Question

The mean of 10 numbers is 12.5; the mean of the first six is 15 and the last five is 10. The sixth number is

• A. 15
• B. 12
• C. 18
• D. none of these

Answer 1

The correct option is A 15

Let the mean of the last four be $A_2$.
Then by the formula for combined mean,
$12.5=\frac{6\times 15+4\times A_2}{6+4};\text{or 125=90+4}{A}_2;$
$\therefore A_2=\frac{35}{4}$
Let the sixth number = x; then taking the sixth number as a collection, the combined mean of this collection and the collection of the last five is 10, by question.
$\therefore$ By definition of combined mean
$10=\frac{1\times x+4\times \frac{35}{4}}{1+4};50=x+35;\therefore x=15$
$\therefore$ sixth number = 15