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.
OA : E
Source : Veritas Prep
Prisoners
This topic has expert replies
- GMATGuruNY
- GMAT Instructor
- Posts: 15539
- Joined: Tue May 25, 2010 12:04 pm
- Location: New York, NY
- Thanked: 13060 times
- Followed by:1906 members
- GMAT Score:790
Statement 1: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.
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.
Private tutor exclusively for the GMAT and GRE, with over 20 years of experience.
Followed here and elsewhere by over 1900 test-takers.
I have worked with students based in the US, Australia, Taiwan, China, Tajikistan, Kuwait, Saudi Arabia -- a long list of countries.
My students have been admitted to HBS, CBS, Tuck, Yale, Stern, Fuqua -- a long list of top programs.
As a tutor, I don't simply teach you how I would approach problems.
I unlock the best way for YOU to solve problems.
For more information, please email me (Mitch Hunt) at [email protected].
Student Review #1
Student Review #2
Student Review #3
Followed here and elsewhere by over 1900 test-takers.
I have worked with students based in the US, Australia, Taiwan, China, Tajikistan, Kuwait, Saudi Arabia -- a long list of countries.
My students have been admitted to HBS, CBS, Tuck, Yale, Stern, Fuqua -- a long list of top programs.
As a tutor, I don't simply teach you how I would approach problems.
I unlock the best way for YOU to solve problems.
For more information, please email me (Mitch Hunt) at [email protected].
Student Review #1
Student Review #2
Student Review #3
-
- GMAT Instructor
- Posts: 2630
- Joined: Wed Sep 12, 2012 3:32 pm
- Location: East Bay all the way
- Thanked: 625 times
- Followed by:119 members
- GMAT Score:780
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.
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.
-
- Master | Next Rank: 500 Posts
- Posts: 137
- Joined: Fri Nov 13, 2015 11:01 am
- Thanked: 1 times
- Followed by:2 members
Why in case two the number of prisoners is 5 not 6?
GMATGuruNY wrote:Statement 1: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.
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.
GMAT/MBA Expert
- [email protected]
- Elite Legendary Member
- Posts: 10392
- Joined: Sun Jun 23, 2013 6:38 pm
- Location: Palo Alto, CA
- Thanked: 2867 times
- Followed by:511 members
- GMAT Score:800
Hi All,
There is a 'visual component' to certain types of GMAT questions, so it often helps to draw pictures so that you can physically see the possibilities. You could probably answer this type of question faster using that type of approach (than say, trying to work algebraically).
There's a brief discussion of this question here:
https://www.beatthegmat.com/prisoners-t287172.html
GMAT assassins aren't born, they're made,
Rich
There is a 'visual component' to certain types of GMAT questions, so it often helps to draw pictures so that you can physically see the possibilities. You could probably answer this type of question faster using that type of approach (than say, trying to work algebraically).
There's a brief discussion of this question here:
https://www.beatthegmat.com/prisoners-t287172.html
GMAT assassins aren't born, they're made,
Rich
-
- GMAT Instructor
- Posts: 2630
- Joined: Wed Sep 12, 2012 3:32 pm
- Location: East Bay all the way
- Thanked: 625 times
- Followed by:119 members
- GMAT Score:780
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.