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
OA is A
Why OA cannot be B
Suppose i need the sum of integers from 10 to 20. I will calculate the sum of (1 to 10) and subtract it from (1 to 20)
(sum of 1 to 20) - (sum of 1 to 10) = (sum of 10 to 20)
(m(m+1)-(n+1)n)/2 (where i am wrong)
If the sum of the first k positive integers is equal to
This topic has expert replies
- sachin_yadav
- Master | Next Rank: 500 Posts
- Posts: 212
- Joined: Mon Dec 06, 2010 12:52 am
- Location: India
- Thanked: 5 times
- Followed by:1 members
- GMATGuruNY
- GMAT Instructor
- Posts: 15539
- Joined: Tue May 25, 2010 12:04 pm
- Location: New York, NY
- Thanked: 13060 times
- Followed by:1906 members
- GMAT Score:790
Let m=5 and n=3.sachin_yadav 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
Sum of the integers 3 through 5 = 3+4+5 = 12. This is our target.
Now we plug m=5 and n=3 into the answers to see which yields our target of 12.
Answer choices A, B and C include m(m+1)/2:
m(m+1)/2 = 5(5+1)/2 = 15.
To yield our target of 12, we need to subtract 3.
Only answer choice C works:
(n-1)n/2 = (3-1)3/2 = 3.
Since m(m+1)/2 yields our target, the expression in D and E -- (m-1)m/2 -- will NOT yield our target.
The correct answer is C.
Private tutor exclusively for the GMAT and GRE, with over 20 years of experience.
Followed here and elsewhere by over 1900 test-takers.
I have worked with students based in the US, Australia, Taiwan, China, Tajikistan, Kuwait, Saudi Arabia -- a long list of countries.
My students have been admitted to HBS, CBS, Tuck, Yale, Stern, Fuqua -- a long list of top programs.
As a tutor, I don't simply teach you how I would approach problems.
I unlock the best way for YOU to solve problems.
For more information, please email me (Mitch Hunt) at [email protected].
Student Review #1
Student Review #2
Student Review #3
Followed here and elsewhere by over 1900 test-takers.
I have worked with students based in the US, Australia, Taiwan, China, Tajikistan, Kuwait, Saudi Arabia -- a long list of countries.
My students have been admitted to HBS, CBS, Tuck, Yale, Stern, Fuqua -- a long list of top programs.
As a tutor, I don't simply teach you how I would approach problems.
I unlock the best way for YOU to solve problems.
For more information, please email me (Mitch Hunt) at [email protected].
Student Review #1
Student Review #2
Student Review #3
GMAT/MBA Expert
- Brent@GMATPrepNow
- GMAT Instructor
- Posts: 16207
- Joined: Mon Dec 08, 2008 6:26 pm
- Location: Vancouver, BC
- Thanked: 5254 times
- Followed by:1268 members
- GMAT Score:770
The part in red SHOULD be "(sum of 1 to 9)" otherwise you are subtracting 10 from the sum.sachin_yadav wrote:
Suppose i need the sum of integers from 10 to 20. I will calculate the sum of (1 to 10) and subtract it from (1 to 20)
(sum of 1 to 20) - (sum of 1 to 10) = (sum of 10 to 20)
(m(m+1)-(n+1)n)/2 (where i am wrong)
Here's what I mean:
(1+2+3+4+5+6+7+8+9+10+11+12+13+14+15+16+17+18+19+20) - (1+2+3+4+5+6+7+8+9) = 10+11+12+13+14+15+16+17+18+19+20
Cheers,
Brent
- GMATGuruNY
- GMAT Instructor
- Posts: 15539
- Joined: Tue May 25, 2010 12:04 pm
- Location: New York, NY
- Thanked: 13060 times
- Followed by:1906 members
- GMAT Score:790
The portion is red is incorrect.sachin_yadav wrote:Suppose i need the sum of integers from 10 to 20. I will calculate the sum of (1 to 10) and subtract it from (1 to 20)
First 20 positive integers:
1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20.
One way to yield the sum of the integers from 10 to 20, inclusive is to subtract the sum of the integers in blue from the sum of all 20 integers.
Thus:
(sum of the integers from 10 to 20, inclusive) = (sum of the integers from 1 to 20, inclusive) - (sum of the integers from 1 to 9, inclusive).
Private tutor exclusively for the GMAT and GRE, with over 20 years of experience.
Followed here and elsewhere by over 1900 test-takers.
I have worked with students based in the US, Australia, Taiwan, China, Tajikistan, Kuwait, Saudi Arabia -- a long list of countries.
My students have been admitted to HBS, CBS, Tuck, Yale, Stern, Fuqua -- a long list of top programs.
As a tutor, I don't simply teach you how I would approach problems.
I unlock the best way for YOU to solve problems.
For more information, please email me (Mitch Hunt) at [email protected].
Student Review #1
Student Review #2
Student Review #3
Followed here and elsewhere by over 1900 test-takers.
I have worked with students based in the US, Australia, Taiwan, China, Tajikistan, Kuwait, Saudi Arabia -- a long list of countries.
My students have been admitted to HBS, CBS, Tuck, Yale, Stern, Fuqua -- a long list of top programs.
As a tutor, I don't simply teach you how I would approach problems.
I unlock the best way for YOU to solve problems.
For more information, please email me (Mitch Hunt) at [email protected].
Student Review #1
Student Review #2
Student Review #3
- sachin_yadav
- Master | Next Rank: 500 Posts
- Posts: 212
- Joined: Mon Dec 06, 2010 12:52 am
- Location: India
- Thanked: 5 times
- Followed by:1 members