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# If the sum of the first k positive integers is equal to, k(k+1)/2, Wha

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Math Revolution GMAT Instructor
Joined: 16 Aug 2015
Posts: 4886
GPA: 3.82
If the sum of the first k positive integers is equal to, k(k+1)/2, Wha [#permalink]

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25 Jan 2016, 16:40
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If the sum of the first k positive integers is equal to, k(k+1)/2, What is the sum of the integers from n to m, inclusive, where 0<n<m?

A. (m(m+1)-(n-1)n)/2
B. (m(m+1)-(n+1)n)/2
C. (m(m-1)-(n-1)n)/2
D. (m(m-1)-(n+1)n)/2
E. (m(m+1)-(n-1)n)/4

* A solution will be posted in two days.

OPEN DISCUSSION OF THIS QUESTION IS HERE: https://gmatclub.com/forum/the-sum-of-t ... 26289.html
[Reveal] Spoiler: OA

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Last edited by Bunuel on 27 Sep 2017, 02:21, edited 3 times in total.
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Re: If the sum of the first k positive integers is equal to, k(k+1)/2, Wha [#permalink]

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26 Jan 2016, 00:06
MathRevolution wrote:
If the sum of the first k positive integers is equal to, k(k+1)/2, What is the sum of the integers from n to m, inclusive, where 0<n<m?

A. (m(m+1)-(n-1)n)/2
B. (m(m+1)-(n+1)n)/2
C. (m(m-1)-(n-1)n)/2
D. (m(m-1)-(n+1)n)/2
E. (m(m+1)-(n-1)n)/4

* A solution will be posted in two days.

1+2+3+4..+n+...+m

m(m+1)/2 - (n-1)(n-1+1)/2
= (m(m+1) - (n-1)(n))/2

Math Revolution GMAT Instructor
Joined: 16 Aug 2015
Posts: 4886
GPA: 3.82
Re: If the sum of the first k positive integers is equal to, k(k+1)/2, Wha [#permalink]

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27 Jan 2016, 17:23
If the sum of the first k positive integers is equal to, k(k+1)/2, What is the sum of the integers from n to m, inclusive, where 0<n<m?

A. (m(m+1)-(n-1)n)/2
B. (m(m+1)-(n+1)n)/2
C. (m(m-1)-(n-1)n)/2
D. (m(m-1)-(n+1)n)/2
E. (m(m+1)-(n-1)n)/4

==> n+(n+1)+…….+(m-1)+m={1+2+…+(n-1)+n+(n+1)+…+(m-1)+m}-{1+2+…+(n-1)}=m(m+1)/2-n(n-1)/2.

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Re: If the sum of the first k positive integers is equal to, k(k+1)/2, Wha [#permalink]

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25 Aug 2017, 06:19
Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

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Re: If the sum of the first k positive integers is equal to, k(k+1)/2, Wha [#permalink]

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26 Aug 2017, 11:01
1
KUDOS
MathRevolution wrote:
If the sum of the first k positive integers is equal to, k(k+1)/2, What is the sum of the integers from n to m, inclusive, where 0<n<m?

A. (m(m+1)-(n-1)n)/2
B. (m(m+1)-(n+1)n)/2
C. (m(m-1)-(n-1)n)/2
D. (m(m-1)-(n+1)n)/2
E. (m(m+1)-(n-1)n)/4

* A solution will be posted in two days.

If you don't know how to manipulate that particular formula, or if the manipulation takes too long, choose values.

Let n = 2 and m = 4

Find the sum of the integers from n to m, inclusive. Either

1) 2 + 3 + 4 = 9, or

2) [IF you choose numbers too far apart]: (average) * (# of terms) is

$$\frac{(2+4)}{2}$$ * 3 = 9

Check answer choices with n = 2, m = 4. The one that yields 9 as the answer is correct.

The arithmetic with these numbers is quick.

(4*5 - 1*2)/2 = 18/2 = 9. MATCH

I checked the others, quickly.

B. (m(m+1)-(n+1)n)/2
(20 - 6)/2 = 7. NOT a match

C. (m(m-1)-(n-1)n)/2
(12 - 1) = 11 won't work as a numerator. Move on. NOT a match

D. (m(m-1)-(n+1)n)/2
(12 - 6) = 6, already too small without division. Move on. NOT a match.

E. (m(m+1)-(n-1)n)/4
(20 - 1) = 19 won't work as a numerator. Move on. NOT a match

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Posts: 43810
Re: If the sum of the first k positive integers is equal to, k(k+1)/2, Wha [#permalink]

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27 Sep 2017, 02:21
MathRevolution wrote:
If the sum of the first k positive integers is equal to, k(k+1)/2, What is the sum of the integers from n to m, inclusive, where 0<n<m?

A. (m(m+1)-(n-1)n)/2
B. (m(m+1)-(n+1)n)/2
C. (m(m-1)-(n-1)n)/2
D. (m(m-1)-(n+1)n)/2
E. (m(m+1)-(n-1)n)/4

* A solution will be posted in two days.

OPEN DISCUSSION OF THIS QUESTION IS HERE: https://gmatclub.com/forum/the-sum-of-t ... 26289.html
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Re: If the sum of the first k positive integers is equal to, k(k+1)/2, Wha   [#permalink] 27 Sep 2017, 02:21
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