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If the Average of 10 consecutive integers is 19.5 then the 10th term i

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stonecold
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If the Average of 10 consecutive integers is 19.5 then the 10th term i [#permalink] New post   06 Aug 2016, 21:54
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If the Average of 10 consecutive integers is 19.5 then the 10th integer is :-

A) 15
B) 20
C) 23
D) 24
E) 25
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khamdy71
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Re: If the Average of 10 consecutive integers is 19.5 then the 10th term i [#permalink] New post   06 Aug 2016, 22:03
khamdy71 wrote:
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Sent from my SM-N920R4 using GMAT Club Forum mobile app

The average falls between the 5th and 6th integers, so integer 5 = 19, integer 6 = 20. Counting up to the tenth integer we get 24.

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keats
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Re: If the Average of 10 consecutive integers is 19.5 then the 10th term i [#permalink] New post   14 Aug 2016, 14:07
Can anyone help solve this question. I did it by back solving i.e. by picking the options and luckily the second option worked for me. Any other way to deal with this question?
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stonecold
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Re: If the Average of 10 consecutive integers is 19.5 then the 10th term i [#permalink] New post   14 Aug 2016, 14:13
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Hi Keats
See here is what i would do =>
The mean is 19.5
so as we know that for an AP series the mean = median => 6th term = 20
Now 7 term = 21 and so the tenth term = 24

Alternatively we can assume => Let the term be N,N+1 and so on solve for N and get the tenth integer.

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Stone Cold
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Re: If the Average of 10 consecutive integers is 19.5 then the 10th term i [#permalink] New post   14 Aug 2016, 14:21
stonecold wrote:
Hi Keats
See here is what i would do =>
The mean is 19.5
so as we know that for an AP series the mean = median => 6th term = 20
Now 7 term = 21 and so the tenth term = 24

Alternatively we can assume => Let the term be N,N+1 and so on solve for N and get the tenth integer.

Regards
Stone Cold


Yes, this makes sense stonecold. Since this is the case of AP, mean = median = (fifth + sixth)/2. So, the fifth and sixth term will be 19 and 20 respectively confirming that the tenth term will be 24!
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If the Average of 10 consecutive integers is 19.5 then the 10th term i [#permalink] New post   28 Feb 2018, 21:21
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stonecold wrote:
If the Average of 10 consecutive integers is 19.5 then the 10th integer is :-

A) 15
B) 20
C) 23
D) 24
E) 25

I usually use more formal solving methods. This time I wrote

19.5
then
19 (19.5) 20
then

15,16,17,18,19 (19.5) 20, 21,22,23,24

Not even half a minute. Okay, yes, you have to know that mean = median in consecutive integers, and that there will be five integers on each side of the mean, but ... maybe scribbling has its merits. :)
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If the Average of 10 consecutive integers is 19.5 then the 10th term i [#permalink]
28 Feb 2018, 21:21
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