If the sum of the first k positive integers is equal to

[sachin_yadav]

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)

[GMATGuruNY]

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

Let m=5 and n=3.
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.

[Brent@GMATPrepNow]

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)

The part in red SHOULD be "(sum of 1 to 9)" otherwise you are subtracting 10 from the sum.
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]

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)

The portion is red is incorrect.

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).

[sachin_yadav]

Thank you