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# Is the positive integer p the sum of the positive prime

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Is the positive integer p the sum of the positive prime [#permalink]  21 Aug 2010, 03:24
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Is the positive integer p the sum of the positive prime numbers m and n?

(1) m - n = 8
(2) p = 50

I don't quite get how to solve the Q, inspite of the Explanation below. Pls help

[Reveal] Spoiler:
OA: C
Explanation: To answer this question, you at the very least need the value of p; it would help to know something about m and n as well. Statement (1) is insuff; there are many possible prime number pairs that are 8 apart, and without knowing the value of p, we have no idea whether their sum is equal to p.
Statement (2) is insuff: it's helpful to know that p = 50, but m and n could be 3 and 47, or they could be 3 and 5. In one case, the sum is equal to p; in the other, it isn't.
Taken together, the statements are su¢ cient. The only pair of numbers that are 8 apart and sum to 50 are 21 and 29. 21 isn't a prime number, so whatever the values of m and n, they aren't 21 and 29. Thus, so long as m and n are 8 apart, they don't sum to 50, so their sum is not equal to p. (C) is the correct choice

this is a question from Jeff Sackmann's MATH Set
[Reveal] Spoiler: OA
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Re: Sum of Positive Primes [#permalink]  21 Aug 2010, 03:48
Expert's post
wininblue wrote:
this is a question from Jeff Sackmann's MATH Set

Is the positive integer p the sum of the positive prime numbers
m and n?
(1) m - n = 8
(2) p = 50

I don't quite get how to solve the Q, inspite of the Explanation below. Pls help
[Reveal] Spoiler:
OA: C
Explanation: To answer this question, you at the very least need the value of p; it would help to know something about m and n as well. Statement (1) is insuff; there are many possible prime number pairs that are 8 apart, and without knowing the value of p, we have no idea whether their sum is equal to p.
Statement (2) is insuff: it's helpful to know that p = 50, but m and n could be 3 and 47, or they could be 3 and 5. In one case, the sum is equal to p; in the other, it isn't.
Taken together, the statements are su¢ cient. The only pair of numbers that are 8 apart and sum to 50 are 21 and 29. 21 isn't a prime number, so whatever the values of m and n, they aren't 21 and 29. Thus, so long as m and n are 8 apart, they don't sum to 50, so their sum is not equal to p. (C) is the correct choice

Given: $$p=integer>0$$, $$m$$ and $$n$$ are prime numbers. Question: is $$m+n=50$$

(1) m - n = 8, clearly insufficient, as no info about p.

(2) p = 50 --> could 50 be the sum of 2 primes? Yes, 47+3=50. But m and n could be some other primes as well, which don't add up to 50, hence this statement is also not sufficient.

(1)+(2) $$m-n=8$$ and $$p=50$$. Let's assume that $$m+n=p=50$$ is true. Then solving for m and n (2 equations $$m-n=8$$ and $$m+n=50$$) we get that $$m=29$$ and $$n=21$$, but 21 is not prime number and we are given that $$n=prime$$ hence our assumption that $$m+n={p}$$ is false. So $$m+n\neq{p}$$. Sufficient.

Answer: C.
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Re: Sum of Positive Primes [#permalink]  21 Aug 2010, 04:23
Thanks Bunuel for your quick response.

So here, since P cannot be expressed as a sum of primes which differ by 8 - the ans is C
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Re: Sum of Positive Primes [#permalink]  23 Aug 2010, 21:11
Bunuel wrote:
wininblue wrote:
this is a question from Jeff Sackmann's MATH Set

Is the positive integer p the sum of the positive prime numbers
m and n?
(1) m - n = 8
(2) p = 50

I don't quite get how to solve the Q, inspite of the Explanation below. Pls help
[Reveal] Spoiler:
OA: C
Explanation: To answer this question, you at the very least need the value of p; it would help to know something about m and n as well. Statement (1) is insuff; there are many possible prime number pairs that are 8 apart, and without knowing the value of p, we have no idea whether their sum is equal to p.
Statement (2) is insuff: it's helpful to know that p = 50, but m and n could be 3 and 47, or they could be 3 and 5. In one case, the sum is equal to p; in the other, it isn't.
Taken together, the statements are su¢ cient. The only pair of numbers that are 8 apart and sum to 50 are 21 and 29. 21 isn't a prime number, so whatever the values of m and n, they aren't 21 and 29. Thus, so long as m and n are 8 apart, they don't sum to 50, so their sum is not equal to p. (C) is the correct choice

Given: $$p=integer>0$$, $$m$$ and $$n$$ are prime numbers. Question: is $$m+n=50$$

(1) m - n = 8, clearly insufficient, as no info about p.

(2) p = 50 --> could 50 be the sum of 2 primes? Yes, 47+3=50. But m and n could be some other primes as well, which don't add up to 50, hence this statement is also not sufficient.

(1)+(2) $$m-n=8$$ and $$p=50$$. Let's assume that $$m+n=p=50$$ is true. Then solving for m and n (2 equations $$m-n=8$$ and $$m+n=50$$) we get that $$m=29$$ and $$n=21$$, but 21 is not prime number and we are given that $$n=prime$$ hence our assumption that $$m+n={p}$$ is false. So $$m+n\neq{p}$$. Sufficient.

Answer: C.

Bunuel
Should not the question be is p=m+n? Why is the question is m+n=50?

"But m and n could be some other primes as well, which don't add up to 50, hence this statement is also not sufficient."

I am confused. By 2, we have p=50. If 47+3 is the ONLY combination of positive primes that gives us 50, then isn't 2 sufficient? You mention that there could be other primes that don't add up to 50 here, but then it is given that p=50. What am I missing?
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Re: Sum of Positive Primes [#permalink]  24 Aug 2010, 01:02
mainhoon wrote:
Bunuel
Should not the question be is p=m+n? Why is the question is m+n=50?

"But m and n could be some other primes as well, which don't add up to 50, hence this statement is also not sufficient."

I am confused. By 2, we have p=50. If 47+3 is the ONLY combination of positive primes that gives us 50, then isn't 2 sufficient? You mention that there could be other primes that don't add up to 50 here, but then it is given that p=50. What am I missing?

Hi,

you're correct, the question is "does p = m + n?" Since (2) tells us that p=50, we can now substitute that value into the question to get a new question: "does 50 = m + n?"

However, since we have no idea what the actual values of m and n are, we're allowed to pick any primes.

So, if m=3 and n=47, then we ask "does 50 = 3 + 47?" and get the answer YES.

However, if m=5 and n=7, we ask "does 50 = 5 + 7?" and get the answer NO.

Since statement (2) can generate both a YES and a NO answer, it's insufficient.

Here's your error (a very common one in data sufficiency): you turned the question into a statement; in other words, to answer the question "is p = m + n?", you assumed that "p = m + n".
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one more from GMAT Hacks [#permalink]  16 Apr 2014, 06:21
Is the positive integer p the sum of the positive prime numbers m and n?
(1) m-n=8
(2) p = 50

Couldn't understand the explanation provided - can someone help please?
Math Expert
Joined: 02 Sep 2009
Posts: 29750
Followers: 4894

Kudos [?]: 53368 [0], given: 8155

Re: one more from GMAT Hacks [#permalink]  16 Apr 2014, 06:32
Expert's post
brobeedle wrote:
Is the positive integer p the sum of the positive prime numbers m and n?
(1) m-n=8
(2) p = 50

Couldn't understand the explanation provided - can someone help please?

Merging similar topics. Please refer to the discussion above.

Hope it helps.

P.S. Please name the topics properly (rule #3 here: rules-for-posting-please-read-this-before-posting-133935.html) and search before posting. Thank you.
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Re: one more from GMAT Hacks   [#permalink] 16 Apr 2014, 06:32
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# Is the positive integer p the sum of the positive prime

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