Question

There are 6 consecutive even numbers M₁, M₂, M₃, M₄, M₅, M₆ and 5 consecutive odd numbers N₁, N₂, N₃, N₄, N₅, N₆. The average of the even numbers is 4 more than the average of the odd numbers. If the sum of the even numbers is 24 more than the sum of the odd numbers, find the average of the odd numbers.

• A. 7
• B. 0
• C. 9
• D. 10

Answer 1

Answer:

B. 0

There appears to be a typo in the problem statement:

• It says 5 consecutive odd numbers, but then lists (N_1, N_2, N_3, N_4, N_5, N_6) (which is 6 numbers).

If the intended meaning is 5 consecutive odd numbers, then the solution is:

Let the average of the odd numbers be (x).

The average of the even numbers is then (x+4).

Since there are:

• 6 even numbers, their sum is (6(x+4)).

• 5 odd numbers, their sum is (5x).

Given:
6(x+4)-5x=24
6x+24-5x=24
x=0.

$Answer: (\boxed{0})$