The computational complexity of sorting type problems using pairwise comparisons has been studied extensively. For example, let $W_k ( n )$ denote the number of pairwise comparisons needed to find the $k$ largests among $n$ distinct real numbers. It is known that $W_1 ( n ) = n - 1$, $W_2 ( n ) = n - 2 + lceil log n ceil$ and, for fixed $k$, $W_k ( n ) = n + ( k - 1 ) lceil log n ceil + O ( 1 )$. In this thesis, we study the computational complexity for selection problems when some more powerful type of queries, namely, the queries ``$xprod:0$' are allowed. We call queries of the type ``$xprod:0$' partiy-like tests. In some problems, using parity-like tests can significantly reduced the number of queries needed to be asked to find an answer. For example, $ heta ( n log n )$ queries are necessary to determine whether $n$ real numbers are distinct if the queries are restricted to pairwise comparisons. On the other hand, one query ``$prod_{i ot= j} (x_i - x_j ) > 0 ?$' is sufficient to solve the problem. In the thesis, we study the problem of selecting the $k$ largests of $n$ distinct real numbers. We show that when queries are restricted to parity-like tests, $n-k+lceil log((n(n-1)...(n-k+2)) ceil$ queries are necessary to solve the problem. In other words, the parity-like tests are not much more powerful than the simple pairwise comparisons in this problem. We also study the problem of finding the maximum of $n$ numbers using small number of queries. The result on selecting the $k$ largests implies $n-1$ parity-like tests are necessary to find the maximum of $n$ numbers. However, we show that for any fixed $varepsilon>0$, there is a decision tree algorithm which finds the maximum of $n$ numbers with error probability $