# 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

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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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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