# Mean of n numbers is p .... Multiple Choice Question

#### Dr.Peterson

##### Elite Member
View attachment 28867Answer is A but I am unsure how to tackle this question.

I wrote the mathematical expressions for each sentence but I am unsure where to go from there.
Please show those expressions, so we can know where you are! Then also tell us what ideas you have for the next step.

#### Jomo

##### Elite Member
Let the n numbers be a1, a2, a3, ...., an.
Then the average would be (a1+a2+...+an)/n = p

The mean of a1 and a2 is q. That is (a1+a2)/2 = q. So how much is a1+a2

The remaining numbers have a mean of (a3+a4+...+an)/(n-2) = 10. How much is a3+a4+...+an?

Continue from here. 1st find out what a1+a2+...an equals in terms of n, p and q.

#### HallsofIvy

##### Elite Member
I hope you understand that the "mean" of n numbers is the sum of those number divided by n so that the sum of the numbers is n times that mean.

If "the mean of n numbers is p" then the sum of the n numbers is np. If the mean of two numbers is q then the sum of those two numbers is 2q. If the mean of the remaining n- 2 numbers is 10 then the sum of those remaining numbers is 10(n-2).

Of course, the sum of those two numbers and the remaining n-2 number is the sum of all n numbers: np= 2q+ 10(n- 2).

np= 2q+ 10n- 20

np- 10n= 2q- 20
n(p- 10)= 2q- 20
$$\displaystyle n= \frac{2q- 20}{p- 10}$$

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