Let x be the first even number. Then adding 2 consecutively gives us the subsequent even numbers. That is
\(x,x+2,x+4,x+6\)
From the question, the mean of these four numbers is 15. That is;
\(\frac{\sum x}{n} =15\)
\(\Rightarrow \frac{x+(x+2)+(x+4)+(x+6)}{4} =15\)
\(\Rightarrow \frac{x+x+2+x+4+x+6}{4} =15\)
\(\Rightarrow \frac{x+x+x+x+2+4+6}{4} =15\)
\(\Rightarrow \frac{4x+12}{4} =15\)
Multiply both sides by 4 to obtain,
\(\Rightarrow 4\times \frac{4x+12}{4} =4 \times15\)
\(\Rightarrow 4x+12 =60\)
\(\Rightarrow 4x =60-12\)
\(\Rightarrow 4x =48\)
Divide both sides by 4 to obtain,
\(x =12\)
Hence the greatest of the numbers is \(12+6=18\)
and the least of the numbers is \(12\).
