Question:
Is x a perfect square?
I) x is a positive integer.
II) x is a product of two equal prime numbers.
Is x a perfect square?
I) x is a positive integer.
II) x is a product of two equal prime numbers.
I) x is a positive integer.
II) x is a product of two equal prime numbers.
Show Hint
Any number multiplied by itself results in a perfect square.
Updated On: Jun 26, 2026
- Statement I alone is sufficient
- Statement II alone is sufficient
- Statements I and II together are sufficient
- Statements I and II together are not sufficient
Show Solution
Verified By Collegedunia
The Correct Option is B
Solution and Explanation
Step 1: Concept
A perfect square is an integer that is the square of an integer (e.g., $n^2$).
Step 2: Analysis of Statement I
'x' is a positive integer (e.g., 1, 2, 3, 4...). Some are perfect squares (1, 4), and some are not (2, 3). Not sufficient.
Step 3: Analysis of Statement II
'x' is the product of two equal prime numbers. Let the prime number be 'p'. Then $x = p \times p = p^2$. By definition, $p^2$ is a perfect square. Statement II alone is sufficient.
Step 4: Conclusion
Since Statement II alone is sufficient, the correct answer is (2). Final Answer: (2)
A perfect square is an integer that is the square of an integer (e.g., $n^2$).
Step 2: Analysis of Statement I
'x' is a positive integer (e.g., 1, 2, 3, 4...). Some are perfect squares (1, 4), and some are not (2, 3). Not sufficient.
Step 3: Analysis of Statement II
'x' is the product of two equal prime numbers. Let the prime number be 'p'. Then $x = p \times p = p^2$. By definition, $p^2$ is a perfect square. Statement II alone is sufficient.
Step 4: Conclusion
Since Statement II alone is sufficient, the correct answer is (2). Final Answer: (2)
Was this answer helpful?
0
0
Top APICET Analytical Ability Questions
- In which year was Rahul born?
I) Rahul is 25 years younger to his mother.
II) Rahul's brother, who was born in 1964, is 35 years younger to his mother. - Who among P, Q, T, V and M is exactly in the middle when they are arranged in ascending order of their heights?
I) V is taller than Q but shorter than M.
II) T is taller than Q and M but shorter than P. - The last Sunday of March 2006 fell on which date?
I) The first Sunday of that month fell on 5th.
II) The last day of month was not Saturday. - Which code word stands for ‘good’ in the coded sentence ‘sin co bye’ which means ‘He is good’?
I) In the same code language, ‘co mot det’ means ‘They are good’.
II) In the same code language, ‘sin mic bye’ means ‘He is honest’. - What is the buying cost of the shirt? Statements:
I) The shirt was sold for Rs.800 at a 20% profit.
II) The difference between the selling price and the cost price is Rs.160.
View More Questions
Top APICET Data Sufficiency Questions
- In which year was Rahul born?
I) Rahul is 25 years younger to his mother.
II) Rahul's brother, who was born in 1964, is 35 years younger to his mother. - Who among P, Q, T, V and M is exactly in the middle when they are arranged in ascending order of their heights?
I) V is taller than Q but shorter than M.
II) T is taller than Q and M but shorter than P. - The last Sunday of March 2006 fell on which date?
I) The first Sunday of that month fell on 5th.
II) The last day of month was not Saturday. - Which code word stands for ‘good’ in the coded sentence ‘sin co bye’ which means ‘He is good’?
I) In the same code language, ‘co mot det’ means ‘They are good’.
II) In the same code language, ‘sin mic bye’ means ‘He is honest’. - What is the buying cost of the shirt? Statements:
I) The shirt was sold for Rs.800 at a 20% profit.
II) The difference between the selling price and the cost price is Rs.160.
View More Questions