Question

The arithmetic mean of six numbers is $\mathrm{20.5.}$ If two numbers are added to the progression, then the new arithmetic mean is $17.5$, then which of the following pair(s) of numbers can be correct?

• A. $10$ and $7$
• B. $5$ and $12$
• C. $6$ and $12$
• D. $5$ and $10$

Answer 1

Answer: (A), (B)

The correct options are
A $10$ and $7$
B $5$ and $12$

Sum of all $6$ numbers
$=6\times 20.5=123$
Let the two number added be $x$ and $y$, we get
$\frac{123+x+y}{8}=17.5\Rightarrow 123+x+y=140\therefore x+y=17$
Checking the options.