Compound (A) $C_{6} H_{12} O_{2}$ is optically active, Gives positive tollens reagents test, which of on oxidation with $K M n O_{4}$ gives (B) $C_{6} H_{10} O_{3}$ . Compound B upon strong heating ( undergo decarboxylation) produces symmetrical ketone (C) $C_{5} H_{10} O$ . Compound (C) will not undergo addition reaction with $N a H S O_{3}$ . Compound (A) reacts with excess of $E t M g B r$ followed by quenching gives product (D) $C_{8} H_{18} O_{2}$ .
If x is the number of stereoisomers Possible for the compound (D) and y is the total number of stereoisomers possible for the compound (A) find the value of $x + y$

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answer is 8.

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$\begin{array}{l} x = 4 \\ y = 4 \\ A n s = 8 \end{array}$

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