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# At a certain arena, with five levels, level I has 30 vacant

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Manager
Joined: 14 Oct 2008
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At a certain arena, with five levels, level I has 30 vacant [#permalink]

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01 Nov 2008, 06:49
This topic is locked. If you want to discuss this question please re-post it in the respective forum.

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

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Joined: 30 Jun 2008
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01 Nov 2008, 07:07
gameCode wrote:
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

is it A?

I took the 3 levels with max num of vacant seats .... 45 + 40 + 30 = 115
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Manager
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01 Nov 2008, 07:59
That is what i got the answer, but its wrong . The QA is 148.
Here's the explanation.( from kaplan )

You may have gotten tripped up by the wording on this one. The question is not asking for the minimum possible number of seats filled that could completely fill 3 levels, it's asking for the minimum possible number of seats that guarantees that 3 levels will be completely filled. So, first figure out the maximum number of seats that can be filled without completely filling any of the five levels. That means filling all but one vacant seat in each level, that is, 29 in level I, 44 in level II, 39 in level III, 24 in level IV, and 9 in level V, for a total of 145 vacant seats filled. Since there is only one vacant seat in each section now, filling in one more seat will necessarily completely fill a level. Filling in a second additional seat will complete a second level, and filling in a third will complete a third level. So filling in 145 + 3 = 148 seats will ensure that 3 levels are completely filled.

The wordings in this one are tricky i must say, i would have never got this QA on my own !

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VP
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01 Nov 2008, 08:14
gameCode wrote:
That is what i got the answer, but its wrong . The QA is 148.
Here's the explanation.( from kaplan )

You may have gotten tripped up by the wording on this one. The question is not asking for the minimum possible number of seats filled that could completely fill 3 levels, it's asking for the minimum possible number of seats that guarantees that 3 levels will be completely filled. So, first figure out the maximum number of seats that can be filled without completely filling any of the five levels. That means filling all but one vacant seat in each level, that is, 29 in level I, 44 in level II, 39 in level III, 24 in level IV, and 9 in level V, for a total of 145 vacant seats filled. Since there is only one vacant seat in each section now, filling in one more seat will necessarily completely fill a level. Filling in a second additional seat will complete a second level, and filling in a third will complete a third level. So filling in 145 + 3 = 148 seats will ensure that 3 levels are completely filled.

The wordings in this one are tricky i must say, i would have never got this QA on my own !

I get it now .... we missed the trick
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VP
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01 Nov 2008, 10:19
gameCode wrote:
That is what i got the answer, but its wrong . The QA is 148.
Here's the explanation.( from kaplan )

You may have gotten tripped up by the wording on this one. The question is not asking for the minimum possible number of seats filled that could completely fill 3 levels, it's asking for the minimum possible number of seats that guarantees that 3 levels will be completely filled. So, first figure out the maximum number of seats that can be filled without completely filling any of the five levels. That means filling all but one vacant seat in each level, that is, 29 in level I, 44 in level II, 39 in level III, 24 in level IV, and 9 in level V, for a total of 145 vacant seats filled. Since there is only one vacant seat in each section now, filling in one more seat will necessarily completely fill a level. Filling in a second additional seat will complete a second level, and filling in a third will complete a third level. So filling in 145 + 3 = 148 seats will ensure that 3 levels are completely filled.

The wordings in this one are tricky i must say, i would have never got this QA on my own !

OOOO....that's cool....

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01 Nov 2008, 12:00
gameCode wrote:
That is what i got the answer, but its wrong . The QA is 148.
Here's the explanation.( from kaplan )

You may have gotten tripped up by the wording on this one. The question is not asking for the minimum possible number of seats filled that could completely fill 3 levels, it's asking for the minimum possible number of seats that guarantees that 3 levels will be completely filled. So, first figure out the maximum number of seats that can be filled without completely filling any of the five levels. That means filling all but one vacant seat in each level, that is, 29 in level I, 44 in level II, 39 in level III, 24 in level IV, and 9 in level V, for a total of 145 vacant seats filled. Since there is only one vacant seat in each section now, filling in one more seat will necessarily completely fill a level. Filling in a second additional seat will complete a second level, and filling in a third will complete a third level. So filling in 145 + 3 = 148 seats will ensure that 3 levels are completely filled.

The wordings in this one are tricky i must say, i would have never got this QA on my own !

I do not think the OE is pretty much convincing cuz the question says "seats are filled randomly". if seats are filled randomly, then there is no guarantee that after 148 seats 3rd level will be filled. The next seat could be from 4th or 5th floor. So only after filling 149 seats, the next fill guarantee that 3rd level will certainly be filled.

So we need 150 seats to be filled to gurantee the 3rd level filled..

KAPLAN problems? Kaplan and PTR have a record of having ambigious and flawed questions..

Code:
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 [b][color=#FF0080]vacant seats are filled randomly[/color][/b], 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

If answer choices are as straight as 115, they are not correct in most of the cases. We need a second thought in that case.
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01 Nov 2008, 13:42
GMAT TIGER wrote:
I do not think the OE is pretty much convincing cuz the question says "seats are filled randomly". if seats are filled randomly, then there is no guarantee that after 148 seats 3rd level will be filled. The next seat could be from 4th or 5th floor. So only after filling 149 seats, the next fill guarantee that 3rd level will certainly be filled.

So we need 150 seats to be filled to gurantee the 3rd level filled..

KAPLAN problems? Kaplan and PTR have a record of having ambigious and flawed questions..

If answer choices are as straight as 115, they are not correct in most of the cases. We need a second thought in that case.

The question askes for "three levels" and not "third level".

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01 Nov 2008, 13:54
scthakur wrote:
GMAT TIGER wrote:
I do not think the OE is pretty much convincing cuz the question says "seats are filled randomly". if seats are filled randomly, then there is no guarantee that after 148 seats 3rd level will be filled. The next seat could be from 4th or 5th floor. So only after filling 149 seats, the next fill guarantee that 3rd level will certainly be filled.

So we need 150 seats to be filled to gurantee the 3rd level filled..

KAPLAN problems? Kaplan and PTR have a record of having ambigious and flawed questions..

If answer choices are as straight as 115, they are not correct in most of the cases. We need a second thought in that case.

The question askes for "three levels" and not "third level".

Agreed..

Huuuhhh.... 3 levels, 3rd and level III.

3 levels is killer.
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Kudos [?]: 843 [0], given: 19

Re: probability and statistics   [#permalink] 01 Nov 2008, 13:54
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