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Is the positive integer p the sum of the positive prime [#permalink]
 21 Aug 2010, 04:24
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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 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 |
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Re: Sum of Positive Primes [#permalink]
21 Aug 2010, 04:48
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 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, 05:23
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]
21 Aug 2010, 07:54
I agree. The answer is C. Similar explanation Abhishek 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 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 |
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Re: Sum of Positive Primes [#permalink]
23 Aug 2010, 22:11
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 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, 02:02
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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Re: Sum of Positive Primes
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24 Aug 2010, 02:02
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