If you use the "Reduce" button twice, you'll see the following text:


Inferences:
1. Since the fifth digit of the code must be more than the third, the fifth digit cannot be zero.

2. The second digit must be twice the first, and the only numbers available for the code are 1, 2, 3, 4, 5. Therefore, you can infer that one of the following two scenarios will arise:


Scenario A:

1 2 __ __ __

In scenario A, the 3RD slot can be either 0 OR 3, and the 5TH slot can be either 3 OR 4.




Scenario B:

2 4 __ __ __


In scenario B, the 3RD slot can be either 0 OR 1, and the 5TH slot can be either 1 OR 3.


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Go to the answer choices, and start going through the process of elimination:

Since scenario B is possible, you can rule out choice "A".

Look at scenario A. Is it possible for 3 to appear before 1? No it is not. Now look at scenario B. You could have 2, 4, 0, 3, 1. You can rule out choice "B".

Look at both scenarios. In each case, 2 MUST come before 3. Choice "C" is correct.


You can stop here. But if you need proof that choices "D" and "E" are wrong, consider:

The sequence 1, 2, 0, 4, 3 proves choice "D" is wrong.

The sequence 1, 2, 3, 0, 4 proves choice "E" is wrong.

Zakya, it appears you answer your own question. This problem asks which must be true for "any" product code. Since you've already stated that all product codes start only with 1,2 or 2,4. Since 2 will always be either the first or second digit, and the only time it is the second digit is when 1 is the first digit, in all acceptable scenarios, 3 must follow 2.

Ok never mind I got it. C is possible but it wants to know "what must be true".

James, I think you misread. Instead of "in the same position", it's "in some position".

Yes, you are reading it incorrectly, Jorge. Answer A is not technically correct. The key phrase is "must be true". The explanation provides shows that in scenario B, 2 appears before 1.

Thanks, Avin.

Elizabeth, this problem has been analyzed several times previously. Please look through the thread. The key phrase you should pay attention to is "must be true".