Prisoners

manik11 wrote:After an attempted breakout at Folsom State Prison, the warden lines the prisoners up for a headcount. (Assume the warden counts correctly and that no prisoners switch positions or leave/escape during either headcount.) When the warden counts from left to right, Gurby is the 20th prisoner counted, but when the warden counts from right to left, Gus is the 20th prisoner counted. How many prisoners are lined up for the headcount?

(1) There are 13 prisoners between Gurby and Gus.

(2) The total number of prisoners is odd.

Statement 1:
Case 1:
<--19 prisoners--> GURBY <--13 prisoners--> GUS <--19 prisoners-->
In this case
Prisoners to the left of Gurby = 19, with the result that Gurby is the 20th when the count is made from left to right.
Prisoners to the right of Gus = 19, with the result that Gus is the 20th when the count is made from right to left.
Total prisoners = 19 + Gus + 13 + Gurby + 19 = 53.

Case 2:
<--5 prisoners--> GUS <--13 prisoners--> GURBY <--5 prisoners-->
In this case:
Prisoners to the left of Gurby = 5 + Gus + 13 = 19, with the result that Gurby is the 20th when the count is made from left to right.
Prisoners to the right of Gus = 13 + Gurby + 5 = 19, with the result that Gus is the 20th when the count is made from right to left.
Total prisoners= 5 + Gus + 13 + Gurby + 5 = 25.

Since the total number of priosners can be 53 or 25, INSUFFICIENT.

Cases 1 and 2 satisfy both statements.
Thus:
Even when the statements are combined, the total number of prisoners can be 53 or 25, implying that the two statements combined are INSUFFICIENT.

The correct answer is E.

I wrote this question, so I shouldn't rehash my own solution; let me suggest something else. One trick on test day that might help is trying the scenario with a smaller number of prisoners to see how the lineup behaves.

For instance, suppose that we have Gus third from the left, Gurby third from the right, and one prisoner between them. Then we could have

Gurby A Gus

or

A B Gus C Gurby D E

This generalizes reasonably well to larger sets, so in a pinch we can use it to see that the problem is unlikely to be solvable, given this information.

Why in case two the number of prisoners is 5 not 6?

GMATGuruNY wrote:

manik11 wrote:After an attempted breakout at Folsom State Prison, the warden lines the prisoners up for a headcount. (Assume the warden counts correctly and that no prisoners switch positions or leave/escape during either headcount.) When the warden counts from left to right, Gurby is the 20th prisoner counted, but when the warden counts from right to left, Gus is the 20th prisoner counted. How many prisoners are lined up for the headcount?

(1) There are 13 prisoners between Gurby and Gus.

(2) The total number of prisoners is odd.

Statement 1:
Case 1:
<--19 prisoners--> GURBY <--13 prisoners--> GUS <--19 prisoners-->
In this case
Prisoners to the left of Gurby = 19, with the result that Gurby is the 20th when the count is made from left to right.
Prisoners to the right of Gus = 19, with the result that Gus is the 20th when the count is made from right to left.
Total prisoners = 19 + Gus + 13 + Gurby + 19 = 53.

Case 2:
<--5 prisoners--> GUS <--13 prisoners--> GURBY <--5 prisoners-->
In this case:
Prisoners to the left of Gurby = 5 + Gus + 13 = 19, with the result that Gurby is the 20th when the count is made from left to right.
Prisoners to the right of Gus = 13 + Gurby + 5 = 19, with the result that Gus is the 20th when the count is made from right to left.
Total prisoners= 5 + Gus + 13 + Gurby + 5 = 25.

Since the total number of priosners can be 53 or 25, INSUFFICIENT.

Cases 1 and 2 satisfy both statements.
Thus:
Even when the statements are combined, the total number of prisoners can be 53 or 25, implying that the two statements combined are INSUFFICIENT.

The correct answer is E.

Amrabdelnaby wrote:Why in case two the number of prisoners is 5 not 6?

Because Gurby and Gus count as prisoners too, so you have 13+5+1 (the other prisoner), for a total of 20.