What is Glory's age? I. Glory, Vijay and Katie are all of the same age. II.…

2025

What is Glory's age?

I. Glory, Vijay and Katie are all of the same age.

II. Total age of Vijay, Katie and Arica is 32, and Arica is as old as Vijay and Katie together.

  1. A.

    If the data in Statement I alone are sufficient to answer the question

  2. B.

    If the data in Statement II alone are sufficient to answer the question

  3. C.

    If the data either in Statement I or in Statement II alone are sufficient to answer the question

  4. D.

    If the data in both statements together are needed to answer the question

Show answer & explanation

Correct answer: D

Concept: In a data-sufficiency question, a statement (or a combination of statements) is "sufficient" only when it pins the asked quantity to one unique, determinate number. A statement that merely states a relationship among several unknowns -- with no numeric anchor -- cannot by itself fix any one of those unknowns; and a statement that never mentions the target quantity at all cannot determine it either, no matter what other numbers it supplies.

Application:

  1. Statement I alone: it gives Glory = Vijay = Katie -- a relation among three unknowns, but no actual number. It cannot fix Glory's age by itself.

  2. Statement II alone: it gives Vijay + Katie + Arica = 32 and Arica = Vijay + Katie, but never mentions Glory. With no link to Glory, it cannot fix Glory's age either.

  3. Combine both: substitute Arica = Vijay + Katie into Vijay + Katie + Arica = 32, giving Arica + Arica = 32, so Arica = 16 and Vijay + Katie = 16.

  4. From Statement I, Vijay = Katie, so 2 x Vijay = 16, giving Vijay = Katie = 8.

  5. From Statement I again, Glory = Vijay = Katie = 8 -- a single determinate value, obtained only by using both statements together.

Cross-check: with Vijay = Katie = 8, Arica = Vijay + Katie = 16, so Vijay + Katie + Arica = 8 + 8 + 16 = 32, matching Statement II; and Glory = Vijay = Katie = 8 matches Statement I. Since neither statement alone determines Glory's age but both together do, the data in both statements together are needed.

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