Hi again, there will be another couple of postings and thanks in advance for sharing your approaches on these questions.

The question in this instances asks: If P is a positive integer, what is P?

1) p/4 is a prime number

2) p is divisible by 3

I could easily rule out answers ADB, but I wasn't sure (having exhausted the prime numbers until 23) when checking 1 and 2 whether I had really eliminated any possibility of there being more than one possible solution. What if there was a prime number resulting from p/4 much higher than 23 and also divisible by 3. So my gut feeling was to go for E over C - bad instinct

So my question is, in this context, it is reasonable to assume that you have eliminated any other values by approaching as I did?

Thanks

Orla

## DS integer properties: all possibilities eliminated?

##### This topic has expert replies

st(1) p=(2^2)*a where a is prime number. Since p>0 and a can be any prime number, this is not suffOrla M wrote:Hi again, there will be another couple of postings and thanks in advance for sharing your approaches on these questions.

The question in this instances asks: If P is a positive integer, what is P?

1) p/4 is a prime number

2) p is divisible by 3

st(2) p/3 implies p is by 3, obviously not suff., as any number >0 could be divisble by 3

combining st(1&2): p=(2^2)*a and a is prime number which must be divisble by 3 for the whole expression to be divisble by 3, i.e. for p/3=integer. Hence suff., as a can be only 3

answer C and p=4*3=12

Success doesn't come overnight!

### GMAT/MBA Expert

- [email protected]
- GMAT Instructor
**Posts:**15372**Joined:**08 Dec 2008**Location:**Vancouver, BC**Thanked**: 5254 times**Followed by:**1266 members**GMAT Score:**770

Target question: What is p?Orla M wrote:If P is a positive integer, what is P?

1) p/4 is a prime number

2) p is divisible by 3

Statement 1: p/4 is a prime number

There are several values of p that meet this condition. Here are two:

Case a: p = 8, (in which case p/4 = 2)

Case b: p = 12, (in which case p/4 = 3)

Since we cannot answer the target question with certainty, statement 1 is NOT SUFFICIENT

Statement 2: p is divisible by 3

There are several values of p that meet this condition. Here are two:

Case a: p = 3

Case b: p = 6

Since we cannot answer the target question with certainty, statement 2 is NOT SUFFICIENT

Statements 1 and 2 combined:

From statement 2, we know that p = 3k (for some integer k)

From statement 1, we know that p/4 is a prime number, which means 3k/4 is a prime number.

This means that 3k/4 is also an integer.

Since 3 is not divisible by 4, we can see that k must be divisible by 4. In other words k/4 is an integer.

So, we know that (3)(k/4) is an integer (which is also prime)

For (3)(k/4) to be prime, k/4 must equal 1, which means k must equal 4.

Since p = 3k (from statement 2), we can now be certain that p = 3(4) = 12

Since we can now answer the target question with certainty, the combined statements are SUFFICIENT

Answer = C

Cheers,

Brent