Discussion
If the third digit of an acceptable product code is not 0,
which one of the following must be true?
*This question is included in LG Sample 1: Basic Game, question #3
| (A) | The second digit of the product code is 2. |
| (B) | ... |
| (C) | ... |
| (D) | ... |
| (E) | ... |
| (F) | ... |
The solution is
Posted: 05/19/2011 19:56
I want to know why B is wrong and C is right.
Posted: 05/21/2011 14:36
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:
1st 2nd 3rd 4th 5th
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:
1st 2nd 3rd 4th 5th
2 4 __ __ __
In scenario A, the 3RD slot can have either 0 OR 1, and the 5TH slot can have either 1 OR 3.
-----------------------------------
We know that 0 cannot be 3RD, and we know it cannot be 5TH (see "Inference 1", above). Therefore, 0 MUST be 4TH.
Based on our scenarios above, PLUS the fact that 0 must be 4TH, we can infer that there are two possible sequences:
Seq. 1:
1, 2, 3, 0, 4
Seq. 2:
2, 4, 1, 0, 3
(Remember, the 5TH digit must be greater than the 3RD.)
As you can see, in both cases 0 is 4th. And in the second sequence, 3 is 5TH, which makes choice B wrong.
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:
1st 2nd 3rd 4th 5th
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:
1st 2nd 3rd 4th 5th
2 4 __ __ __
In scenario A, the 3RD slot can have either 0 OR 1, and the 5TH slot can have either 1 OR 3.
-----------------------------------
We know that 0 cannot be 3RD, and we know it cannot be 5TH (see "Inference 1", above). Therefore, 0 MUST be 4TH.
Based on our scenarios above, PLUS the fact that 0 must be 4TH, we can infer that there are two possible sequences:
Seq. 1:
1, 2, 3, 0, 4
Seq. 2:
2, 4, 1, 0, 3
(Remember, the 5TH digit must be greater than the 3RD.)
As you can see, in both cases 0 is 4th. And in the second sequence, 3 is 5TH, which makes choice B wrong.
Posted: 06/25/2012 22:00
I don't understand, in the second sequence the 5th digit (3) is larger than the third digit (1).
|
Edit
Posted: 12/06/2012 12:34
Hi, Arynne -
If you'll re-read the last constraint of the original problem, it states that "The value of the third digit is less than the value of the fifth digit." In other words, the fifth digit is supposed to be greater, so sequences 1and 2 are both correct.
Best,
Lyn
If you'll re-read the last constraint of the original problem, it states that "The value of the third digit is less than the value of the fifth digit." In other words, the fifth digit is supposed to be greater, so sequences 1and 2 are both correct.
Best,
Lyn
Posted: 09/16/2011 21:06
I struggled with choosing between b and e. I chose b, but it honestly was a guess between then two. Why is b right and e wrong?
Posted: 09/18/2011 14:29
Dashe,
"B" in wrong.
"C" is the correct answer choice.
This question asks which answer choice MUST be true, so we've got to find the answer choice that makes a statement that can't not be true. What does this mean?
Let's illustrate by taking a look at the answer choices.
But first, we need to take a look at the rules:
[Step 1]: We know that the third digit CANNOT be zero.
[Step 2]: And we know that the first two digits must be 1, 2 or 2,4.
[Step 3]: Finally, we know that the fifth digit cannot be zero.
This leaves only the 4th digit as the digit that can be zero. This give us our answer--no need to guess. 0 MUST be 4th. And if we know that choice "C" is correct, we can rest assured that all of the other choices are wrong.
The logic games section is all about progressing through a series of logical inferences. You should go through each rule carefully in order determine how it limits/affects your setup. Go step-by-step, one rule to the next. With enough practice (and practice is KEY here), you will not have to guess on logic games.
Now, let's see why the wrong answer choices are wrong (remember, this is a MUST be true question:
"A": The second digit can be 4 without violating any of the Rules. Example: 2, 4, 1, 0, 3
"B": The third digit can be 1 without violating any of the Rules. Example: 2, 4, 1, 0, 3
"D": The fifth digit can be 4 without violating any of the Rules. Example: 1, 2, 3, 0, 4
"E": The fifth digit can be 3 without violating any of the Rules. Example: 2, 4, 1, 0, 3
"B" in wrong.
"C" is the correct answer choice.
This question asks which answer choice MUST be true, so we've got to find the answer choice that makes a statement that can't not be true. What does this mean?
Let's illustrate by taking a look at the answer choices.
But first, we need to take a look at the rules:
[Step 1]: We know that the third digit CANNOT be zero.
[Step 2]: And we know that the first two digits must be 1, 2 or 2,4.
[Step 3]: Finally, we know that the fifth digit cannot be zero.
This leaves only the 4th digit as the digit that can be zero. This give us our answer--no need to guess. 0 MUST be 4th. And if we know that choice "C" is correct, we can rest assured that all of the other choices are wrong.
The logic games section is all about progressing through a series of logical inferences. You should go through each rule carefully in order determine how it limits/affects your setup. Go step-by-step, one rule to the next. With enough practice (and practice is KEY here), you will not have to guess on logic games.
Now, let's see why the wrong answer choices are wrong (remember, this is a MUST be true question:
"A": The second digit can be 4 without violating any of the Rules. Example: 2, 4, 1, 0, 3
"B": The third digit can be 1 without violating any of the Rules. Example: 2, 4, 1, 0, 3
"D": The fifth digit can be 4 without violating any of the Rules. Example: 1, 2, 3, 0, 4
"E": The fifth digit can be 3 without violating any of the Rules. Example: 2, 4, 1, 0, 3
Posted: 07/08/2012 05:13
hi. with 24103 wouldnt D also be the correct answer along with C?
Posted: 12/06/2012 12:38
Hi, Aram --
Answer D "could be" true, i.e., one of the correct sequences satisfies it. However, the problem asks for the answer that "must be" true, i.e., the answer that is satisfied by ALL correct sequences. Only answer C does so.
Best,
Lyn
Answer D "could be" true, i.e., one of the correct sequences satisfies it. However, the problem asks for the answer that "must be" true, i.e., the answer that is satisfied by ALL correct sequences. Only answer C does so.
Best,
Lyn
Posted: 12/05/2012 13:00
I got two different 5 digit codes and was wondering of I skipped a step or if I was trying to find the answer that applied to both codes I found
Posted: 12/06/2012 04:26
Morgan,
First we'll set the conditions into definitions:
Def. 1 Digit = { 0, 1, 2, 3, 4 }
Def. 2 ( Nth != Mth )
Def. 3 ( 2nd == 2( 1st ) )
Def. 4 ( 3rd smaller than 5th )
Def. 5 ( 3rd != 0 )
We can make an additional more algebraic system of definitions
Def. 6 Sequence = { A, 2A, B, C, D }
Def. 7 ( B != 0 )
Def. 8 ( B smaller than D )
Answer A. ( 2nd == 2 )
-, 2, -, -, - >>> def. 3 or 6
1, 2, -, -, - >>> def. 5 or 7 and def. 4 or 8 make 0 must be 4th
1, 2, 3, 0, 4 >>> doesn't conflict with definitions thus valid
Answer B. ( 3rd == 3 )
We can use the exact same sequence as with answer A.
Answer C. ( 4th == 0 )
We can use the exact same sequence as with answer A.
Answer D. ( 5th == 3 )
-, -, -, -, 3 >>> Def. 4 or 8 and def. 5 or 7 make
-, -, 1, -, 3 or -, -, 2, -, 3 >>> Def. 3 or 6 make
2, 4, 1, 0, 3 >>> doesn't conflict with definitions thus valid
At this point we can see that answers A and B become false and answer C remains true
Answer E. ( 5th == 1 )
-, -, -, -, 1 >>> Def. 4 or 8 make
-, -, 0, -, 1 >>> Conflicts with def. 5 and 7 thus false
We now have enough information to declare answer C as the correct one.
Niels
First we'll set the conditions into definitions:
Def. 1 Digit = { 0, 1, 2, 3, 4 }
Def. 2 ( Nth != Mth )
Def. 3 ( 2nd == 2( 1st ) )
Def. 4 ( 3rd smaller than 5th )
Def. 5 ( 3rd != 0 )
We can make an additional more algebraic system of definitions
Def. 6 Sequence = { A, 2A, B, C, D }
Def. 7 ( B != 0 )
Def. 8 ( B smaller than D )
Answer A. ( 2nd == 2 )
-, 2, -, -, - >>> def. 3 or 6
1, 2, -, -, - >>> def. 5 or 7 and def. 4 or 8 make 0 must be 4th
1, 2, 3, 0, 4 >>> doesn't conflict with definitions thus valid
Answer B. ( 3rd == 3 )
We can use the exact same sequence as with answer A.
Answer C. ( 4th == 0 )
We can use the exact same sequence as with answer A.
Answer D. ( 5th == 3 )
-, -, -, -, 3 >>> Def. 4 or 8 and def. 5 or 7 make
-, -, 1, -, 3 or -, -, 2, -, 3 >>> Def. 3 or 6 make
2, 4, 1, 0, 3 >>> doesn't conflict with definitions thus valid
At this point we can see that answers A and B become false and answer C remains true
Answer E. ( 5th == 1 )
-, -, -, -, 1 >>> Def. 4 or 8 make
-, -, 0, -, 1 >>> Conflicts with def. 5 and 7 thus false
We now have enough information to declare answer C as the correct one.
Niels
Posted: 12/06/2012 12:42
Hi, Morgan --
There are exactly two sequences that satisfy all the constraints, as described in the Arcadia Admin post above. If you found the same two sequences, you haven't missed anything; you are looking for the answer that applies to both.
If you have any further questions, please feel free to post again!
Best,
Lyn
There are exactly two sequences that satisfy all the constraints, as described in the Arcadia Admin post above. If you found the same two sequences, you haven't missed anything; you are looking for the answer that applies to both.
If you have any further questions, please feel free to post again!
Best,
Lyn