mystiquethinker wrote:

For all even integers n, h(n) is defined to be the sum of the even integers between 2 and n, inclusive. What is the value of h(18)/h(10) ?

(A) 1.8

(B) 3

(C) 6

(D) 18

(E) 60

First, notice that h(18) will be the sum of the even integers between 2 and 18 inclusive. We can thus calculate h(18) using the formula sum = avg x quantity.

First, find the average of this evenly spaced set of numbers:

avg = (18 + 2)/2 = 10

Now calculate how many numbers are in this set:

quantity = (18 - 2)/2 + 1 = 9

Now we use the formula sum = avg x quantity:

sum = (10)(9)

sum = 90 = h(18)

Next we can determine h(10) using the same procedure we used to calculate h(18):

avg = (10 + 2)/2 = 6

quantity = (10 - 2)/2 + 1 = 5

sum = 30

Thus, h(18)/h(10) = 90/30 = 3

Answer: B

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