Types of Numbers

[GMAT-Zenith]

If p is a positive integer, what is the value of p?
1). p/4 is a prime number 2). p is divisible by 3

The given ans is C

[alex.gellatly]

If p is a positive integer, what is the value of p?
1). p/4 is a prime number 2). p is divisible by 3

This question is dealing with prime factorization. In the question stem it asks us to find the value of p.

Statement 1: p/4 is a prime number
This is insufficient because:

both 12/4=3 and 8/4=2. Both 3 and 2 are prime numbers and the value of p is different. Clearly the answer is not A or D.

Statement2: p is divisible by 3.
This is insufficient because:
p could be any factor of 3. For example p could be 3,6,9,12.....

Statements 1 and 2 combined: This is sufficient because if p/4 is prime and p is a factor of 3, then p must be 12. The only factor of 3 which is prime is 3 itself.

Hope this helps. Please ask if you have other questions

[Anurag@Gurome]

If p is a positive integer, what is the value of p?
1). p/4 is a prime number 2). p is divisible by 3

The given ans is C

(1) p/4 is a prime number.
If p = 12, then p/4 = 3, which is a prime number.
If p = 20, then p/4 = 5, which is a prime number again.
So, there is no definite value of p; NOT sufficient.

(2) p is divisible by 3.
p can be any of the values, 3, 6, 9, 12, 15, ...
Again, there is no definite value of p; NOT sufficient.

Combining (1) and (2), the only possible value of p is 12, as p/4 = 3, which is a prime number. Also, p is divisible by 3; SUFFICIENT.

The correct answer is C.

[GMAT-Zenith]

Thanks.. will be putting up a few more questions on Numbers