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# The average (arithmetic mean) of 9 scores is N. If a 10th score is the

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The average (arithmetic mean) of 9 scores is N. If a 10th score is the  [#permalink]

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Updated on: 30 Oct 2018, 01:01
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Difficulty:

15% (low)

Question Stats:

90% (01:07) correct 10% (01:06) wrong based on 38 sessions

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The average (arithmetic mean) of 9 scores is N. If a 10th score is then included with the original 9, the average of the 10 scores is T. Which of the following expressions represents the value of the 10th score?

(A) $$10(T - N)$$

(B) $$10T - 9N$$

(C) $$\frac{10T - 9N}{10}$$

(D) $$\frac{10T - 9N}{9}$$

(E) $$\frac{10T - 9N}{2}$$

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Originally posted by pushpitkc on 30 Oct 2018, 00:56.
Last edited by Bunuel on 30 Oct 2018, 01:01, edited 1 time in total.
Edited the question.
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The average (arithmetic mean) of 9 scores is N. If a 10th score is the  [#permalink]

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Updated on: 30 Oct 2018, 01:17
The average of the nine numbers is given by $$\frac{a1+a2+a3+...+a9}{9}=N$$.

Therefore, $$a1+a2+a3...+a9= 9N$$. (Let this be equation 1)

Now the average of the nine numbers and an added 10th number is given=T.
9
Therefore $$\frac{a1+a2+a3+...+a9+a10}{10}=T$$ (Let this be equation 2)

From equation 1, we can substitute a1+a2+...a9 with 9N in equation 2; giving us:

$$\frac{9N+a10}{10}=T.$$

Therefore, $$a10=10T-9N$$ (Choice B)

Originally posted by manavivarma on 30 Oct 2018, 01:13.
Last edited by manavivarma on 30 Oct 2018, 01:17, edited 1 time in total.
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Re: The average (arithmetic mean) of 9 scores is N. If a 10th score is the  [#permalink]

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30 Oct 2018, 01:16
Sum initially=9*N
Sum finally=9N+x where x is the 10th term
Given,
(9N+x)/10=T
So, x=10T-9N
B should be the correct choice

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Re: The average (arithmetic mean) of 9 scores is N. If a 10th score is the   [#permalink] 30 Oct 2018, 01:16
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