A function g(n), where n is an integer, is defined as the product of

Hi jfranciscocuencag

In my opinion, GMAT would not ask questions like say g(6) + 7 which is 727. As finding the Prime nature of that number will be extremely difficult without any method.
But yes, i would expect them to ask the number you gave g(5) + 7 = 127.

However there is method to find whether a given number is prime or not

How to find a given number N is prime or not ?

Step 1: Find the nearest integral square root of N
Step 2: List all the prime numbers less than or equal to \(\sqrt{N}\)
Step 3: Find whether the given number N divides any of the numbers from step 2.

Conclusion: 1) If any number divides N, then N is NOT A PRIME Number
2) If no number divides N, then N is A PRIME Number

Eg1: Find whether 197 is prime or not ?

Step 1: \(\sqrt{197}\) --> Nearest integral square root = 14
Step 2: Prime numbers less than or equal to 14 --> 2, 3, 5, 7, 11, 13
Step 3: Divisibility: 2 - NO, 3 - NO, 5 - NO, 7 - NO, 11 - NO, 13 - NO.

Conclusion: 197 is A PRIME Number

Eg2: Find whether 459 is prime or not ?

Step 1: \(\sqrt{459}\) --> Nearest integral square root = 21
Step 2: Prime numbers less than or equal to 21 --> 2, 3, 5, 7, 11, 13, 17, 19
Step 3: Divisibility: 2 - NO, 3 - YES, 5 - NO, 7 - NO, 11 - NO, 13 - NO, 17 - YES, 19 - NO

Conclusion: 459 is NOT A PRIME Number

Though the above method would take around 2-2:30 minutes to solve. It's very unlikely that GMAT would test for such high numbers

Hope it's clear!