Sum of integers

Expert replies

GMAT/MBA Expert

Brent@GMATPrepNow: GMAT Instructor; 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 » Sat Feb 21, 2009 1:36 pm

2 – 4 + 6 – 8 + 10 – 12 + . . . 994 – 996 + 998 – 1000 =

A) -250
B) -498
C) -500
D) -998
E) -1000

Oops, I fogot to make all of the answers negative (the original question featured only 1 negative answer)
The corrected answer choices are now displayed - sorry

Brent Hanneson - Creator of GMATPrepNow.com

Like this post

Source: Beat The GMAT — Problem Solving | Sat Feb 21, 2009 1:36 pm

cramya: Legendary Member; Posts: 2467; Joined: Thu Aug 28, 2008 6:14 pmFollowed by: 11 members; Thanked: 331 times

by cramya » Sat Feb 21, 2009 1:59 pm

Should it not be -500.??

I am missing something.

Between 2 to 1000 there are 500 evens and 499 odd's

2-4+6-8 = -4

Sum of each set of 4 is -4

500/4 = 125 sets possible

125*-4 = -500

Like this post

cramya: Legendary Member; Posts: 2467; Joined: Thu Aug 28, 2008 6:14 pmFollowed by: 11 members; Thanked: 331 times

by cramya » Sat Feb 21, 2009 2:00 pm

Just saw ur corrected post. Thanks!

Regards,
Cramya

Like this post

canindia: Newbie | Next Rank: 10 Posts; Posts: 3; Joined: Fri Feb 06, 2009 2:08 pm

by canindia » Sat Feb 21, 2009 2:03 pm

Just trying my way to beat this one.

2,-4,6,-8,10,-12.......,

1)If you add two terms you will get 2 ( 2-4 or 6-8 or 10-12) etc.
2) Find how many two's you will get like this: i.e...(1000-2)/2 +1 = 500.
3) 500 * 2 = 1000.

Let me know does it make sense.

Like this post

canindia: Newbie | Next Rank: 10 Posts; Posts: 3; Joined: Fri Feb 06, 2009 2:08 pm

by canindia » Sat Feb 21, 2009 2:08 pm

Just trying my way to beat this one.

2,-4,6,-8,10,-12.......,

1)If you add two terms you will get -2 ( 2-4 or 6-8 or 10-12) etc.
2) Find how many two's you will get like this: i.e...(1000-2)/2 +1 = 500.
3) 500 * -2 = -1000.

Let me know does it make sense.

Like this post

GMAT/MBA Expert

Brent@GMATPrepNow: GMAT Instructor; 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 » Sat Feb 21, 2009 2:18 pm

canindia wrote:Just trying my way to beat this one.

2,-4,6,-8,10,-12.......,

1)If you add two terms you will get -2 ( 2-4 or 6-8 or 10-12) etc.
2) Find how many two's you will get like this: i.e...(1000-2)/2 +1 = 500.
3) 500 * -2 = -1000.

Let me know does it make sense.

This looks good.
The only problem is that there aren't 1000 terms in 2 – 4 + 6 – 8 + 10 – 12 + . . . 994 – 996 + 998 – 1000. We are skipping all of the odd numbers, so there are 500 terms (or 250 pairs that add to -2)

Here's my solution as well:

2 – 4 + 6 – 8 + 10 – 12 + . . . 994 – 996 + 998 – 1000
= (2 – 4) + (6 – 8) + (10 – 12) + . . . +(994 – 996) + (998 – 1000)
= (-2) + (-2) + (-2) + . . . (-2) + (-2)
How many -2’s must we add?
The original sum, 2 – 4 + 6 – 8 + 10 – 12 + . . . 994 – 996 + 998 – 1000 consists of 500 pieces “addends,” which means that there were 250 pairs of numbers (which added to -2)

Sum = 250(-2) = -500

Last edited by Brent@GMATPrepNow on Sat Feb 21, 2009 2:24 pm, edited 1 time in total.

Brent Hanneson - Creator of GMATPrepNow.com

Like this post

truplayer256: Master | Next Rank: 500 Posts; Posts: 392; Joined: Thu Jan 15, 2009 12:52 pm; Location: New Jersey; Thanked: 76 times

by truplayer256 » Sat Feb 21, 2009 2:20 pm

I agree with Cramya on this one. Here's what I did:
Each -2 comes after adding 4 to each term. For example: 2+4=6, 6+4=10
This is a perfect example of an arithmetic sequence.
an=dn+c
an=4n-2
998=4n-2
n=250
-2(250)=-500 C

Like this post

Post new topic Post Reply

• Page 1 of 1

GMAT Course Reviews

560 reviews

1168 reviews

431 reviews

359 reviews

147 reviews

5/5

5 Star (560 Reviews)

"Target Test Prep is the closest to the official version of the GMAT exam, about 99% accuracy in terms of the quality and quantity of information. The course has excellently created singular sets of focused lessons and tests for every possible topic that one could come across in the official GMAT exam."

"The TTP course maximizes the efficiency of the time you spend studying. It will take time and effort but I could almost guarantee that if you complete the course exactly as it is laid out you will get an amazing score. They also have a very responsive team willing to help with any questions you might have."

"TTP has two things that I think no other test prep company offers: A teaching approach that reinforces understanding and an attitude that will give you the mental preparedness needed to succeed on the test. TTP gives you a deep understanding of the concept you need to know while teaching you how to think."

Write a Review