Concept:
According to IUPAC nomenclature rules, the longest continuous carbon chain containing the principal functional group is selected as the parent chain. The chain is then numbered in such a way that the principal functional group receives the lowest possible locant.
For alcohols, the hydroxyl group \((-OH)\) is the principal functional group and takes priority over alkyl substituents during numbering.
Step 1: Identify the longest carbon chain.
The given structure is
\[
CH_3-CH(CH_3)-CH_2-CH(OH)-CH_3
\]
The longest continuous chain containing the hydroxyl group consists of five carbon atoms.
Therefore, the parent hydrocarbon is
\[
\boxed{\text{Pentane}}
\]
Since the compound contains an alcohol functional group, the suffix will be
\[
\boxed{\text{-ol}}
\]
Step 2: Number the carbon chain.
Numbering must begin from the end nearest to the hydroxyl group.
Numbering from the right:
\[
CH_3-CH(OH)-CH_2-CH(CH_3)-CH_3
\]
gives
\[
OH \text{ at C-2}
\]
and
\[
CH_3 \text{ substituent at C-4}
\]
Numbering from the left would place the hydroxyl group at carbon 4, which violates the lowest locant rule.
Therefore, numbering from the right is correct.
Step 3: Identify substituents.
A methyl group is attached at carbon number 4.
Hence the substituent name is
\[
\boxed{4\text{-methyl}}
\]
Step 4: Write the complete IUPAC name.
Combining the substituent name, parent chain and alcohol suffix:
\[
4\text{-Methyl} + Pentan + 2\text{-ol}
\]
\[
\boxed{\text{4-Methylpentan-2-ol}}
\]
Final Answer
\[
\boxed{\text{4-Methylpentan-2-ol}}
\]
Hence, the correct option is
\[
\boxed{\text{(A)}}
\]