M40-57

Question

If the sum of four consecutive even integers is equal to the sum of eight consecutive integers, what is the difference between the sums of the non-identical elements in the two sets?

A. 0
B. 2
C. 4
D. 6
E. 8

Bunuel · Answer

Official Solution:

If the sum of four consecutive even integers is equal to the sum of eight consecutive integers, what is the difference between the sums of the non-identical elements in the two sets?

A. 0
B. 2
C. 4
D. 6
E. 8

The question has a simple solution that does not involve any algebra.
 
If the sums of both sets are equal and we exclude the common elements—the sum of which would be the same—then the sums of the remaining unique elements must also be equal, leading to a difference of 0.

Answer: A

Anugmat740 · Answer

Sum of First 8 integers starting from 1 to 8 = 36

Sum of Four even integers whose sum is equal to 36.
(To get these even integers, 36/4=9. Take even integers close to 9 to get sum as 36. We get (6,8,10,12)

Common integers in these two sets are 6 and 8.

Sum of remaining integers from 1-8 (excluding 6 and 8) = 36-14 = 22

Sum of even integers (6,8,10,12) (excluding common terms (6 and 8)) we get = 36-14 =22

The difference between the sums of the non-identical elements in the two sets= 22-22 =0

ManifestMBAbay25 · Answer

I have solved it using the below method

even consecutive integers - {2k, 2k+2, 2k+4, 2k+6}
Sum of even consecutive integers - 8k+12

8 consecutive integers set - { 2k+1, 2k+2, 2k+3, 2k+4, 2k+5 2k+6, 2k+7, 2k+8}
Sum of 8 consecutive integers - 16k + 36

now as per the question 
8k +12 = 16k +36
k = -3

Now difference between the sums of non - identical elements in the two sets 
 2k+1+2k+2+2k+3+2k+4 + 2k+5+2k+6+2k+7+2k+8 - ( 2k+2k+2+2k+4+2k+6)
 2k+1+ 2k+2 +2k+3+ 2k+4 +2k+5  2k+6 +2k+7+ 2k +8 -  2k - 2k - 2  -  2k-4  -  2k-6 
2k+1+2k+3+2k+5+2k+7+8
8k+24
8(-3) +24 = 0

Bunuel

sb995 · Answer

I like the solution - it’s helpful.

Paattaa · Answer

I like the solution - it’s helpful.

chattyyee · Answer

This is a great question that’s helpful for learning.

gemministorm · Answer

i reached till here using y, y+2, y+4, y+6 = x, x+1, x+2, x+3, x+4, x+5, x+6, x+7 4y + 12 = 8x + 16 y = 2x + 4 ....got stuck what next maybe x = 1, i get y = 6 and one sample values I would have 6, 8, 10, 12 = 1, 2, 3, 4, 5, 6, 7, 8 and further acc to question i could have solved....darn it

AdarshSambare · Answer

Given:
Sum of 4 consecutive even numbers = sum of 8 consecutive numbers
S(4 even numbers) = S(8 consecutive numbers)
Sn = n/2(2a+(n-1)d)
putting n =4 and d=2 for even numbers
and n=8 and d=1 for consecutive numbers
4/2(2a+3(2)) = 8/2(2a+7(1))
==> a=-4
So our sets are -4,-2,0,2
and -4,-3,-2,-1,0,1,2 & 3
Difference between the sums of the non-identical elements in the two sets:
Sum of non-identical elements: -3,-1,1,3 = 0
So our the difference is 0
 Option A

M40-57

Prep Toolkit

Top 5 GMAT Debrief Videos

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards