The formulas of A and B for the following reaction sequence are

Step 1: Cyanohydrin Addition — Reaction of glucose ($C_6H_{12}O_6$) with $\ce{HCN}$ adds one carbon atom, forming a cyanohydrin with the formula $C_7H_{13}O_6N$.

Step 2: Hydrolysis — Subsequent hydrolysis of the nitrile group ($\ce{-CN}$) to a carboxylic acid ($\ce{-COOH}$) results in a hydroxy acid 'A' with the formula $C_7H_{14}O_8$.

Step 3: Reduction — Treatment with $\ce{HI}$ and red phosphorus reduces the hydroxy groups to a straight-chain hydrocarbon. The resulting product is n-heptane or a related reduced structure. Matching 'A' as $C_7H_{14}O_8$ identified the correct option.

Key Point: This Kiliani-Fischer-like sequence confirms the presence of an aldehyde and a straight six-carbon chain in glucose.