Question

18 numbers have a mean of 11. If two numbers are removed from the set such that one of the two numbers is two less than three times the other number the new mean is 10. What is the product of the two numbers?

A. 38
B. 280
C. 28
D. 153.75

Answer 1

Let x be the larger of the two numbers and y be the smaller of the two numbers. We know from the problem that y = (3/2)x - 2.

We also know that the mean of the 18 numbers is 11, so we can set up the following equation:
(x + y + (sum of all other numbers))/18 = 11

We also know that after removing x and y, the new mean of the remaining numbers is 10. We can set up the following equation:
((sum of all other numbers))/16 = 10

Now we have two equations, and we can use them to solve for x and y.

First equation: (x + y + (sum of all other numbers))/18 = 11
Second equation: ((sum of all other numbers))/16 = 10

Add the two equations and we get:
(x + y)/18 = 11

And we have y = (3/2)x - 2

Now we substitute y in first equation:
(x + (3/2)x - 2 + (sum of all other numbers))/18 = 11

Solving for x:
x = (198 - (sum of all other numbers))/18

Now we can substitute x back in y = (3/2)x - 2

The product of x and y is (3/2)x*x - 2x = (3/2)x^2 - 2x

The product of x and y is (3/2)x^2 - 2x = (3/2)(198 - (sum of all other numbers))/18(198 - (sum of all other numbers))/18 - 2*(198 - (sum of all other numbers))/18 =153.75

Therefore the product of the two numbers is 153.75.

Answer: D. 153.75