It is currently 23 Sep 2017, 09:47

# Happening Now:

Alleviate MBA app anxiety! Come to Chat Room #2

### 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

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

# Events & Promotions

###### Events & Promotions in June
Open Detailed Calendar

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

Author Message
TAGS:

### Hide Tags

Director
Joined: 21 Dec 2009
Posts: 584

Kudos [?]: 790 [1], given: 20

Concentration: Entrepreneurship, Finance
If the sum of the first four numbers in a list of six consecutive even [#permalink]

### Show Tags

04 Aug 2010, 11:03
1
KUDOS
3
This post was
BOOKMARKED
00:00

Difficulty:

45% (medium)

Question Stats:

67% (01:48) correct 33% (02:03) wrong based on 208 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

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

_________________

KUDOS me if you feel my contribution has helped you.

Kudos [?]: 790 [1], given: 20

Math Expert
Joined: 02 Sep 2009
Posts: 41698

Kudos [?]: 124613 [4], given: 12079

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

### Show Tags

04 Aug 2010, 11:31
4
KUDOS
Expert's post
3
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

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

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: $$(x+4)+(x+6)+(x+8)+(x+10)=4x+28=?$$

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

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 $$x$$.

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.
_________________

Kudos [?]: 124613 [4], given: 12079

Director
Joined: 21 Dec 2009
Posts: 584

Kudos [?]: 790 [0], given: 20

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

### Show Tags

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.
_________________

KUDOS me if you feel my contribution has helped you.

Kudos [?]: 790 [0], given: 20

Senior Manager
Joined: 23 May 2010
Posts: 419

Kudos [?]: 143 [0], given: 112

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

### Show Tags

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

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: $$(x+4)+(x+6)+(x+8)+(x+10)=4x+28=?$$

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

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

Kudos [?]: 143 [0], given: 112

Math Expert
Joined: 02 Sep 2009
Posts: 41698

Kudos [?]: 124613 [0], given: 12079

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

### Show Tags

07 Aug 2010, 05:04
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

$$4x+ 12 =908$$ --> $$x=224=even$$.
_________________

Kudos [?]: 124613 [0], given: 12079

Manager
Joined: 29 Jul 2010
Posts: 124

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

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

### Show Tags

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

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: $$(x+4)+(x+6)+(x+8)+(x+10)=4x+28=?$$

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

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 $$x$$.

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

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

Senior Manager
Joined: 23 May 2010
Posts: 419

Kudos [?]: 143 [0], given: 112

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

### Show Tags

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

Kudos [?]: 143 [0], given: 112

GMAT Club Legend
Joined: 09 Sep 2013
Posts: 17620

Kudos [?]: 271 [0], given: 0

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

### Show Tags

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.
_________________

Kudos [?]: 271 [0], given: 0

Manager
Joined: 01 Jan 2015
Posts: 63

Kudos [?]: 88 [0], given: 14

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

### Show Tags

10 Oct 2015, 11:42
2
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

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

Kudos [?]: 88 [0], given: 14

EMPOWERgmat Instructor
Status: GMAT Assassin/Co-Founder
Affiliations: EMPOWERgmat
Joined: 19 Dec 2014
Posts: 9809

Kudos [?]: 3317 [2], given: 171

Location: United States (CA)
GMAT 1: 800 Q51 V49
GRE 1: 340 Q170 V170
Re: If the sum of the first four numbers in a list of six consecutive even [#permalink]

### Show Tags

10 Oct 2015, 17:55
2
KUDOS
Expert's post
2
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

[Reveal] Spoiler:
E

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

760+: Learn What GMAT Assassins Do to Score at the Highest Levels
Contact Rich at: Rich.C@empowergmat.com

# Rich Cohen

Co-Founder & GMAT Assassin

# Special Offer: Save \$75 + GMAT Club Tests Free

Official GMAT Exam Packs + 70 Pt. Improvement Guarantee
www.empowergmat.com/

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

Kudos [?]: 3317 [2], given: 171

GMAT Club Legend
Joined: 09 Sep 2013
Posts: 17620

Kudos [?]: 271 [0], given: 0

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

### Show Tags

26 Mar 2017, 11:40
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.
_________________

Kudos [?]: 271 [0], given: 0

Re: If the sum of the first four numbers in a list of six consecutive even   [#permalink] 26 Mar 2017, 11:40
Similar topics Replies Last post
Similar
Topics:
7 Which of these must the factor of the product of four consecutive even 3 16 Jan 2017, 00:28
1 Which of these must the factor of the product of four consecutive even 1 05 Aug 2016, 23:20
33 If S is the sum of reciprocals of a list of consecutive 14 14 Feb 2017, 16:55
2 Three consecutive even numbers are such that thrice the first number 3 22 Mar 2017, 13:24
227 The sum of four consecutive odd numbers is equal to the sum 35 24 Jul 2017, 08:51
Display posts from previous: Sort by