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(30-1) + (45-1) + (40-1) + (25-1) + (10-1) + 3 = 148
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(30-1) + (45-1) + (40-1) + (25-1) + (10-1) + 3 = 148


Hi, please explain in detail. Am lost.
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pandeyashwin
(30-1) + (45-1) + (40-1) + (25-1) + (10-1) + 3 = 148


Hi, please explain in detail. Am lost.

"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"

First thing that comes to mind is simply select level 1 , 4, 5 but the seats are filled randomly so you cannot say with 100% certainty that it'll be the case.

So what we do is reduce the seats in all the levels by 1.
So Level 1 = 30-1 = 29 seats ; level 2 = 44 ; level 3 = 39 ; level 4 = 24 ; level 5 = 9.

Now all the levels are on the verge of being filled. Now when the next 3 seats are selected , it'll ensure that 3 levels are completely filled.
(29 + 44 + 39 + 24 + 9 ) + 3 = 148
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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) 65
C) 140
D) 148
E) 149

The seats are to be filled randomly. We need 3 levels to be completely filled. We are looking for the worst case scenario - when will we be sure that 3 levels are completely filled?

Think of the worst case - Each of the 5 levels are filled to (Capacity - 1). Then the last 3 people take seats in 3 levels to finally have 3 levels completely full.
If another 2 people come, all seats would be occupied.

So we are looking for (total seats - 2) = (30 + 45 + 40 + 25 + 10 - 2) = 148

Answer (D)
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Hello from the GMAT Club BumpBot!

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