Positive integer P lies between 1 and 30. What is the value of P?(1) P...
Steps 1 & 2: Understand Question and Draw Inferences
Given that P is a positive integer and that 1 < P < 30.
We need to find the value of P
Step 3: Analyze Statement 1
Given that P has at least two prime factors.
- P is a composite number with two or more prime factors.
However, there are more than one composite number between 1 and 30. The possible values of P are:
Clearly, Statement (1) doesn’t lead us to a unique value of P.
Not Sufficient.
Step 4: Analyze Statement 2
Statement 2 says that the cube of P is less than 300.
Let us list out the cubes of natural numbers.
There are 5 natural numbers between 1 and 30 whose cubes are less than 300.
Statement 2 alone is not sufficient to arrive at a unique answer.
Step 5: Analyze Both Statements Together (if needed)
From Statement 1,
Possible values of P: 6, 10, 14, 15, 21, 22, 26
From Statement 2,
Possible values of P: 2, 3, 4, 5, 6
By combining the two statements, we get:
P = 6
Therefore statement 1 and statement 2 combined are sufficient to arrive at a unique answer.
Correct Answer: C