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# QOTD #2 The average (arithmetic mean) bowling score of n bo

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QOTD #2 The average (arithmetic mean) bowling score of n bo [#permalink]  02 Jul 2016, 07:15
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Question Stats:

91% (00:39) correct 8% (01:28) wrong based on 12 sessions
The average (arithmetic mean) bowling score of n bowlers is 160. The average of these n scores together with a score of 170 is 161. What is the number of bowlers, n?

[Reveal] Spoiler: OA
9

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Re: QOTD #2 The average (arithmetic mean) bowling score of n bo [#permalink]  04 Jul 2016, 05:13
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Re: QOTD #2 The average (arithmetic mean) bowling score of n bo [#permalink]  15 Jul 2016, 02:17
Expert's post
The average formula is $$\frac{S}{N}= Average$$ OR $$S = Average * N$$

Now we do have that your first average is 160, from this follow that $$S = 160N$$

If you add a number I.E n + 1 that is 170 you end up with : $$\frac{S + 170}{n + 1} = 161$$ (the new average)

So S = 160N from this we do have $$\frac{160N + 170}{N +1} = 161(N + 1 )$$

Solving you do have $$N = 9$$

Hope this helps
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Re: QOTD #2 The average (arithmetic mean) bowling score of n bo [#permalink]  20 Mar 2018, 18:02
I'm very confused by the wording on this question. It says, "The average of these n scores together with...". It doesn't say, "The sum of these n scores together with...", but that appears to be how they write the equation. This is why I keep getting this question wrong. The average is 160 so I write the equation as follows:

(160 + 170) / (n + 1) = 161

Which is, of course, wrong. It should be:

(160n + 170) / (n + 1) = 161

Anyone have insight in to how to read this question so it lines up with the correct answer? Thanks!
Founder
Joined: 18 Apr 2015
Posts: 11898
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Kudos [?]: 2961 [0], given: 11149

Re: QOTD #2 The average (arithmetic mean) bowling score of n bo [#permalink]  21 Mar 2018, 15:16
Expert's post
Quote:
The average of these n scores together with a score of 170 is 161

Means: the score of n players is 160 plus a new data (in this case a new score = 170) gives you a new average = 161

Hope this helps.

Regards
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Re: QOTD #2 The average (arithmetic mean) bowling score of n bo   [#permalink] 21 Mar 2018, 15:16
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# QOTD #2 The average (arithmetic mean) bowling score of n bo

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