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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
A) 115
B) 139
C) 140
D) 148
E) 149
28 Sep 2018, 01:22
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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.
General Discussion
23 Sep 2018, 08:26
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Harshgmat
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) 65
C) 140
D) 148
E) 149
A) 115
B) 65
C) 140
D) 148
E) 149
Sir, Kindly solve this.
