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Of the science books in a certain supply room, 50 are on [#permalink]

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22 Mar 2008, 15:50

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Of the science books in a certain supply room, 50 are on botany, 65 are on zoology, 90 are on physics. 50 are on geology, and 110 are on chemistry. If science books are removed randomly from the supply room, how many must be removed to ensure that 80 of the books removed are on the same science? (A) 81 (B) 159 (C) 166 (D) 285 (E) 324

Of the science books in a certain supply room, 50 are on botany, 65 are on zoology, 90 are on physics. 50 are on geology, and 110 are on chemistry. If science books are removed randomly from the supply room, how many must be removed to ensure that 80 of the books removed are on the same science? (A) 81 (B) 159 (C) 166 (D) 285 (E) 324

From the question if we need 80 of one kind, botany, zoology and geology are out of the race. Physics and Chemistry are the ones remaining. if I remove 80 books of physics out of 90 then I have 10 remaining. Similarly if I removed 80 chemistry books then I have 30 remaining. So I add up the 10 + 30 = 40 books. However if I got 80 of the physics books then I have 31 of the chemistry books left and vice versa. So the total is 10 +31 = 41 or 11 + 30 = 41.

Of the science books in a certain supply room, 50 are on botany, 65 are on zoology, 90 are on physics. 50 are on geology, and 110 are on chemistry. If science books are removed randomly from the supply room, how many must be removed to ensure that 80 of the books removed are on the same science? (A) 81 (B) 159 (C) 166 (D) 285 (E) 324

From the question if we need 80 of one kind, botany, zoology and geology are out of the race. Physics and Chemistry are the ones remaining. if I remove 80 books of physics out of 90 then I have 10 remaining. Similarly if I removed 80 chemistry books then I have 30 remaining. So I add up the 10 + 30 = 40 books. However if I got 80 of the physics books then I have 31 of the chemistry books left and vice versa. So the total is 10 +31 = 41 or 11 + 30 = 41.

Subtract the total 365 - 41 = 324. Answer is E.

You are correct!

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how did you get 41? could you please clarify "if I got 80 of the physics books then I have 31 of the chemistry books left and vice versa. So the total is 10 +31 = 41 or 11 + 30 = 41."

i don't understand the above explanation also. Using pigeon hole theory, left Phy and Chem, need to take out to ensure at least 80 bks on same topic -> 79+80=159 plus the rest get E

I definitely dont understand the logic of this kind problem. Can you guys mind giving detail of this logic? Your support is appreciated!
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Of the science books in a certain supply room, 50 are on botany, 65 are on zoology, 90 are on physics. 50 are on geology, and 110 are on chemistry. If science books are removed randomly from the supply room, how many must be removed to ensure that 80 of the books removed are on the same science? (A) 81 (B) 159 (C) 166 (D) 285 (E) 324

E

When you asked "how many must be removed," it means the same thing as "how many must you takeout to GUARANTEE that 80 books on the same science" are removed.

In order for there to be a GUARANTEE that you will get 80 books on the same science (either physics or chemistry) you must take out 50 + 50 + 65 + 79 (of either physics or chem) + 80 (either physics or chem) = 324.

When you take out 79 of either physics or chem, the next 80 GUARANTEES that you will have 80 books on the same science.