Pointing to a woman, Raj said, "She is the daughter-in-law of the grandmother of my father’s only son." How is the woman related to Raj?

Correct — D.
Rule: collapse the phrase from the inside out.

My father's only son = Raj himself.
Raj's grandmother's daughter-in-law = the wife of her son.
On the paternal side that son is Raj's father, and his wife is Raj's mother → option (d).

Why the others are wrong

• (a)
  Wife — Raj's wife would be the daughter-in-law of Raj's parents. The grandmother's daughter-in-law sits a generation higher, as the wife of Raj's father.
• (b)
  Sister-in-law — A sister-in-law belongs to Raj's own generation. The grandmother's daughter-in-law married her son, so she belongs to the parents' generation.
• (c)
  Cousin — A cousin is the grandmother's grandchild, not her daughter-in-law. Cousins sit in Raj's generation, one below the woman described.

Long relation chains are read from the innermost phrase outward, replacing each piece with a person.

My father's only son is the speaker. Grandmother of that person moves two generations up. Daughter-in-law of her comes one generation down, as the wife of her son.

Net movement: one generation above Raj, and female. Of the four options, Mother is the one at that level.

Key facts

• A woman's daughter-in-law is her son's wife.
• My father's only son is the speaker himself when the speaker is male.
• Raj's paternal grandmother's son is Raj's father, whose wife is Raj's mother.

Common traps

• Stopping at grandmother and answering in her generation
• Reading daughter-in-law as daughter, which would make the woman Raj's aunt

No directly related past PYQ was found.