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

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If x is equal to the sum of the even integers from m to n, inclusive,  [#permalink]

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New post 27 Aug 2018, 10:15
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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. \((\frac{m+n}{2})(\frac{n-m}{2})\)

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Re: If x is equal to the sum of the even integers from m to n, inclusive,  [#permalink]

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New post 27 Aug 2018, 10:27
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Sum = Mean * Nos
Mean of evenly spaced set = (n+m)/2
nos for evenly spaced set = (n-m)/2+1
Sum = (n+m)/2 * (n-m)/2+1
A
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Re: If x is equal to the sum of the even integers from m to n, inclusive,  [#permalink]

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New post 27 Aug 2018, 10:41
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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. \((\frac{m+n}{2})(\frac{n-m}{2})\)


Let's m=2 and n=10, so, the numbers are 2+4+....+10
thus X=30

let's check each of the answer choices which equals 30
A) \((\frac{10+2}{2})(\frac{10-2}{2} + 1)\) = 30
B)\(3(10+2)\) =36
C) \(\frac{10^2 - 2^2}{2}\) = 48
D)\(6(2+10)\) = 72
E) \((\frac{2+10}{2})(\frac{10-2}{2})\)[/quote] =24

IMO, A
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Re: If x is equal to the sum of the even integers from m to n, inclusive,  [#permalink]

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New post 27 Aug 2018, 10:49
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Re: If x is equal to the sum of the even integers from m to n, inclusive,  [#permalink]

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New post 27 Aug 2018, 12:12
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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. \((\frac{m+n}{2})(\frac{n-m}{2})\)



Given

x = the sum of all the even integer between m and n, inclusive, where m and n are even.

plug value:

m = 2
n= 10

So x = 2 + 4 + 6 + 8 + 10 = 30.

So x = 30.

We are going to analyse each option until we got 30 as a result.

Option A:

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

\(\frac{m + n}{2}\)

=\(\frac{2 + 10}{2}\)

= 6

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

=\(\frac{10 - 2}{2}\) + 1

= 5 .

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

= 6 * 5

= 30.

The best answer is A.
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Re: If x is equal to the sum of the even integers from m to n, inclusive,  [#permalink]

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New post 27 Aug 2018, 14:36
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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. \((\frac{m+n}{2})(\frac{n-m}{2})\)


Even Series:- A.P.
1st term=m
Last term=n
No of terms=\(\frac{n-m}{2}+1\)
Sum of terms=No of terms* \(\frac{(First_term+Last_term)}{2}\)=\((\frac{n-m}{2}+1)(\frac{m+n}{2})\)

Ans. (A)
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Re: If x is equal to the sum of the even integers from m to n, inclusive,   [#permalink] 27 Aug 2018, 14:36
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