Introducing a woman, Jay said, “She is the daughter of the only child of my grandfather.” How is the woman related to Jay?

Correct — B.
Rule: decode one link at a time: grandfather → his only child → that child's daughter.

The grandfather has one child, so that child is Jay's parent (father or mother).
The woman is a daughter of Jay's parent, and she is not Jay.

So she is Jay's sister → option (b).

Why the others are wrong

• (a)
  Aunt — Aunt sits a generation above Jay, as a sister of Jay's parent. The woman is a daughter of Jay's parent, which puts her in Jay's own generation.
• (c)
  Niece — Niece would make her the daughter of Jay's brother or sister. Her parent is Jay's parent, which puts her in Jay's generation, one above a niece.
• (d)
  Cousin — Cousin needs a parent who is Jay's uncle or aunt. The grandfather has a single child, so there is no uncle or aunt on this side, and her parent is Jay's own.

Blood-relation statements are decoded one link at a time, starting from the person the speaker names last in the chain, here Jay's grandfather.

The phrase 'only child' does the work. A grandfather's children are the speaker's parent, uncles and aunts. With a single child, that child must be the speaker's parent, and whether it is Jay's father or mother does not change the answer.

Key facts

• A grandfather's only child is the speaker's own parent.
• Any daughter of your parent, other than yourself, is your sister.
• Generations: cousin and sister sit level with you, aunt one above, niece one below.

Common traps

• Reading 'daughter of the only child' as a niece, as if the child were Jay's sibling
• Answering Cousin, which needs an uncle or aunt that an only child rules out

No directly related past PYQ was found.