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

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

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

Well done!!!!

Thx and kudos

i am so sorry ...i reckon sleep of mind ...i dont know how could I write this ..thanx anyways for spending time on this

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.

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:

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

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

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