908
x=228

sum of last four: 2x + (2x+2) + (2x+4) + (2x+6)
= 8x+12
=8(228) + 12
=1836...... non of the answers

Please what is the correct approach?

Let the six consecutive even numbers be \(x\), \(x+2\), \(x+4\), \(x+6\), \(x+8\), \(x+10\).

Given: \(x+(x+2)+(x+4)+(x+6)=4x+12=908\). Question: \((x+4)+(x+6)+(x+8)+(x+10)=4x+28=?\)

\((x+4)+(x+6)+(x+8)+(x+10)=4x+28=(4x+12)+16=908+16=924\).

Answer: E.

The way you are doing is also valid. You've just made an error in calculations, plus no need even number to be \(2x\) it can be just even \(x\).

But anyway your approach:

Sum of the first four: \((2x-4)+(2x-2)+(2x)+(2x+2)=8x-4=908\);
Sum of the last four: \(2x+(2x+2)+(2x+4)+(2x+6)=8x+12=(8x-4)+16=908+16=924\).

Hope it's clear.
_________________

New to the Math Forum?
Please read this: 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

Director
Director
avatar
Joined: 21 Dec 2009
Posts: 591
Concentration: Entrepreneurship, Finance
Followers: 18

Kudos [?]: 611 [0], given: 20

Re: If the sum of the first four numbers in a list of six consecutive even [#permalink]

Show Tags

New post 04 Aug 2010, 12:11
oh, thanks Bunuel for the corrections.
Hope you aren't tired of receiving kudos; you know, people like you have made
kudos a trite, and one simply wonders what else to give.

Methinks, there should be a different category of kudos for genius such as Bunuel.
If I may ask, please what was you GMAT score like?
_________________

KUDOS me if you feel my contribution has helped you.

Senior Manager
Senior Manager
avatar
Joined: 23 May 2010
Posts: 442
Followers: 5

Kudos [?]: 93 [0], given: 112

Re: If the sum of the first four numbers in a list of six consecutive even [#permalink]

Show Tags

New post 07 Aug 2010, 04:44
Bunuel wrote:
gmatbull wrote:
If the sum of the first four numbers in a list of six consecutive even numbers is 908,
what is the sum of the last four numbers in the list?
A. 912
B. 914
C. 916
D. 920
E. 924

I tried it, but got screwed up:
let 2x be one of the numbers;
list: 2x-4, 2x-2, 2x, 2x+2, 2x+4, 2x+6
sum of the first four: (2x-4) + (2x-2) + (2x) + 2x+2)
--> 4x-4=908
x=228

sum of last four: 2x + (2x+2) + (2x+4) + (2x+6)
= 8x+12
=8(228) + 12
=1836...... non of the answers

Please what is the correct approach?

Let the six consecutive even numbers be \(x\), \(x+2\), \(x+4\), \(x+6\), \(x+8\), \(x+10\).

Given: \(x+(x+2)+(x+4)+(x+6)=4x+12=908\). Question: \((x+4)+(x+6)+(x+8)+(x+10)=4x+28=?\)

\((x+4)+(x+6)+(x+8)+(x+10)=4x+28=(4x+12)+16=908+16=924\).

Answer: E.
Hi Bunuel
i did the same way ..
however kindly explain this if I solve
4x+ 12 =908 , I get x = 99 ..which is not an even number . hence I was confuded whether I missed something !!
thanx
Expert Post
Math Expert
User avatar
Joined: 02 Sep 2009
Posts: 34457
Followers: 6279

Kudos [?]: 79682 [0], given: 10022

Re: If the sum of the first four numbers in a list of six consecutive even [#permalink]

Show Tags

New post 07 Aug 2010, 05:04
Manager
Manager
avatar
Joined: 29 Jul 2010
Posts: 125
Followers: 1

Kudos [?]: 3 [0], given: 47

Re: If the sum of the first four numbers in a list of six consecutive even [#permalink]

Show Tags

New post 07 Aug 2010, 06:38
Bunuel wrote:
gmatbull wrote:
If the sum of the first four numbers in a list of six consecutive even numbers is 908,
what is the sum of the last four numbers in the list?
A. 912
B. 914
C. 916
D. 920
E. 924

I tried it, but got screwed up:
let 2x be one of the numbers;
list: 2x-4, 2x-2, 2x, 2x+2, 2x+4, 2x+6
sum of the first four: (2x-4) + (2x-2) + (2x) + 2x+2)
--> 4x-4=908
x=228

sum of last four: 2x + (2x+2) + (2x+4) + (2x+6)
= 8x+12
=8(228) + 12
=1836...... non of the answers

Please what is the correct approach?

Let the six consecutive even numbers be \(x\), \(x+2\), \(x+4\), \(x+6\), \(x+8\), \(x+10\).

Given: \(x+(x+2)+(x+4)+(x+6)=4x+12=908\). Question: \((x+4)+(x+6)+(x+8)+(x+10)=4x+28=?\)

\((x+4)+(x+6)+(x+8)+(x+10)=4x+28=(4x+12)+16=908+16=924\).

Answer: E.

The way you are doing is also valid. You've just made an error in calculations, plus no need even number to be \(2x\) it can be just even \(x\).

But anyway your approach:

Sum of the first four: \((2x-4)+(2x-2)+(2x)+(2x+2)=8x-4=908\);
Sum of the last four: \(2x+(2x+2)+(2x+4)+(2x+6)=8x+12=(8x-4)+16=908+16=924\).

Hope it's clear.

Well done!!!!

Thx and kudos
Senior Manager
Senior Manager
avatar
Joined: 23 May 2010
Posts: 442
Followers: 5

Kudos [?]: 93 [0], given: 112

Re: If the sum of the first four numbers in a list of six consecutive even [#permalink]

Show Tags

New post 08 Aug 2010, 01:49
Bunuel wrote:
gauravnagpal wrote:
Hi Bunuel
i did the same way ..
however kindly explain this if I solve
4x+ 12 =908 , I get x = 99 ..which is not an even number . hence I was confuded whether I missed something !!
thanx


\(4x+ 12 =908\) --> \(x=224=even\).

i am so sorry ...i reckon sleep of mind ...i dont know how could I write this ..thanx anyways for spending time on this
GMAT Club Legend
GMAT Club Legend
User avatar
Joined: 09 Sep 2013
Posts: 11103
Followers: 511

Kudos [?]: 134 [0], given: 0

Premium Member
Re: If the sum of the first four numbers in a list of six consecutive even [#permalink]

Show Tags

New post 10 Oct 2015, 11:02
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
avatar
Joined: 01 Jan 2015
Posts: 63
Followers: 0

Kudos [?]: 43 [0], given: 14

Re: If the sum of the first four numbers in a list of six consecutive even [#permalink]

Show Tags

New post 10 Oct 2015, 11:42
1
This post was
BOOKMARKED
gmatbull wrote:
If the sum of the first four numbers in a list of six consecutive even numbers is 908, what is the sum of the last four numbers in the list?

A. 912
B. 914
C. 916
D. 920
E. 924

[Reveal] Spoiler:
I tried it, but got screwed up:
let 2x be one of the numbers;
list: 2x-4, 2x-2, 2x, 2x+2, 2x+4, 2x+6
sum of the first four: (2x-4) + (2x-2) + (2x) + 2x+2)
--> 4x-4=908
x=228

sum of last four: 2x + (2x+2) + (2x+4) + (2x+6)
= 8x+12
=8(228) + 12
=1836...... non of the answers

Please what is the correct approach?


Since this is an evenly spaced set, the median is equal to the average of the set. The average and the median of the first four consecutive even integers are \(\frac{908}{4}=227.\)This implies that the first 4 consecutive even integers are 224,226,228, and 230. So the last two consecutive integers are 232 and 234. To find the sum of 228,230,232, and 234, take the median 231 and multiply by 4. (231*4) = 924

Correct answer choice is E.
Expert Post
1 KUDOS received
EMPOWERgmat Instructor
User avatar
Status: GMAT Assassin/Co-Founder
Affiliations: EMPOWERgmat
Joined: 19 Dec 2014
Posts: 7181
Location: United States (CA)
GMAT 1: 800 Q51 V49
GRE 1: 340 Q170 V170
Followers: 312

Kudos [?]: 2125 [1] , given: 161

Re: If the sum of the first four numbers in a list of six consecutive even [#permalink]

Show Tags

New post 10 Oct 2015, 17:55
1
This post received
KUDOS
Expert's post
1
This post was
BOOKMARKED
Hi All,

If you recognize the 'comparison' taking place in this question, you can avoid a 'calculation-heavy' approach and use the patterns to your advantage.

We're told that the first 4 CONSECUTIVE EVEN numbers (in a group of 6) has a sum of 908.

We can call those 4 terms...

X + (X+2) + (X+4) + (X+6) = 908

We're asked for the sum of the LAST 4 terms in this sequence... We can call those terms...

(X+4) + (X+6) + (X+8) + (X+10)

Notice how each of these four terms is EXACTLY 4 MORE than each of the 4 terms in the original sequence? Those 'differences' lead to an increase of 4(4) = 16 over the original sum.

Thus, the sum of the last 4 terms is 908 + 16 = 924

Final Answer:
[Reveal] Spoiler:
E


GMAT assassins aren't born, they're made,
Rich
_________________

Rich Cohen

Co-Founder & GMAT Assassin

Special Offer: Save $75 + GMAT Club Tests

60-point improvement guarantee
www.empowergmat.com/

***********************Select EMPOWERgmat Courses now include ALL 6 Official GMAC CATs!***********************

Re: If the sum of the first four numbers in a list of six consecutive even   [#permalink] 10 Oct 2015, 17:55
    Similar topics Author Replies Last post
Similar
Topics:
1 Which of these must the factor of the product of four consecutive even stonecold 1 05 Aug 2016, 21:02
5 Which of these must the factor of the product of four consecutive even stonecold 3 05 Aug 2016, 20:43
1 Experts publish their posts in the topic In an increasing sequence of 8 consecutive even integers, the sum of Bunuel 4 20 Dec 2015, 06:09
17 Experts publish their posts in the topic If S is the sum of reciprocals of a list of consecutive gmihir 11 16 May 2012, 09:35
101 Experts publish their posts in the topic The sum of four consecutive odd numbers is equal to the sum bindiyajoisher 19 21 Sep 2011, 11:52
Display posts from previous: Sort by

If the sum of the first four numbers in a list of six consecutive even

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


cron

GMAT Club MBA Forum Home| About| 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®.