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# What is the difference between the sum of the first 2003 positive even

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Math Expert
Joined: 02 Sep 2009
Posts: 59587
What is the difference between the sum of the first 2003 positive even  [#permalink]

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19 Mar 2019, 01:39
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Difficulty:

45% (medium)

Question Stats:

61% (01:38) correct 39% (01:54) wrong based on 51 sessions

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What is the difference between the sum of the first 2003 positive even integers and the sum of the first 2003 positive odd integers ?

(A) 0
(B) 1
(C) 2
(D) 2003
(E) 4006

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Re: What is the difference between the sum of the first 2003 positive even  [#permalink]

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19 Mar 2019, 05:50
Bunuel wrote:
What is the difference between the sum of the first 2003 positive even integers and the sum of the first 2003 positive odd integers ?

(A) 0
(B) 1
(C) 2
(D) 2003
(E) 4006

n even integers : 2+4+6+...+4006
and odd intgers : 1+3+5+...+4005
difference would be of 2003 nos only
IMO D
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What is the difference between the sum of the first 2003 positive even  [#permalink]

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Updated on: 22 May 2019, 15:56
In this case we can just solve it by theory, but it is important to learn the following formulas:

Sum of the first n even integers: $$n(n+1)$$
Sum of the first n odd integers: $$n^2$$

So...

$$((2003(2003+1))-(2003^2))$$

$$((2003*2004)-2003^2)$$

$$2003((1)(2004)-2003)$$

$$2003(2004-2003)$$

$$2003(1)$$

$$2003$$

D

Originally posted by jfranciscocuencag on 19 Mar 2019, 14:47.
Last edited by jfranciscocuencag on 22 May 2019, 15:56, edited 3 times in total.
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Re: What is the difference between the sum of the first 2003 positive even  [#permalink]

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21 Mar 2019, 17:59
1
Bunuel wrote:
What is the difference between the sum of the first 2003 positive even integers and the sum of the first 2003 positive odd integers ?

(A) 0
(B) 1
(C) 2
(D) 2003
(E) 4006

If we pair up each odd and even integer, we have:

1,2

3,4

5,6

…..

4,005, 4,006

We see that each even number is 1 more than its odd counterpart, and since there are 2003 such pairs, the difference between the sum of the even integers and the sum of the odd odd integers is 2003.

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Re: What is the difference between the sum of the first 2003 positive even   [#permalink] 21 Mar 2019, 17:59
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