If p is a positive integer...

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If p is a positive integer...

by ProGMAT » Mon Aug 12, 2013 8:30 am
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.

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by Brent@GMATPrepNow » Mon Aug 12, 2013 9:41 am
ProGMAT wrote: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

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by ProGMAT » Mon Aug 12, 2013 9:55 am
Brent@GMATPrepNow wrote:
ProGMAT wrote: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.

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by lunarpower » Sat Aug 17, 2013 5:24 am
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.
ProGMAT wrote: (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.
Ron has been teaching various standardized tests for 20 years.

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by Brent@GMATPrepNow » Sat Aug 17, 2013 5:35 am
Nice approach.
One question though: Who's this Ron person you're referring to? ....:-)

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by lunarpower » Sat Aug 17, 2013 6:56 am
Brent@GMATPrepNow wrote: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!)
Ron has been teaching various standardized tests for 20 years.

--

Pueden hacerle preguntas a Ron en castellano
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Voit esittää kysymyksiä Ron:lle myös suomeksi

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Quand on se sent bien dans un vêtement, tout peut arriver. Un bon vêtement, c'est un passeport pour le bonheur.

Yves Saint-Laurent

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by Brent@GMATPrepNow » Sat Aug 17, 2013 6:59 am
Judging from all of the wrinkles, he must be quite old!
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by lunarpower » Sat Aug 17, 2013 7:30 am
Brent@GMATPrepNow wrote: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.
Ron has been teaching various standardized tests for 20 years.

--

Pueden hacerle preguntas a Ron en castellano
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Voit esittää kysymyksiä Ron:lle myös suomeksi

--

Quand on se sent bien dans un vêtement, tout peut arriver. Un bon vêtement, c'est un passeport pour le bonheur.

Yves Saint-Laurent

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by masoom j negi » Fri Dec 21, 2018 8:51 pm
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.