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Source: — Problem Solving |

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by Brent@GMATPrepNow » Mon Aug 27, 2012 3:22 pm
grandh01 wrote:If the sum of the first n positive
integers is S, what is the sum of the
first n positive even integers, in terms
of S ?
(A)s/2
(B) S
(C) 2S
(D) 2S + 2
(E) 4S

OA is C
The sum of the first n even numbers looks like this: 2+4+6+8+10+12+..
There will be n terms to add here.
Notice that we can take the sum and factor out a 2 to get:
2+4+6+8+10+12+.. = 2(1+2+3+...+n)
If sum of the first n terms is S, then the sum of the first n even numbers will equal 2S.

So, the answer is C

Cheers,
Brent
Brent Hanneson - Creator of GMATPrepNow.com
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GMAT/MBA Expert

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Posts: 16207
Joined: Mon Dec 08, 2008 6:26 pmFollowed by: 1268 members
Location: Vancouver, BC
Thanked: 5254 times
GMAT Score:770

by Brent@GMATPrepNow » Mon Aug 27, 2012 3:32 pm
grandh01 wrote:If the sum of the first n positive
integers is S, what is the sum of the
first n positive even integers, in terms
of S ?
(A)s/2
(B) S
(C) 2S
(D) 2S + 2
(E) 4S

OA is C
Notice that we can also solve this question through observation.
When n=3, the sum of the first n positive integers is 6 (in other words, S=6)

When we find the sum of the first 3 positive even integers, we get 2+4+6 = 12, and 12 is equal to 2(6).
In other words, the sum of the first 3 positive even integers equals 2S

Answer = C
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