XAT 2022 Question Paper | Quantitative Aptitude and Data Interpretation

XAT Previous Year Paper | XAT QADI Questions | Question 9

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Question 9 : 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. even taking I and II together is not sufficient.
  2. either of I and II, by itself, is sufficient.
  3. only I is sufficient, but II is not.
  4. only II is sufficient, but I is not.
  5. it is necessary and sufficient to take I and II together.

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Explanatory Answer

Nadeem's age is a two-digit number X, squaring which yields a three-digit number, whose last digit is Y.
Let us take the statement I:
The possible numbers which satisfying statement(I) is 225(\(15^{2}\)) and 625 (\(25^{2}\))
So we have two possible outcomes. Hence statement (I) alone is not sufficient
Now let us take statement II:
The possible numbers which satisfy statement(II) are
144(\(12^{2}\)) , 225(\(15^{2}\)) , 729 (\(\left.27^{2}\right)\)
So we have three possible outcomes. Hence statement (II) alone is not sufficient.
But by using I & II we can get only one solution which is 15.
Therefore, both statements I & II are required to answer the question.


The answer is 'it is necessary and sufficient to take I and II together.'

Choice E is the correct answer.

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