MBApyq

Nadeem's Age Data Sufficiency

XAT 2022 · Quantitative Ability & Data Interpretation · Medium · Data Sufficiency

All XAT 2022 questionsMore Data Sufficiency questionsAll XAT QADI

Nadeem's age is a two-digit number X, squaring which yields a three-digit number, whose last digit is Y. Consider the statements below: Statement I: Y is a prime number Statement II: Y is one-third of X

To determine Nadeem's age uniquely:

  1. A.

    either of I and II, by itself, is sufficient.

  2. B.

    only II is sufficient, but I is not.

  3. C.

    only I is sufficient, but II is not.

  4. D.

    it is necessary and sufficient to take I and II together.

  5. E.

    even taking I and II together is not sufficient.

Answer

D

Explanation

For a square to have prime unit digit Y, YY must be 5 (since squares end in 0, 1, 4, 5, 6, 9). Thus Y=5Y = 5. From Statement II: Y=X/3  ⟹  5=X/3  ⟹  X=15Y = X / 3 \implies 5 = X / 3 \implies X = 15. Both statements together uniquely give X=15X = 15.

Related Data Sufficiency questions

Practise this under exam conditions

Sign in to solve it with a live timer, the on-screen CAT calculator, and streak and accuracy tracking across every question you attempt.

Solve in the workspace