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# If x is equal to the sum of the even integers from m to n, i

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If x is equal to the sum of the even integers from m to n, i [#permalink]  27 Aug 2018, 09:15
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If x is equal to the sum of the even integers from m to n, inclusive, where m and n are positive even integers, which of the following represents the value of x in terms of m and n?

A. $$(\frac{m+n}{2})(\frac{n-m}{2} + 1)$$

B. $$3(m+n)$$

C. $$\frac{n^2 - m^2}{2}$$

D. $$6(m+n)$$

E. $$(\frac{m+n}{2})(\frac{n-m}{2})$$
[Reveal] Spoiler: OA

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Re: If x is equal to the sum of the even integers from m to n, i [#permalink]  29 Aug 2018, 12:47
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Carcass wrote:
If x is equal to the sum of the even integers from m to n, inclusive, where m and n are positive even integers, which of the following represents the value of x in terms of m and n?

A. $$(\frac{m+n}{2})(\frac{n-m}{2} + 1)$$

B. $$3(m+n)$$

C. $$\frac{n^2 - m^2}{2}$$

D. $$6(m+n)$$

E. $$(\frac{m+n}{2})(\frac{n-m}{2})$$

This is how I did...

since x is sum of m to n inclusive where m and n are even.

Let take such series => case 1: 2, 4 and 6 (or ) case 2: 2, 4, 6 and 8

Sub since m is starting and n is ending of the series.

case 1: x sum is = 12
m = 2 and n = 6 , sub in the options we get A as 12.

case 2: x sum is 20
m = 2 and n = 8 , sub in the options we get A as 20

Hence A.
Re: If x is equal to the sum of the even integers from m to n, i   [#permalink] 29 Aug 2018, 12:47
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