Is the positive integer P a prime number? (1) 67 > P > 61 (2) is even.

with all the respect i have little doubt in my mind regarding your 2nd option. 2nd option says that P is even. Now as we know that 2 is the only prime number that is even , thus it provides us a clear evidence that the integer P is not a prime number as 2 is not localized between 61 and 67. So my point is that statement 2nd also gives us decisive indication that P is not a prime number. Please elaborate it a bit.

The second statement is not sufficient. It works sometimes and it fails other times. For example if P is equal to 2, then it is in fact a prime number, otherwise its not. There is no indication in the statement of the problem that P is even or odd.

Sorry, but the question CLEARLY STATES that P is between 61 and 67… so how come 2 CAN be between 61 and 67? Unless I come from a different universe, P will ALWAYS be less than 61 and 67, therefore, making the 2nd. clause ALSO correct…

Maybe I'm misreading something, but I read it like a million times and can't find the error in my line of thought. Regads

Sorry, but the question CLEARLY STATES that P is between 61 and 67

Statement (1) tells so.

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so how come 2 CAN be between 61 and 67?

2 is NOT between 61 an 67. However it can be a value of P if we consider Statement (2) by itself. When we consider Statement (2) by itself we disregard information in Statement (1) as if it does NOT exist.

I don't understand the explanation for this question. The premise A said that 61 < P < 67. So, P can be anything among 62, 63, 64, 65, 66. We have to determine whether P is a prime number. The explanation given seems to be the mistakes that mostly we do where we see very much beyond the given premise. The premise do not give information that it is divisible by 2 or 3. So in this case, A does not seems to be the right answer.

The premise A said that 61 < P < 67. So, P can be anything among 62, 63, 64, 65, 66. We have to determine whether P is a prime number.

This is correct. Statement (1) limits P to only five possible values: 62, 63, 64, 65, and 66. P can not be any other integer except these five choices. But no matter which one of the five it is, P will always be a composite number (the term for a number that is not prime).

Definition: A prime number is a positive integer greater than 1, which is divisible by itself and 1 only. If a number is divisible by any other positive integer except itself and 1, such number is a composite number (not prime).

62 - is an even number, it is divisible by 2. 63 - is divisible by 3, 63 = 21 × 3 64 - is an even number, it is divisible by 2. 65 - is divisible by 5, 65 = 13 × 5 66 - is an even number, it is divisible by 2.

So we have the definite answer to the main question – "Is the positive integer P a prime number?" – "No, it is not."

Thus, statement (1) by itself is sufficient.

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The premise do not give information that it is divisible by 2 or 3.

Statement (1) doesn't tell us this directly, but it limits the value of P to the five choices. P must be one of these choices. Depending on which choice it is, P will be divisible by 2, 3 or 5.

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