In a school function ceremony, seven students, Amy, Bob, Chad, Dom, Elisa, Fischer, and Grant have to deliver their performances in seven consecutive slots, not necessarily in the order of their given names. The following information is known about the order in which the students perform:
Chad performs immediately before Dom
Grant performs sometime after Chad
There are exactly two performances made between the performances of Amy and Elisa
If it is known that Bob performs before Fischer, for which of the following positions of Amy can the exact order of all the performers be determined?
Select an option, then click Submit answer.
Reference / correct answer:
None of the seven positions
However, there are two possibilities: A performs before E OR E performs before
Here, we need to find the position of Amy such that the exact order of all the performers can be determined; and to answer that we have another piece of information – Bob performs before Fischer.
We know that there are exactly two performers between A and
E. However, there are two possibilities: A performs before E OR E performs before
A. Thus, we have multiple scenarios as shown below:
Case I: A in the 1st place
Here, clearly, C and D can be either 2nd and 3rd, or 5th and 6th without violating any conditions given. Also, in each case, B can come before
F. Thus, the exact order cannot be determined. Thus, A cannot be in the 1st slot (though the answer options did not have this slot at all, we still did this to show why the 1st slot is not a viable option).
Case II: A in the 2nd place
Here, there are multiple possibilities for B, F and G:
B in 1st slot, F in 6th and G in 7th
B in 1st slot, G in 6th and F in 7th
Thus, the exact order cannot be determined. Case III: A in the 3rd place
Here, clearly, C and D can be either 1st and 2nd, or 4th and 5th. Thus, the exact order cannot be determined.
Case IV: A in the 4th place
Here too, the positions of C and D cannot be uniquely determined. In fact, the position of E is also doubtful. Thus, the exact order cannot be determined.
Case V: A in the 5th place
Here, the position of G cannot be uniquely determined. Thus, the exact order cannot be determined.
Case VI: A in the 6th place
Here too, the positions of C and D cannot be uniquely determined. Thus, the exact order cannot be determined. Case VII: A in the 7th place
Here too, the positions of C and D cannot be uniquely determined. Thus, the exact order cannot be determined.
General
Let us denote the seven slots using the numbers 1 through 7 as shown below:
We need to fill in the names of the performers in each slot depending on the information provided.
Let us name the performers Amy, Bob, Chad, Dom, Elisa, Fischer, and Grant as A, B, C, D, E, F and G.
Let us look at the information given in the question stem and see what we have got:
1. Since Chad performs immediately before Dom, we can write "CD" as an element implying that there is no one else performing between them.
2. Since Grant performs sometime after Chad, and Chad and Dom are consecutive performers, Grant must perform after Dom as well. Thus, we can represent theinformation as shown below:
The "…" above implies that there could be none or at least 1 performer between D and G.
3. There are exactly two performers between Amy and Elisa. This information can be represented as shown below:
Thus, we see that the above information is NOT sufficient to assign even one of the performers to his/her corresponding slot number. This implies that there would possibly be multiple solutions to the arrangements of the performers. Thus, in order to solve the questions, we would need to use the information given in the questions.
