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# Is the two digit positive integer P a prime number? 1) P + 2

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Kudos [?]: 817 [3] , given: 232

Is the two digit positive integer P a prime number? 1) P + 2 [#permalink]  21 Oct 2010, 16:01
3
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Difficulty:

5% (low)

Question Stats:

28% (02:12) correct 71% (01:13) wrong based on 14 sessions
Is the two digit positive integer P a prime number?

1) P + 2 and P – 2 are prime.
2) P – 4 and P + 4 are prime.

I will post the solution and the explanation later.
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Kudos [?]: 17572 [1] , given: 2212

Re: prime numbers [#permalink]  21 Oct 2010, 16:52
1
KUDOS
Expert's post
gurpreetsingh wrote:
Is the two digit positive integer P a prime number?

1) P + 2 and P – 2 are prime.
2) P – 4 and P + 4 are prime.

I will post the solution and the explanation later.

Good question, +1.

Note that P is the two digit integer .

(1) P + 2 and P – 2 are prime --> out of every 3 consecutive integers one must be divisible by 3 --> consider 5 consecutive integers: {P-2}{P-1}{P}{P+1}{P+2}. Now, P-2 and P+2 are not divisible by 3 as they are primes, P+1 and P-1 are 3 apart from P-2 and P+2 respectively and thus they are also not divisible by 3, which means that P must be divisible by 3 and as it's TWO digit integer it can not be a prime. Sufficient.

(2) P – 4 and P + 4 are prime --> the same here: {P-1}{P}{P+1}. P-1 and P+1 are 3 apart from P-4 and P+4 respectively and thus can not be divisible by 3, which means that P must be divisible by 3 and as it's TWO digit integer it can not be a prime. Sufficient.

_________________
CEO
Status: Nothing comes easy: neither do I want.
Joined: 12 Oct 2009
Posts: 2792
Location: Malaysia
Concentration: Technology, Entrepreneurship
GMAT 1: 670 Q49 V31
GMAT 2: 710 Q50 V35
Followers: 155

Kudos [?]: 817 [0], given: 232

Re: prime numbers [#permalink]  21 Oct 2010, 17:49
Yes Bunuel, Its a very good question. That's why I thought I should share it here.

The only catch was the existence of two digit number. Since you have posted the solution. I will post mine strategy.

All the numbers can be represented as 3k,3k+1, 3k+2

Statement 1: For P+2 and P-2 to be prime the number can not be of the form 3k+1 and 3k+2.
=> P = 3k = not prime if k is not equal to 1
Since two digit number is given => 3k is not a prime number.

Statement 2: using the same strategy. P is not a prime number.

Hence D.
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Kudos [?]: 13 [0], given: 8

Re: prime numbers [#permalink]  22 Oct 2010, 12:09
I solved this by different method,

1) P + 2 and P – 2 are prime.
--> if You can list out all two digit Prime Numbers, you will get P=15 ONLY for which P+2 & P-2 are primes.
since 15 is not prime, Sufficient

2) P – 4 and P + 4 are prime.
--> Again, if You can list out all two digit Prime Numbers, you will get P=15 ONLY for which P+4 & P-4 are primes.
since 15 is not prime, Sufficient

hence D.

though the answer is correct by this method, I feel Bunuel's Method was more proper !!
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Kudos [?]: 13 [0], given: 8

Re: prime numbers [#permalink]  22 Oct 2010, 21:53
Ohh yes... I missed many pairs...
gurpreetsingh , Thanks for the correction
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Re: prime numbers   [#permalink] 22 Oct 2010, 21:53
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