The function f(x) represents the number of ways that...

[BTGmoderatorLU]

The function f(x) represents the number of ways that prime numbers can be uniquely summed to form a certain number x such that x = a + b + c + d... Where those summed variables are each prime and a ≤ b ≤ c ≤ d... For instance f(8) = 3 and the unique ways are 2 + 2 + 2 + 2 and 2 + 3 + 3 and 3 + 5. What is f(12)?

A. 4
B. 5
C. 6
D. 7
E. 8

The OA is D.

I don't understand this PS question. Why D is the correct answer? Can any expert explain it please? Thanks.

[EconomistGMATTutor]

The function f(x) represents the number of ways that prime numbers can be uniquely summed to form a certain number x such that x = a + b + c + d... Where those summed variables are each prime and a ≤ b ≤ c ≤ d... For instance f(8) = 3 and the unique ways are 2 + 2 + 2 + 2 and 2 + 3 + 3 and 3 + 5. What is f(12)?

A. 4
B. 5
C. 6
D. 7
E. 8

The OA is D.

I don't understand this PS question. Why D is the correct answer? Can any expert explain it please? Thanks.
LIKE QUOTE FLAG

Hi LUANDATO,
Let's take a look at your question.

We are asked to find out the number of ways 12 can be written as sum of prime numbers.
Let's explore.
12 = 2 + 2 + 2 + 2 + 2 + 2
12 = 2 + 2 + 3 + 5
12 = 2 + 2 + 2 + 3 + 3
12 = 2 + 5 + 5
12 = 3 + 3 + 3 + 3 + 3
12 = 7 + 3 + 2
12 = 7 + 5
Hence, there are 7 ways to write 12 as a sum of prime numbers.

Therefore, option D is correct.

Hope it helps.
I am available if you'd like any follow up.