Hey guys,
Nice use of the answer choices by Sanju - don't let me step on your toes, but I figured I'd chime in with an explanation of how to just purely solve this, too, since I've seen a few variations of "how many are necessary to guarantee/ensure that X condition is met" questions.
In order to guarantee that we get 80 of the same science, we have to look at the "worst case scenario" of continuing to draw books and never finding an 80th match until it's absolutely certain.
Well, that means that we draw the maximum allowable number of each books until the last book must be an 80th copy. So, we would end up with 79 of each book for which there are even 79 possible books, and the maximum number of all of the other books, until the last draw is bound to be the 80th copy of one.
We have 50 botany, 65 zoology, and 50 geology - none of those is even a possibility to hit 80, so our "worst case scenario" should include all of those, or a total of 165 books.
Then, we'd want to have the max number of each of physics and chemistry before getting to 80, so we'd have 79 of each of those, or a total of 158 books.
At this point, with 165 + 158 = 323 books without an 80th copy, the last draw is guaranteed to get us our 80th match, and so we add one for that last draw to get to 324 books.
To summarize, if the question asks you to guarantee a certain outcome, you can calculate the maximum number of outcomes before that final one is met - just max out all of the possibilities until you have no choice but to get what they ask for.
Brian Galvin
GMAT Instructor
Chief Academic Officer
Veritas Prep
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