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What is the sum of the even integers from 100 to 300 inclusive?

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Bunuel
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What is the sum of the even integers from 100 to 300 inclusive? [#permalink] New post   07 Oct 2020, 00:45
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What is the sum of the even integers from 100 to 300 inclusive?

A. 20,196

B. 20,198

C. 20,200

D. 20,202

E. 20,204
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C
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What is the sum of the even integers from 100 to 300 inclusive? [#permalink] New post   Updated on: 23 Oct 2020, 09:18
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number of even integers = ((300-100)/2) + 1 =100 +1 = 101
formula of sum =n/2(2*a+(n-1)d)
here a = 1st term and d =distance between two even integers=2
=101/2*(2*100+(101-1)*2)
=101/2(200+200)
=101*200
=20200

Originally posted by tanu11 on 07 Oct 2020, 00:55.
Last edited by tanu11 on 23 Oct 2020, 09:18, edited 2 times in total.
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Re: What is the sum of the even integers from 100 to 300 inclusive? [#permalink] New post   07 Oct 2020, 01:55
sum of even from 1 to 300 ; 300*302 /4 ; 22650
sum of even from 1 to 98 ; 98*100/4 ; 2450
22650-2450 ; 20200
option C

Bunuel wrote:
What is the sum of the even integers from 100 to 300 inclusive?

A. 20,196

B. 20,198

C. 20,200

D. 20,202

E. 20,204
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What is the sum of the even integers from 100 to 300 inclusive? [#permalink] New post   07 Oct 2020, 02:31
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First even number: 100

Last even number: 300

300 = 100 + (n - 1)2 [every consecutive even number will have common difference of '2']

=> 202 = 2n

=> n = 101

Another way: Total numbers: \(\frac{(300 - 100)}{ 2 }\)+ 1 = 101[dividing by '2' as we are considering only even numbers. And there are even + odd numbers from 100 to 300]

Sum: \(\frac{n}{2}\) * [First term + Last term]

=> Sum = \(\frac{101 }{ 2}\) * [100 + 300]

=> Sum = \(\frac{101 }{ 2}\) * [400]

=> Sum = 101 * 200

=> Sum = 20,200

Answer C
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Re: What is the sum of the even integers from 100 to 300 inclusive? [#permalink] New post   07 Oct 2020, 10:34
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No Need to Solve this question, as it is a 10 sec question with logic[ after seeing the options].

Now to find the sum of even numbers between 100 & 300-->
This would be your series: 100, 102, 104, 108, 110,......296, 298, 300. So if you sum the units digit of every even number in this range, you can easily get to know that only option C satisfies this.

Eg: 102, 104, 106, 108--> corresponding sum of units digits is 20 i.e. ending with 0 and since the same units digits will be repeated across the series, your sum of the entire series should be something ending in zero, which is only a case in option C.

Hence C, IMO.
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What is the sum of the even integers from 100 to 300 inclusive? [#permalink] New post   20 Oct 2020, 07:08
Answer C

Mean = Median = 200

= 200 / 2 = 100

= 100 + 1 = 101

= 101 * 200

= 202,00
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Re: What is the sum of the even integers from 100 to 300 inclusive? [#permalink] New post   20 Oct 2020, 07:19
Expert Reply
Given

    • Set of even integers from 100 to 300, inclusive.

To Find

    • The sum of all of them.



Approach and Working Out


    • Let us visualize it.
      o Least = 100, highest = 300 so average 200
      o 2nd least = 102 and second highest = 298, again the average is 200.
    • Number of terms in the series = (300 – 100)/2 + 1 = 101
    • Sum = 101 * 200 = 20200

Correct Answer: Option C
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Re: What is the sum of the even integers from 100 to 300 inclusive? [#permalink]
20 Oct 2020, 07:19
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