If p is a positive integer...

[ProGMAT]

Data Sufficiency:
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.

[Brent@GMATPrepNow]

Data Sufficiency:
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.

Target question: What is the value of p?

Given: p is a positive integer

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 (since 8/4 = 2, which is a prime number)
Case b: p = 12 (since 12/4 = 3, which is a prime number)
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 = 6
Case b: p = 9
Since we cannot answer the target question with certainty, statement 2 is NOT SUFFICIENT

Statements 1 and 2 combined
Statement 1 says that p is divisible by 4 (since p/4 results in an integer)
Statement 2 says that p is divisible by 3
So, we know that p must be divisible by 12.
If p is divisible by 12, some possible values of p are: 12, 24, 36, 48, 60, . . . etc.
HOWEVER, since p/4 must be prime, only one of these possible values of p (p = 12) will yield a prime number (3) when divided by 4. Any other value of p, when divided by 4, will yield a multiple of 3 that is not prime.
So, it MUST be the case that p = 12
Since we can answer the target question with certainty, the combined statements are SUFFICIENT

Answer = C

Cheers,

[ProGMAT]

Data Sufficiency:
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.

Target question: What is the value of p?

Given: p is a positive integer

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 (since 8/4 = 2, which is a prime number)
Case b: p = 12 (since 12/4 = 3, which is a prime number)
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 = 6
Case b: p = 9
Since we cannot answer the target question with certainty, statement 2 is NOT SUFFICIENT

Statements 1 and 2 combined
Statement 1 says that p is divisible by 4 (since p/4 results in an integer)
Statement 2 says that p is divisible by 3
So, we know that p must be divisible by 12.
If p is divisible by 12, some possible values of p are: 12, 24, 36, 48, 60, . . . etc.
HOWEVER, since p/4 must be prime, only one of these possible values of p (p = 12) will yield a prime number (3) when divided by 4. Any other value of p, when divided by 4, will yield a multiple of 3 that is not prime.
So, it MUST be the case that p = 12
Since we can answer the target question with certainty, the combined statements are SUFFICIENT

Answer = C

Cheers,

Thanks for the solution Brent, it looks so easy now.

[lunarpower]

Brent's solution is cool.

Ron's solution is much simpler (not necessarily "easier"; just simpler), because Ron is a simple man.

Ron would just make a list for each statement.

(1) p/4 is a prime number.

ok, p is 4 times a prime number.
hmm...
4 x 2 = 8
4 x 3 = 12
4 x 5 = 20
4 x 7 = 28
4 x 11 = 44
etc.
plenty of values. not sufficient.

(2) p is divisible by 3.

ok...
3
6
9
12
etc.
plenty of values. not sufficient.

--

together:
well, looking back at my first list, i see "4" times an ascending list of primes. in other words, i'm never going to see the number "3" again.
looks like it's 12.
sufficient.

[Brent@GMATPrepNow]

Nice approach.
One question though: Who's this Ron person you're referring to? ....

Cheers,
Brent

[lunarpower]

Nice approach.
One question though: Who's this Ron person you're referring to? ....:-)

Cheers,
Brent

From what I can gather on here, his face looks a lot like a Louisville basketball jersey. (Go Cards!)

[Brent@GMATPrepNow]

Judging from all of the wrinkles, he must be quite old!

[lunarpower]

Judging from all of the wrinkles, he must be quite old!

Hater. (:
That jersey is a beautiful thing. My face, not so much.

This is getting a bit off-topic; let's kill it here.

[masoom j negi]

Statement 1. p/4 is a prime no. i.e. p = 4k where k is a prime no.
So, p could be anything like 8, 12, 20,.........
Hence, Insufficient.
Statement 2. P = 3a
P could be any positive integer. Hence, Insufficient.
Statement 1 & 2 together.
P = 4k where k is a prime no and p = 3a
So, k = 3. Hence, P = 4 x 3 = 12.
Hence, Sufficient.