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DS integer properties: all possibilities eliminated?

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by Orla M » Sat Feb 16, 2013 5:52 am
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
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by pemdas » Sat Feb 16, 2013 7:52 am
Orla 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(1) p=(2^2)*a where a is prime number. Since p>0 and a can be any prime number, this is not suff
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
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by Brent@GMATPrepNow » Sat Feb 16, 2013 9:25 am
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
Target question: What is p?

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
Brent Hanneson - Creator of GMATPrepNow.com
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