## Discussion

Which one of the following must be true about any
acceptable product code?

*This question is included in LG Sample 1: Basic Game, question #5

(A) | There is exactly one digit between the digit 0 and the digit 1. |

(B) | ... |

(C) | ... |

(D) | ... |

(E) | ... |

(F) | ... |

The solution is

Posted: 05/19/2011 19:56

I want to know why this answer is right.

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 have either 0 OR 3, and the 5TH slot can have either 3 OR 4.

Scenario B:

2 4 __ __ __

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

-----------------------------------

This one requires a little experimentation. However, since it's the last question, you should be pretty familiar with the rules of the game by now. This will help.

Choice "A": We know that zero can be 4TH from a previous question. So let's try 0 4TH with scenario A:

1, 2, 3, 0, 4.

This shows that choice "A" is wrong.

Choice "B": Scenario A has no space between 1 and 2. Strike choice "B".

Choice "C": Is it possible for there to be three spaces between 1 and 3? Let's try it with 1 in 1ST (which is scenario A). We know that we want 3 to be 5TH, so how about:

1, 2, 0, 4, 3.

This works. We have MORE THAN two spaces between 1 and 3. Strike choice "C".

Choice "D": Let's start with scenario B here. We'll try to put 2 1ST and 3 5TH:

2, 4, 0, 4, 3

This works, so we can strike choice "D".

Choice "E": This better work, because if it doesn't we've done something wrong up to this point. Let's look at our two scenarios:

Scenario A:

1 2 __ __ __

For scenario A, if 4 were 5TH, you still wouldn't have MORE than two spaces between 2 and 4. So this checks out.

Scenario B:

2 4 __ __ __

For scenario B, 2 is right next to 4. This checks out.

Choice "E" is correct.

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 have either 0 OR 3, and the 5TH slot can have either 3 OR 4.

Scenario B:

2 4 __ __ __

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

-----------------------------------

This one requires a little experimentation. However, since it's the last question, you should be pretty familiar with the rules of the game by now. This will help.

Choice "A": We know that zero can be 4TH from a previous question. So let's try 0 4TH with scenario A:

1, 2, 3, 0, 4.

This shows that choice "A" is wrong.

Choice "B": Scenario A has no space between 1 and 2. Strike choice "B".

Choice "C": Is it possible for there to be three spaces between 1 and 3? Let's try it with 1 in 1ST (which is scenario A). We know that we want 3 to be 5TH, so how about:

1, 2, 0, 4, 3.

This works. We have MORE THAN two spaces between 1 and 3. Strike choice "C".

Choice "D": Let's start with scenario B here. We'll try to put 2 1ST and 3 5TH:

2, 4, 0, 4, 3

This works, so we can strike choice "D".

Choice "E": This better work, because if it doesn't we've done something wrong up to this point. Let's look at our two scenarios:

Scenario A:

1 2 __ __ __

For scenario A, if 4 were 5TH, you still wouldn't have MORE than two spaces between 2 and 4. So this checks out.

Scenario B:

2 4 __ __ __

For scenario B, 2 is right next to 4. This checks out.

Choice "E" is correct.

Posted: 02/07/2014 04:47

Reply:

Why is E the answer? Sure it works in the case of 1 and 2 being the first and second product codes respectively. However, when two and four are the first and second product codes respectively, there are no two spaces between the numbers.

Choice E says that it MUST BE TRUE that there are "AT MOST" two digits between 2 and 4.

So you could have:

2, 4

or

2, __, 4

or

2, __, __ 4

and this answer choice would still be correct.

So you could have:

2, 4

or

2, __, 4

or

2, __, __ 4

and this answer choice would still be correct.

For question 5 is it not possible to have the series 1,2,3,0,4.....if so that would make 2 and 4 three digits apart which would make the correct answer false. 2 is twice that of 1, 3 is less then 4, and all numbers are used only once.

Hey Mike,

The correct answer says that there are "at most" two digits between 2 and 4.

So you actually could have 1, 2, 3, 0, 4.

If you had that sequence, you'd have 3, 0 between 2 and 4.

This would be exactly two numbers, which the correct answer choice allows for.

The correct answer says that there are "at most" two digits between 2 and 4.

So you actually could have 1, 2, 3, 0, 4.

If you had that sequence, you'd have 3, 0 between 2 and 4.

This would be exactly two numbers, which the correct answer choice allows for.

Posted: 11/25/2011 08:37

Why is there not an explanation of the 4th position ?

Posted: 11/25/2011 08:39

Do we just accept 4th position as 0 because the third and fifth rule?

Hey Christina,

It turns out we don't have to figure out what the 4th digit is in order to answer this question.

We only need to identify which answer choice contains a statement that MUST be true.

For this question, we can't really determine for sure what the 4th digit is.

Here are a few possibilities:

(i) 1, 2, 0, 3, 4

(ii) 2, 4, 0, 3, 1

(iii) 2, 4, 1, 0, 3

The trick to the Logic Games section is to figure out just enough to answer the question. If you spend time figuring out all of the possible scenarios for each question, you'll run out of time long before you finish all four games. (On an actual LSAT, the LG section has four games, for a total of 23 or 24 questions.)

Hope this helps.

It turns out we don't have to figure out what the 4th digit is in order to answer this question.

We only need to identify which answer choice contains a statement that MUST be true.

For this question, we can't really determine for sure what the 4th digit is.

Here are a few possibilities:

(i) 1, 2, 0, 3, 4

(ii) 2, 4, 0, 3, 1

(iii) 2, 4, 1, 0, 3

The trick to the Logic Games section is to figure out just enough to answer the question. If you spend time figuring out all of the possible scenarios for each question, you'll run out of time long before you finish all four games. (On an actual LSAT, the LG section has four games, for a total of 23 or 24 questions.)

Hope this helps.

Thank you very much for this explanation. Too much and not enough seems to be a fine line in this area!

It means 2, [#], [#], 4 which can be proven by 1,2,[304 034 043] and 2,4,[103 031 013] through all possibilities the digits.2 and 4 never have more than 2 other digits between them.

Answer c won't work because of the code 1 2 0 4 3. There are 3 digest between 1 and 3 with this one :)

Posted: 04/30/2012 17:30

Ji Kwak, thanks for realizing that you can attach a picture to the post!

Posted: 05/28/2012 13:48

Disregard. Didn't take into account 1 2 0 4 3

Why doesn't code 24013 work? Because then there are 3 digits between 2 and 3

Posted: 11/22/2012 16:43

Yeah I read the question wrong!

Posted: 02/07/2014 04:36

What?