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If a equals the sum of the even integers from 2 to 20, inclusive, and [#permalink]

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04 Apr 2007, 20:30

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If a equals the sum of the even integers from 2 to 20, inclusive, and b equals the sum of the odd integers from 1 to 19, inclusive, what is the value of a - b ?

Re: If a equals the sum of the even integers from 2 to 20, inclusive, and [#permalink]

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04 Apr 2007, 20:36

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The sum is 10.

The fastest way is to notice that since we're taking a-b, all we are going to end up with is addings ten '1' since each even number is one larger than the odd.

Re: If a equals the sum of the even integers from 2 to 20, inclusive, and [#permalink]

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03 Nov 2014, 22:23

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If a equals the sum of the even integers from 2 to 20, inclusive, and b equals the sum of the odd integers from 1 to 19, inclusive, what is the value of a - b ?

A. 1 B. 10 C. 19 D. 20 E. 21

Hi, Another way.. Without getting into the sum etc, the answer can be found easily... 2-20 contains 10 integers and similarily 1-19 also has 10 integers.. smallest integer of a is greater by 1 than the corresponding integer of b.. and these is same for all 10 integers.. so a-b=1*10=10
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Re: If a equals the sum of the even integers from 2 to 20, inclusive, and [#permalink]

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07 Feb 2016, 03:18

chetan2u wrote:

faifai0714 wrote:

If a equals the sum of the even integers from 2 to 20, inclusive, and b equals the sum of the odd integers from 1 to 19, inclusive, what is the value of a - b ?

A. 1 B. 10 C. 19 D. 20 E. 21

Hi, Another way.. Without getting into the sum etc, the answer can be found easily... 2-20 contains 10 integers and similarily 1-19 also has 10 integers.. smallest integer of a is greater by 1 than the corresponding integer of b.. and these is same for all 10 integers.. so a-b=1*10=10

how to count number of odd integers from 1 to n inclusive? Please advise
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If a equals the sum of the even integers from 2 to 20, inclusive, and b equals the sum of the odd integers from 1 to 19, inclusive, what is the value of a - b ?

A. 1 B. 10 C. 19 D. 20 E. 21

Hi, Another way.. Without getting into the sum etc, the answer can be found easily... 2-20 contains 10 integers and similarily 1-19 also has 10 integers.. smallest integer of a is greater by 1 than the corresponding integer of b.. and these is same for all 10 integers.. so a-b=1*10=10

how to count number of odd integers from 1 to n inclusive? Please advise

Hi, If n is odd, add 1to it and divide by 2... If n is even, straight way divide by 2... In this example, n is 19.. Add one,so 20.. 20/2=10..

smartguy595, at times it might be that you are given some integer in between to another integer ahead.. example, it may not be 1 to n, but n to x.. few points to note in that scenario..

1) both x and n are even total integers will be (x-n)+1... even will be 1 more than odd.. even= (x-n)/2+1 and odd=(x-n)/2..

2) x is even and n is odd.. total integers = x-n +1.. even will be equal to odd.. even= odd={(x-n)+1}/2 ..

3)x is odd and n is even.. total integers = x-n +1.. even will be equal to odd.. even= odd={(x-n)+1}/2 ..

4) both x and n are odd total integers will be (x-n)+1... odd will be 1 more than even.. odd= (x-n)/2+1 and even=(x-n)/2..

Your query on 1 to 19 will fall under 3) and 4) above.. hope this helps..
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Re: If a equals the sum of the even integers from 2 to 20, inclusive, and [#permalink]

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29 Aug 2016, 00:33

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faifai0714 wrote:

If a equals the sum of the even integers from 2 to 20, inclusive, and b equals the sum of the odd integers from 1 to 19, inclusive, what is the value of a - b ?

A. 1 B. 10 C. 19 D. 20 E. 21

Solution :

a = Sum of all even integers between 2 to 20 Theory : Sum of n even integers = n(n+1) Therefore a = n^2+n

b = sum of all odd integers between 1 to 19 Theory : Sum of n odd integers = n^2

Therefore a-b = n^2+n-n^2 = n

Here n = no of even integers between 2 to 20 = no of odd integers between 1 to 19 = 10

Re: If a equals the sum of the even integers from 2 to 20, inclusive, and [#permalink]

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29 Aug 2016, 01:26

faifai0714 wrote:

If a equals the sum of the even integers from 2 to 20, inclusive, and b equals the sum of the odd integers from 1 to 19, inclusive, what is the value of a - b ?

A. 1 B. 10 C. 19 D. 20 E. 21

Option B sum of even integers = 10*22/2= 110 sum of odd integers = 10*20/2 =100 a - b= 110-100 =10
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Re: If a equals the sum of the even integers from 2 to 20, inclusive, and [#permalink]

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02 Sep 2017, 00:21

Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

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Re: If a equals the sum of the even integers from 2 to 20, inclusive, and [#permalink]

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02 Sep 2017, 05:14

We can list numbers as 2 4 6 .....20 and odd numbers 1 3 5 ....19 There are a total of 10 even 10 odd numbers so if we subtract each corresponding odd number from even numbers we will get 1 so total will be 10
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