hmgp22 wrote:I think I'm confused with the wording of the question. To me, it seems like the question is asking for the POSSIBILITY of n being written as a sum of 2 distinct positive primes. In both cases, it's clear that the given statements are sufficient to answer that question. If it's asking whether n IS.... then the question is very straightforward.
Can the positive integer n be written as the sum of
two different positive prime numbers?
(1) n is greater than 3.
(2) n is odd.
OA: E
Some numbers can be written as the sum of two different positive prime numbers. For example, 5 can be written as the sum of 2 and 3. Similarly, 10 can be written as the sum of 3 and 7.
Some numbers cannot be written as the sum of two different positive prime numbers. For example, 4 cannot be written as the sum of two
different positive prime numbers.
Target question:
Can the positive integer n be written as the sum of two different positive prime numbers?
Statement 1: n is greater than 3.
n can have many possible values. Consider these two cases:
Case a: n = 5, in which case
n can be written as the sum of two different positive prime numbers
Case b: n = 11, in which case
n cannot be written as the sum of two different positive prime numbers
Since we cannot answer the
target question with certainty, statement 1 is NOT SUFFICIENT
Statement 2: n is odd.
n can have many possible values. Consider these two cases:
Case a: n = 5, in which case
n can be written as the sum of two different positive prime numbers
Case b: n = 11, in which case
n cannot be written as the sum of two different positive prime numbers
Since we cannot answer the
target question with certainty, statement 1 is NOT SUFFICIENT
Statements 1 and 2 combined:
n can still have many possible values. Consider these two cases:
Case a: n = 5, in which case
n can be written as the sum of two different positive prime numbers
Case b: n = 11, in which case
n cannot be written as the sum of two different positive prime numbers
Since we cannot answer the
target question with certainty, statement 1 is NOT SUFFICIENT
Since we cannot answer the
target question with certainty, the combined statements are NOT SUFFICIENT
Answer =
E
Cheers,
Brent
