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

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Updated on: 27 Sep 2017, 03:21
00:00

Difficulty:

65% (hard)

Question Stats:

48% (01:30) correct 52% (00:54) wrong based on 77 sessions

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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

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MathRevolution: Finish GMAT Quant Section with 10 minutes to spare
The one-and-only World’s First Variable Approach for DS and IVY Approach for PS with ease, speed and accuracy.
"Only $99 for 3 month Online Course" "Free Resources-30 day online access & Diagnostic Test" "Unlimited Access to over 120 free video lessons - try it yourself" Originally posted by MathRevolution on 25 Jan 2016, 17:40. Last edited by Bunuel on 27 Sep 2017, 03:21, edited 3 times in total. Added the OA. Manager Joined: 12 Mar 2015 Posts: 97 Concentration: Leadership, Finance GPA: 3.9 WE: Information Technology (Computer Software) Re: If the sum of the first k positive integers is equal to, k(k+1)/2, Wha [#permalink] ### Show Tags 26 Jan 2016, 01:06 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 Answer A Math Revolution GMAT Instructor Joined: 16 Aug 2015 Posts: 6227 GMAT 1: 760 Q51 V42 GPA: 3.82 Re: If the sum of the first k positive integers is equal to, k(k+1)/2, Wha [#permalink] ### Show Tags 27 Jan 2016, 18:23 1 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. Therefore, the answer is A. _________________ MathRevolution: Finish GMAT Quant Section with 10 minutes to spare The one-and-only World’s First Variable Approach for DS and IVY Approach for PS with ease, speed and accuracy. "Only$99 for 3 month Online Course"
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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, 12:01
1
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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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, 03:21
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 &nbs [#permalink] 27 Sep 2017, 03:21
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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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