4. In a list of five numbers, the first number is 60 and the last number is 300 . The product of the first three numbers is 810000 , the product of the three in the middle is 2430000 and the product of the last three numbers is 8100000 .
Which number is third in the list?
Solution
150

Let the list be $60, x, y, z, 300$.
(i) Since $60 x y=810000$ we find that $x y=13500$.
(ii) Since $x y z=2430000$ and $x y=13500$, we find that $z=180$.
(iii) Since $300 y z=8100000$ and $z=180$, we find that $y=150$.

We may also find $x=\frac{13500}{150}=90$. As $y$ is the middle number in the list the answer to the problem is 150 .