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Sum of integers

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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 :oops:
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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
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by cramya » Sat Feb 21, 2009 2:00 pm
Just saw ur corrected post. Thanks!

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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.
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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.
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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.
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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
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