$20$ Points$)$ Consider a relation R $($A$,$ B$,$ C$).$ Assume that the only index on relation R is

an unclustered B$+-$tree on attribute A$.$ The B$+-$tree has height $3$ and are all in memory.

B$+-$tree data entries are also in memory. R has $500,000$ tuples in $2,000$ pages. The

values of attribute A are uniformly distributed from $1$ to $50.$ Now consider the following

query:

SELECT A$,$ B

FROM R

WHERE A $>$ val

Compute the minimum value of val such that the most efficient way of executing the

above query is to use the B$+-$tree index. Assume that the cost metric is the number of

page I$/$Os$.$