A set of statements is given. A) P is a perfect square, B) P is greater than…
2018
A set of statements is given.
A) P is a perfect square, B) P is greater than 2000.
Which of the given set of statements should be used to decide the solution to problem: Is P a prime number if P>1?
- A.
Both A and B together
- B.
Only B
- C.
Only A
- D.
Not possible to decide even with both A and B
Attempted by 4 students.
Show answer & explanation
Correct answer: C
To determine if P is a prime number given P > 1, let's analyze the statements provided.
Analysis of the Mathematical Definitions
Definition of a Prime Number: A prime number is a natural number greater than 1 that has no positive divisors other than 1 and itself.
Definition of a Perfect Square: A perfect square is a number that is the product of an integer multiplied by itself (e.g., 1, 4, 9, 16, 25...).
If a number is a perfect square and greater than 1, it must have at least three divisors: 1, the square root of the number, and the number itself. Therefore, any perfect square greater than 1 is a composite number, not a prime number.
Evaluating the Statements
Statement A: "P is a perfect square."
If P is a perfect square and P > 1 (as specified in the question), then P must be a composite number. We can definitively say that P is not a prime number. Therefore, statement A is sufficient to decide the answer (the answer is "No, it is not prime").
Statement B: "P is greater than 2000."
Knowing only that a number is greater than 2000 does not tell us if it is prime. Some numbers greater than 2000 are prime (e.g., 2003), and some are composite (e.g., 2004). This statement is insufficient on its own.