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# What is the sum of the even integers between 200 and 400, inclusive?

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Manager
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What is the sum of the even integers between 200 and 400, inclusive?  [#permalink]

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07 Mar 2017, 17:55
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What is the sum of the even integers between 200 and 400, inclusive?

A 29,700
B 30,000
C 30,300
D 60,000
E 60,300
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Re: What is the sum of the even integers between 200 and 400, inclusive?  [#permalink]

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10 Mar 2017, 09:42
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BPHASDEU wrote:
What is the sum of the even integers between 200 and 400, inclusive?

A 29,700
B 30,000
C 30,300
D 60,000
E 60,300

We can use this formula: sum = average x quantity

Since we have an evenly spaced set of integers, average = (200 + 400)/2 = 300.

Since there are (400-200)/2 + 1 = 101 even integers from 200 to 400 inclusive, the sum is:

(300)(101) = 30,300

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Re: What is the sum of the even integers between 200 and 400, inclusive?  [#permalink]

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07 Mar 2017, 18:20
C. Using the formula for sum of Arithmetic progression.

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Re: What is the sum of the even integers between 200 and 400, inclusive?  [#permalink]

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08 Mar 2017, 01:21
2
first digit = 200, last digit = 400, d =2
therefore 400=200 +(n-1)2 or n =101

sum = n/2 x (first term +last term)
(101/2) x (200+400) =30300

Option C
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Re: What is the sum of the even integers between 200 and 400, inclusive?  [#permalink]

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18 Mar 2017, 09:39
number of even integers !inclusive: 400-200=200/2=100+1=101
(400+200)/2*101=300300
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Re: What is the sum of the even integers between 200 and 400, inclusive?  [#permalink]

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02 Sep 2017, 02:57
1
BPHASDEU wrote:
What is the sum of the even integers between 200 and 400, inclusive?

A 29,700
B 30,000
C 30,300
D 60,000
E 60,300

2+4+6+8 ......+2n = n(n+1)
So sum of even number from 2 to 400 = n(n+1) = 200 (201) = 40,200
Now, we need to subtract the sum of even number from 2 to 198 = n(n+10) = 99(100) = 9,900
40,200 -9,900 = 30,300.

Here are some Formula for finite series you need memorize:

1+2+3...(n(n+1))/2

1+3+5+7....n^2

1^2 + 2^2 + 3^2 + 4^2....(n(n+1)(n+2))/6
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Re: What is the sum of the even integers between 200 and 400, inclusive?  [#permalink]

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28 Aug 2018, 02:08
The mistake I made in this question was to assume that since the number range is mentioned between 200 & 400 inclusive, I considered the sequence from 202 instead of 200. Would appreciate clarity on whether this ideology applies when the question stem states "from" instead of between.
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Re: What is the sum of the even integers between 200 and 400, inclusive?  [#permalink]

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21 Aug 2019, 05:13
BPHASDEU wrote:
What is the sum of the even integers between 200 and 400, inclusive?

A 29,700
B 30,000
C 30,300
D 60,000
E 60,300

sum of even integers 1 to 400 ; 400 * 402/ 4 ; 40200
and sum of even integers from 1 to 199 ; 199 * 200 /4 ; 9900
∆ ; 30300
IMO C
Re: What is the sum of the even integers between 200 and 400, inclusive?   [#permalink] 21 Aug 2019, 05:13
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# What is the sum of the even integers between 200 and 400, inclusive?

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