Question

Five numbers are represented by $x,2x-3,2x+1,3x-4$, and $3x+1$. If the arithmetic mean of the five numbers is $10$, find the mode of numbers.

• A. $10$
• B. $11$
• C. $12$
• D. There is not enough infomation to determine the value of the mode.

Answer 1

The correct option is B $11$

Arithemetic mean $=$ $\frac{x_1+x_2+x_3+x_4....}{n}$

$\Rightarrow 10=\frac{x+2x-3+2x+1+3x-4+3x+1}{5}$

$\Rightarrow 10=\frac{11x-5}{5}$

$\Rightarrow 11x=50+5$

$\Rightarrow x=\frac{55}{11}=5$

$\Rightarrow x=5$

$\Rightarrow 2x-3=2\times 5-3=10-3=7$

$\Rightarrow 2x+1=2\times 5+1=10+1=11$

$\Rightarrow 3x-4=3\times 5-4=15-4=11$

$\Rightarrow 3x+1=3\times 5+1=15+1=16$

Then the five numbers are $7,11,11,16$.

Mode of numbers are $11$.