Question

If the average of $a,b,c$ and $d$ is the average of $b$ and $c$, then which one of the following is necessarily true?

• A. $a+d=b+c$
• B. $a+b=c+d$
• C. $a-d=b-c$
• D. $\frac{a+d}{4}=\frac{b+c}{2}$

Answer 1

The correct option is A $a+d=b+c$

Average of a data set is the $\frac{\text{sum of the values}}{\text{total number of values}}$

Therefore, average of $a,b,c,d$ is $\frac{a+b+c+d}{4}$ ——-(1)

Similarly average of $b,c$ is $\frac{b+c}{2}$ ———(2)

Given that both the averages are equal. Hence by equating (1) and (2) we get

$\frac{a+b+c+d}{4}=\frac{b+c}{2}$

$⟹a+b+c+d=2(b+c)$

$⟹a+d=2b+2c-b-c$

$⟹a+d=b+c$