# Any of the following pairs could be the third and fourth digits, respectively, of an acceptable product code, EXCEPT:

yuetngan on March 4, 2019

Restating intial rule

Hi, Do we always re-use the initial rule? Must we re-draw the rule for each question?

Replies
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janibrown97 on March 9, 2019

What is a product code?

janibrown97 on March 9, 2019

What is a product code?

Ravi on March 12, 2019

@yuetngan,

Great question. Yes, unless otherwise stated, all of the initial rules
are present throughout the entire game. I would recommend diagramming
the rules once for each game. Diagramming them for each question
wastes precious time and is not advisable.

There are some games where there is a rule substitution question at
the end where one or more of the rules is swapped out for another
rule. In these cases, it can be helpful to write the new rule next to
the question to help you make sure you understand it.

Regarding what a product code is, a product code is a unique
identifier, assigned to each finished/manufactured productwhich is
ready, to be marketed or for sale. A product code may also refer to:
Universal Product Code, common barcode used to identify packaged
products. Even if we don't know what a product code is, we can still
answer this question just fine. Don't concern yourself too much with
understanding what certain types of things are. Just make sure that
you can diagram what you're supposed to. For the purposes of this
game, a product code is just a series of five digits ranging from 0 to
4. That's really all we need to know, and that's given to us in the
initial rules.

Does this make sense? Let us know if you have any more questions!

appozernick on June 5, 2019

Hi, what do they mean by respectively?

appozernick on June 5, 2019

Both A and E are right... right? How do I continue with this question?

Ravi on June 7, 2019

By "respectively," they're referring to the order.

Any of the following pairs could be the third and fourth digits, respectively...

(A) says "0, 1"

Third and fourth respectively means 0 and 1, so it's to let you know
that 0 would be in the third spot and 1 would be in the 4th spot.

(A) and (E) are not both right. Let's take a look at them.

We know an employee generates a series of 5-digit codes.

The digits used can be 0, 1, 2, 3, or 4.

Each digit is used exactly once.

The 2nd digit is double the 1st digit's value

The 3rd digit is less than the 5th digit.

1 2 _ _ _
2 4 _ _ _

The first and second digits have to be either 1 and 2 or 2 an 4
because those are the only two pairs of numbers are double/half of
each other, which allows us to satisfy the rule about the 2nd and 1st
digits.

Using our rules, we can solve for all possibilities of this game.
There are 6 possibilities for the game:

1 2 3 0 4
1 2 0 3 4
1 2 0 4 3

2 4 1 0 3
2 4 0 1 3
2 4 0 3 1

With (A), we have 0 and 1. We see that this can be a possibility (2 4
0 1 3), so (A) is out.

With (E), we do not see any board with 3 and 4 in the 3rd and 4th
positions, so this isn't possible. Thus, (E) is the correct answer
choice.

Hope this helps. Let us know if you have any more questions!