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

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Joined: 01 Sep 2010
Posts: 3306
If x is equal to the sum of the even integers from m to n, inclusive,  [#permalink]

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27 Aug 2018, 09:15
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Difficulty:

15% (low)

Question Stats:

85% (01:27) correct 15% (01:37) wrong based on 41 sessions

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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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27 Aug 2018, 09:27
1
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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Posts: 21
Concentration: Marketing, Strategy
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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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27 Aug 2018, 09:41
1
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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27 Aug 2018, 09:49
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Guys is a good manner IF the question is good and useful to leave kudos.

Thank you.
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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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27 Aug 2018, 11:12
1
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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WE: Supply Chain Management (Energy and Utilities)
Re: If x is equal to the sum of the even integers from m to n, inclusive,  [#permalink]

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27 Aug 2018, 13:36
1
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, &nbs [#permalink] 27 Aug 2018, 13:36
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# If x is equal to the sum of the even integers from m to n, inclusive,

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