There is a simple and fast way to resolve this question:
First of all you start with the equation that everybody has suggested:
120n + 90p = 60*30
4n + 3p = 60
Now here is the key.
You need only to worry about the first part of the equation "4n + 3p".
You substitute the values of n and p and check if the result is A FACTOR OF 60. If it is, then it is a possible solution, because you know that you need only to multiply the equations by a factor to get 60 as a result.
Step by step:
A 3:16 --> 4*3 + 3*16 = 60 - ok here we are lucky. This is a solution.
B 1:2 --> 4*1 + 3*2 = 10 This is another solution because 10 is a factor of 60. If we multiply the numbers of the ration by 6, we will have 6:12, and the result will be 4*6 + 3*12 = 60. But we don't need to multiply to see that the result will be 60. When we see 12, we think: It is enough!
C 2:3 --> 4*2 + 3*3 = 17 CORRECT. Here is our solution. There is no number to multiply to get a result of 60, therefore it is impossible to have the ratio 2:3
D 9:8 --> 4*9 + 3*8 = 60 lucky again
E 3:1 --> 4*3 + 3*1 = 15. It is a possible solution.
Notice that explaining this in detail might be look time consuming, but try to do this question, following this reasoning, ans you will see it is very fast.
Goos studies. PS.: If you've appreciated the explanation, consider a kudo. I want to access those GMATClub tests!!!