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

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Director
Joined: 21 Dec 2009
Posts: 557
Concentration: Entrepreneurship, Finance
If the sum of the first four numbers in a list of six consecutive even [#permalink]

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04 Aug 2010, 11:03
1
5
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Difficulty:

55% (hard)

Question Stats:

71% (01:40) correct 29% (02:05) wrong based on 273 sessions

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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?

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KUDOS me if you feel my contribution has helped you.

Math Expert
Joined: 02 Sep 2009
Posts: 46143
Re: If the sum of the first four numbers in a list of six consecutive even [#permalink]

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04 Aug 2010, 11:31
4
3
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.
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Joined: 21 Dec 2009
Posts: 557
Concentration: Entrepreneurship, Finance
Re: If the sum of the first four numbers in a list of six consecutive even [#permalink]

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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?
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Senior Manager
Joined: 23 May 2010
Posts: 313
Re: If the sum of the first four numbers in a list of six consecutive even [#permalink]

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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
Math Expert
Joined: 02 Sep 2009
Posts: 46143
Re: If the sum of the first four numbers in a list of six consecutive even [#permalink]

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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

$$4x+ 12 =908$$ --> $$x=224=even$$.
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Manager
Joined: 29 Jul 2010
Posts: 118
Re: If the sum of the first four numbers in a list of six consecutive even [#permalink]

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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
Joined: 23 May 2010
Posts: 313
Re: If the sum of the first four numbers in a list of six consecutive even [#permalink]

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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
Manager
Joined: 01 Jan 2015
Posts: 63
Re: If the sum of the first four numbers in a list of six consecutive even [#permalink]

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10 Oct 2015, 11:42
2
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?

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

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10 Oct 2015, 17:55
2
1
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:

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

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24 Sep 2017, 13:32
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

let x=1st term
4x+12=908
x=224
3rd term=228
6th term=234
(228+234)/2=231=mean of last four terms
4*231=924=sum of last four terms
E
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Re: If the sum of the first four numbers in a list of six consecutive even [#permalink]

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26 Sep 2017, 16:36
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

We can create the following equation in which x is the first number in the list:

x + x + 2 + x + 4 + x + 6 = 908

4x = 896

x = 224

The sum of the last 4 numbers in the list is 228 + 230 + 232 + 234 = 924.

Alternative solution:

Let’s let x, x + 2, x + 4, x + 6, x + 8, and x + 10 be the six consecutive even numbers. We are given that
x + (x + 2) + (x + 4) + (x + 6) = 908 and we are asked to find the value of (x + 4) + (x + 6) + (x + 8) + (x + 10). While x + 4 and x + 6 are the same in both sums, x + 8 is 8 more than x and x + 10 is 8 more than x + 2. Thus, the latter sum will be 16 more than the former sum. Since we know the former sum is 908, the latter sum must be 908 + 16 = 924.

Answer: E
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Re: If the sum of the first four numbers in a list of six consecutive even   [#permalink] 26 Sep 2017, 16:36
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# If the sum of the first four numbers in a list of six consecutive even

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