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hwiya320
Joined: 21 Sep 2008
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Location: Atlanta, Georgia
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20 Nov 2008, 21:35
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At a certain arena, with five levels, level I has 30 vacant seats, level II has 45 vacant seats, level III has 40 vacant seats, level IV has 25 vacant seats and level V has 10 vacant seats. If vacant seats are filled randomly, what is the minimum number of seats that must be filled to ensure that 3 levels are completely filled?
a 115
b 139
c 140
d 148
e 149
any good explanation?
From: Kaplan PS: Statistics and Probability, Part 2 - Challenge Question:4 of 10
a 115
b 139
c 140
d 148
e 149
any good explanation?
From: Kaplan PS: Statistics and Probability, Part 2 - Challenge Question:4 of 10
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20 Nov 2008, 22:34
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D. 148
here's how:
consider it this way, we have only 2 rows having 10, 15 seats respectively and we have to assure that one row is filled up completely.
if we have 15 people, they can seat in 8 + 7 seats
if we have 20 people, they can seat in 8+ 12 seats
if we have 22 people still they can seat in 9+ 13 seats
if we have 23 people still they can seat in 9 + 14 seats
This is the saturation point, addition of one person to this will make either row full.
so if we have 24 ppl, one row must be full
Observe that saturation point is reached when we have
(capacity of row - 1 person) in "each" row.
or (total seats - #of rows) people
&
addition of every one person gaurantees that additional one row is getting full.
here we have 30 45 40 25 10 = 150 total seats.
we have 5 rows => 150 - 5 = 145 is saturating point.
& add one person and it gaurantees that one row is full.
we have to assure that 3 rows are full.
so we have to add 3 people to saturating point
145 + 3 = 148 minimum people will be needed
here's how:
consider it this way, we have only 2 rows having 10, 15 seats respectively and we have to assure that one row is filled up completely.
if we have 15 people, they can seat in 8 + 7 seats
if we have 20 people, they can seat in 8+ 12 seats
if we have 22 people still they can seat in 9+ 13 seats
if we have 23 people still they can seat in 9 + 14 seats
This is the saturation point, addition of one person to this will make either row full.
so if we have 24 ppl, one row must be full
Observe that saturation point is reached when we have
(capacity of row - 1 person) in "each" row.
or (total seats - #of rows) people
&
addition of every one person gaurantees that additional one row is getting full.
here we have 30 45 40 25 10 = 150 total seats.
we have 5 rows => 150 - 5 = 145 is saturating point.
& add one person and it gaurantees that one row is full.
we have to assure that 3 rows are full.
so we have to add 3 people to saturating point
145 + 3 = 148 minimum people will be needed
Archived Topic
Hi there,
This topic has been closed and archived due to inactivity or violation of community quality standards. No more replies are possible here.
Where to now? Join ongoing discussions on thousands of quality questions in our Quantitative Questions Forum
Still interested in this question? Check out the "Best Topics" block above for a better discussion on this exact question, as well as several more related questions.
Thank you for understanding, and happy exploring!
