Xavier Aptitude Test 2022 Paper

Question : 54 of 100

Marks: +1, -0

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:

Either of I and II, by itself, is sufficient.
Only II is sufficient, but I is not.
Only I is sufficient, but II is not.
It is necessary and sufficient to take I and II together.
Even taking I and II together is not sufficient.

Validate

Solution:

The age of Nadeem is a two-digit number. When squared yields a three- digit number whose last digit is

\Y

\Y

is a prime number.
Using statement 1:
When a number is squared :
The last digit of the number can be :

1, 2, 3, 4, 5, 6, 7, 8, 9

When squared the last digit can be :
For a number ending with

1: 1

For a number ending with

2:4

For a number ending with

3: 9

For a number ending with

4: 6

For a number ending with

5: 5

For a number ending with

6: 6

For a number ending with

7: 9

For a number ending with

8: 4

For a number ending with

9: 1

The only possible prime number is

5

Hence the last digit of

\X

5

and

\Y

5

Using statement 2 :

\Y = \X/3

This alone cannot be sufficient to determine the possibilities for

\Y

and

\X

Combining both the statements :
Since

\Y = 5

, then the value of

\X = 15

The age is equal to

15

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