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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

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.

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?
_________________

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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