If the sum of four consecutive even integers is equal to the sum of

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 · Accepted Answer

Right. However, there's a much simpler solution: 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.

Bunuel · Answer

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

gmatophobia · Answer

Let's assume

Set A consists of four consecutive even numbers

A =  { x-2, \quad x, \quad x+2, \quad x+4 }

Set B consists of eight consecutive numbers

B =  {  y-3,\quad y-2, \quad y-1, \quad y, \quad y+1,\quad y+2, \quad y+3, \quad y+4 }

Given   "  ...the sum of four consecutive even integers is equal to the sum of eight consecutive integers...  "

x - 2 + x + x +2 + x + 4 = y - 3 + y - 2 + y -1 + y + y + 1 + y +2 + y + 3 + y + 4

4x + 4 = 8y + 4

4(x + 1) = 4(2y + 1)

Dividing by  4  on both sides

x + 1 = 2y + 1

x = 2y

Let's assume some values to visualize the sets,  A  and  B , better.

x =2 ; y = 1

A =  { 0, \quad 2, \quad 4, \quad 6 }

B =  {  -2,\quad -1, \quad 0, \quad 1, \quad 2,\quad 3, \quad 4, \quad 5 }

The sum of non-identical elements of Set  A = 6 
 
 The sum of non-identical elements of Set  B = -2 + -1 + 1 + 3 + 5 = 6

Difference  = 6 - 6 = 0

Option A

gmatophobia · Answer

Holy Moly ! How did I miss such a simple fact; it seems so obvious in hindsight.

Rishm · Answer

I assumed 1,2,3....till 8 as integers and summed it to 36 and found 6,8,10,12 as those numbers equal 36 too. Hence 22-22=0

Vivek1707 · Answer

If the sum of 4 terms is say x

We are given that the sum of 8 consecutive terms is equal to sum of 4 consecutive terms terms

So sum of 8 consecutive terms is say x + y (here y is the sum of the non identical terms)

We know that x = x + y hence y has to be 0

If the sum of four consecutive even integers is equal to the sum of

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If the sum of four consecutive even integers is equal to the sum of

Prep Toolkit

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

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