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The sum of the first k positive integers is equal to k(k+1)/

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The sum of the first k positive integers is equal to k(k+1)/ [#permalink] New post 19 Jan 2012, 10:16
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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)/2 - (n+1)(n+2)/2
B. m(m+1)/2 - n(n+1)/2
C. m(m+1)/2 - (n-1)n/2
D. (m-1)m/2 - (n+1)(n+2)/2
E. (m-1)m/2 - n(n+1)/2

I got Answer B.
But OA is different.
[Reveal] Spoiler: OA

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Re: The sum of the first k positive integers is equal to k(k+1)/ [#permalink] New post 19 Jan 2012, 10:28
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Baten80 wrote:
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)/2 - (n+1)(n+2)/2
B. m(m+1)/2 - n(n+1)/2
C. m(m+1)/2 - (n-1)n/2
D. (m-1)m/2 - (n+1)(n+2)/2
E. (m-1)m/2 - n(n+1)/2

I got Answer B.
But OA is different.


The sum of the integers from n to m, inclusive, will be the sum of the first m positive integers minus the sum of the first n-1 integers: \frac{m(m+1)}{2}-\frac{(n-1)(n-1+1)}{2}=\frac{m(m+1)}{2}-\frac{(n-1)n}{2}.

Answer: C.
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Re: The sum of the first k positive integers is equal to k(k+1)/ [#permalink] New post 19 Jan 2012, 10:34
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Baten80 wrote:
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)/2 - (n+1)(n+2)/2
B. m(m+1)/2 - n(n+1)/2
C. m(m+1)/2 - (n-1)n/2
D. (m-1)m/2 - (n+1)(n+2)/2
E. (m-1)m/2 - n(n+1)/2

I got Answer B.
But OA is different.


Or try plug-in method: let m=4 and n=3 --> then m+n=7. Let see which option yields 7.
A. m(m+1)/2 - (n+1)(n+2)/2 = 10-10=0;
B. m(m+1)/2 - n(n+1)/2 = 10-6=4;
C. m(m+1)/2 - (n-1)n/2 = 10-3=7 --> OK;
D. (m-1)m/2 - (n+1)(n+2)/2 = 6-10=-4;
E. (m-1)m/2 - n(n+1)/2 = 6-6=0.

Answer: C.
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RESOURCES: [GMAT MATH BOOK]; 1. Triangles; 2. Polygons; 3. Coordinate Geometry; 4. Factorials; 5. Circles; 6. Number Theory; 7. Remainders; 8. Overlapping Sets; 9. PDF of Math Book; 10. Remainders; 11. GMAT Prep Software Analysis NEW!!!; 12. SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) NEW!!!; 12. Tricky questions from previous years. NEW!!!;

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DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS ; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.


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Re: The sum of the first k positive integers is equal to k(k+1)/ [#permalink] New post 03 Jul 2014, 01:09
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Re: The sum of the first k positive integers is equal to k(k+1)/   [#permalink] 03 Jul 2014, 01:09
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