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# What is the average of the first 19 positive even integers?

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Intern
Joined: 16 Mar 2017
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What is the average of the first 19 positive even integers? [#permalink]

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20 Sep 2017, 00:35
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What is the average of the first 19 positive even integers?

A. 12
B. 14
C. 16
D. 18
E. 20
[Reveal] Spoiler: OA

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Veritas Prep GMAT Instructor
Joined: 16 Oct 2010
Posts: 7677

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Location: Pune, India
Re: What is the average of the first 19 positive even integers? [#permalink]

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20 Sep 2017, 03:11
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Note that the first positive even integer is 2 i.e. 2*1.
The second is 4 i.e. 2*2
The third is 6 i.e. 2*3
So there is a natural counting available with positive even integers.
The 19th will be 2*19 = 38

This forms an Arithmetic Progression. The average will be (2 + 38)/2 = 20

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Senior Manager
Joined: 25 Nov 2015
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Location: India
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What is the average of the first 19 positive even integers? [#permalink]

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20 Sep 2017, 04:56
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petrified17 wrote:
What is the average of the first 19 positive even integers?

A. 12
B. 14
C. 16
D. 18
E. 20

If u can remember this formula, it is very quick. I found it on Gmatclub.
Sum of n consecutive even integers = n(n+1)
Sum of 19 positive even integers = 19 x 20
Average = $$\frac{19*20}{19}$$= 20

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Last edited by souvonik2k on 26 Sep 2017, 10:17, edited 1 time in total.

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Re: What is the average of the first 19 positive even integers? [#permalink]

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25 Sep 2017, 18:07
petrified17 wrote:
What is the average of the first 19 positive even integers?

A. 12
B. 14
C. 16
D. 18
E. 20

The first positive even integer is 2 and the nineteenth positive even integer is 38; thus, the average is (2 + 38)/2 = 20.

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Re: What is the average of the first 19 positive even integers?   [#permalink] 25 Sep 2017, 18:07
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