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

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Current Student
Joined: 12 Aug 2015
Posts: 2609
Schools: Boston U '20 (M)
GRE 1: Q169 V154
If the Average of 10 consecutive integers is 19.5 then the 10th term i  [#permalink]

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06 Aug 2016, 21:54
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25% (medium)

Question Stats:

74% (01:19) correct 26% (01:18) wrong based on 103 sessions

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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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Intern
Joined: 13 May 2014
Posts: 11
Re: If the Average of 10 consecutive integers is 19.5 then the 10th term i  [#permalink]

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06 Aug 2016, 22:03
khamdy71 wrote:
D

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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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Current Student
Joined: 28 Nov 2014
Posts: 843
Concentration: Strategy
Schools: Fisher '19 (M\$)
GPA: 3.71
Re: If the Average of 10 consecutive integers is 19.5 then the 10th term i  [#permalink]

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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?
Current Student
Joined: 12 Aug 2015
Posts: 2609
Schools: Boston U '20 (M)
GRE 1: Q169 V154
Re: If the Average of 10 consecutive integers is 19.5 then the 10th term i  [#permalink]

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14 Aug 2016, 14:13
1
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
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Current Student
Joined: 28 Nov 2014
Posts: 843
Concentration: Strategy
Schools: Fisher '19 (M\$)
GPA: 3.71
Re: If the Average of 10 consecutive integers is 19.5 then the 10th term i  [#permalink]

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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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Joined: 22 May 2016
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If the Average of 10 consecutive integers is 19.5 then the 10th term i  [#permalink]

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28 Feb 2018, 21:21
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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