题目信息
Can the positive integer n be written as the sum of two different positive prime numbers?
A:Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.
B:Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.
C:BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.
D:EACH statement ALONE is sufficient.
E:Statements (1) and (2) TOGETHER are NOT sufficient.
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正确答案：
E:Statements (1) and (2) TOGETHER are NOT sufficient.
Arithmetic Properties of integers
Determine if the positive integer n can be written as the sum of two different positive prime numbers.
It is given that n > 3. If n = 5, then n = 2 + 3 and 2 and 3 are different positive prime numbers. However, n = 11, then n can be written as the following sums of two different positive numbers: 1 + 10, 2 + 9, 3 + 8, 4 + 7, and 5 + 6. In no case are the addends both prime; NOT sufficient. It is given that n is odd. The values of n in the examples used to show that (1) is not sufficient also satisfy (2); NOT sufficient.
Taken together, (1) and (2) are not sufficient because the same examples used to show that (1) is not sufficient also show that (2) is not sufficient.
The correct answer is E;both statements together are still not sufficient.
Determine if the positive integer n can be written as the sum of two different positive prime numbers.
It is given that n > 3. If n = 5, then n = 2 + 3 and 2 and 3 are different positive prime numbers. However, n = 11, then n can be written as the following sums of two different positive numbers: 1 + 10, 2 + 9, 3 + 8, 4 + 7, and 5 + 6. In no case are the addends both prime; NOT sufficient. It is given that n is odd. The values of n in the examples used to show that (1) is not sufficient also satisfy (2); NOT sufficient.
Taken together, (1) and (2) are not sufficient because the same examples used to show that (1) is not sufficient also show that (2) is not sufficient.
The correct answer is E;both statements together are still not sufficient.
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