Question

The average of 5 consecutive even numbers A,B,C,D and E is 52. What is the product of B and E?

Answer 1

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Answer 2

I think what this problem wants you to recognize is that, since you have 5, consecutive even integers that average to 52, you know exactly WHAT each of those integers is. That is, notice that you can write:

A=C-4
B=C-2
D=C+2
E=C+4

Then take that average:
\[\Large \dfrac{ (C-4)+(C-2)+C+(C+2)+C+4) }{ 5 }=52\]

If you solve that for C (or maybe you can see what I'm saying intuitively), you'll see a relationship between C and the average, 52.

Once you know C, you know B and E. So just take their product. :)