Consider the following reaction
`underset("Ester(x)")underset()(C_(4)H_(8)O_(2)) underset("(ii)"H_(3)O^(+))overset((i)CH_(3)MgBr("Excess"))to underset("Alcohol(Y)")underset()(C_(4)H_(10)O)` Alcohol (Y) reacts fastest with Lucas reagent. Therefore (X) and (Y) are

Options

A. (a) `CH_(3)overset(O)overset(||)COC_(2)H_(5),(CH_(3))_(3)COH`
B. `Hoverset(O)overset(||)COC_(3)H_(7),(CH_(3))_(2)CHOH`
C. `CH_(3)overset(O)overset(||)COC_(2)H_(5),(CH_(3))_(2)CHOH`
D. `Hoverset(O)overset(||)COC_(3)H_(7),(CH_(3))_(2)COH`

Explanation

To solve the problem, we need to identify the structures of the ester (X) and the alcohol (Y) based on the given reaction and the information about the reactivity of alcohols with Lucas reagent.

### Step-by-Step Solution:

1. **Identify the Reaction Components:**
- We have an ester (C₄H₈O₂) reacting with excess CH₃MgBr (Grignard reagent) and H₃O⁺ to produce an alcohol (C₄H₁₀O).
- The alcohol (Y) reacts fastest with Lucas reagent, indicating it is likely a tertiary alcohol.

2. **Determine the Structure of Alcohol (Y):**
- Since Y is a tertiary alcohol with the formula C₄H₁₀O, it must have a structure that allows for the formation of a stable tertiary carbocation.
- The structure of a tertiary alcohol with four carbon atoms can be represented as:
\[ \text{(CH₃)₃C-OH} \]
- This structure can also be written as:
\[ \text{C(CH₃)₃OH} \]
- Therefore, alcohol (Y) is 2-methylpropan-2-ol (tert-butanol).

3. **Identify the Structure of Ester (X):**
- The ester (X) has the formula C₄H₈O₂. The general structure of an ester can be represented as RCOOR'.
- Since we know that the alcohol formed is a tertiary alcohol, we can deduce that the ester must have a structure that, when reacted with the Grignard reagent, results in the formation of the tertiary alcohol.
- The Grignard reagent (CH₃MgBr) will add to the carbonyl carbon of the ester, replacing the OR' group.
- To produce the tertiary alcohol Y (C₄H₁₀O), the ester must have a structure that includes a two-carbon alkyl group (ethyl) and a methyl group.
- Thus, the ester can be represented as ethyl acetate:
\[ \text{CH₃COOCH₂CH₃} \]
- This corresponds to the formula C₄H₈O₂.

4. **Final Structures:**
- Therefore, we conclude:
- Ester (X) is Ethyl acetate (CH₃COOCH₂CH₃).
- Alcohol (Y) is 2-methylpropan-2-ol (tert-butanol, (CH₃)₃COH).

### Summary:
- **X (Ester)**: Ethyl acetate (CH₃COOCH₂CH₃)
- **Y (Alcohol)**: 2-methylpropan-2-ol (tert-butanol, (CH₃)₃COH)