Discussion
If Larisa's aisles are separated by the maximum number of aisles that could separate her aisles, which one of the following could be true?
*This question is included in Sequencing: Lesson Set 5 (of 5) - Repetition/Omission, question #5
| (A) | Jill stocks aisle 6. |
| (B) | ... |
| (C) | ... |
| (D) | ... |
| (E) | ... |
| (F) | ... |
The solution is
Posted: 01/02/2013 00:12
I do not understand how A was the correct answer. For some reason I had C and D as my answer choices to choose from...
Posted: 01/05/2013 16:01
Hi, Sheila -
To see why (A) is the correct answer, let's start by numbering the conditions for easy reference:
1. Olga stocks exactly one aisle.
2. Kurt stocks aisle 2.
3. Manny does not stock aisle 1.
4. Jill does not stock consecutive aisles.
5. Kurt stocks the only aisle between the two aisles Manny stocks.
6. Exactly one of Larisa's aisles is an end aisle.
7. Olga's aisle is numbered higher than either of Kurt's aisles, and lower than at least one of Larisa's.
For this particular question, we are given an additional constraint:
8. Larisa's aisles are separated by the maximum possible number of aisles.
By (6) we know that exactly one of Larisa's aisles is an end aisle. Therefore if her aisles are separated by the maximum number possible, we know that her other aisle is next to the end; i.e., her two aisles are either 1 and 8 or 2 and 9:
L _ _ _ _ _ _ L _
or
_ L _ _ _ _ _ _ L
However, we know from (2) that Kurt stocks aisle 2. Therefore Larisa's aisles are 1 and 8;
L K _ _ _ _ _ L _
We can also determine who stocks aisle 9 as follows. First, it is not Larisa, because we have already determined her two aisles. Condition (5) tells us that it is neither Kurt nor Manny, since Kurt's remaining aisle and Manny's two must appear in the configuration MKM. Finally, condition (7) tells us that it is not Olga, since her aisle must have a lower number than at least one of Larisa's. Therefore, by elimination, we have determined that Jill stocks aisle 9:
L K _ _ _ _ _ L J
Note that at this point we have eliminated answers [C], [D], and [E].
Now, suppose that answer [B] were correct. Since this is a hypothetical, we will use small letters to fill the resulting information into the chart (remember that Manny's aisles are one apart, and Kurt stocks the aisle between them):
L K _ _ m k m L J
This is not a valid configuration! There is no possible position for Olga's aisle that places it above both of Kurt's, so condition (7) will be violated. Therefore we have eliminated [B], leaving [A] as the only possible answer.
To verify that [A] is correct, consider the following configuration:
L K M K M J O L J
This configuration satisfies [A] as well as all of the conditions of the problem.
Hope this helps! Please post again if you have further questions.
Best,
Lyn
To see why (A) is the correct answer, let's start by numbering the conditions for easy reference:
1. Olga stocks exactly one aisle.
2. Kurt stocks aisle 2.
3. Manny does not stock aisle 1.
4. Jill does not stock consecutive aisles.
5. Kurt stocks the only aisle between the two aisles Manny stocks.
6. Exactly one of Larisa's aisles is an end aisle.
7. Olga's aisle is numbered higher than either of Kurt's aisles, and lower than at least one of Larisa's.
For this particular question, we are given an additional constraint:
8. Larisa's aisles are separated by the maximum possible number of aisles.
By (6) we know that exactly one of Larisa's aisles is an end aisle. Therefore if her aisles are separated by the maximum number possible, we know that her other aisle is next to the end; i.e., her two aisles are either 1 and 8 or 2 and 9:
L _ _ _ _ _ _ L _
or
_ L _ _ _ _ _ _ L
However, we know from (2) that Kurt stocks aisle 2. Therefore Larisa's aisles are 1 and 8;
L K _ _ _ _ _ L _
We can also determine who stocks aisle 9 as follows. First, it is not Larisa, because we have already determined her two aisles. Condition (5) tells us that it is neither Kurt nor Manny, since Kurt's remaining aisle and Manny's two must appear in the configuration MKM. Finally, condition (7) tells us that it is not Olga, since her aisle must have a lower number than at least one of Larisa's. Therefore, by elimination, we have determined that Jill stocks aisle 9:
L K _ _ _ _ _ L J
Note that at this point we have eliminated answers [C], [D], and [E].
Now, suppose that answer [B] were correct. Since this is a hypothetical, we will use small letters to fill the resulting information into the chart (remember that Manny's aisles are one apart, and Kurt stocks the aisle between them):
L K _ _ m k m L J
This is not a valid configuration! There is no possible position for Olga's aisle that places it above both of Kurt's, so condition (7) will be violated. Therefore we have eliminated [B], leaving [A] as the only possible answer.
To verify that [A] is correct, consider the following configuration:
L K M K M J O L J
This configuration satisfies [A] as well as all of the conditions of the problem.
Hope this helps! Please post again if you have further questions.
Best,
Lyn