Five numbers are given by expressions x, `2x-3, 2x+1, 3x-4 and 3x+1`. If the average (arithmetic mean) of these number is 10, what is the mode of the numbers?

Options

A. `10`
B. `11`
C. `12`
D. There is not enough information to determine the value of the mode.

Answer

B

Explanation

Difficult: Hard
Category: Problem Solving and Data Analysis/ Statistics and Probability.
Strategic Advice: Try not to overthink a question like this-Instead, use what you know about finding an average and see where that takes you.
Getting to the Answer: The average of a set of values is the sum of the values divided by the number of values. Use this definition along with the average given in the question (10) to solve for x:
Avg`=("Sum of terms")/("Number of terms")`
`10=(x+(2x-3)+(2x+1)+(3x-4)+(3x+1))/(5)`
`10=(11x-5)/(5)`
`50=11x-5`
`55=11x`
`x=5 `
Now, substitute 5 for x in each of the expressions: `5, 2(5)-3, 2(5)+1, 3(3)-4, and 3(5)+1` give the number that occurs most often, which in this case is 11. This means (B) is correct.