Problem Solving

Dear friends,

This is a question which I have not been able to solve.....



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

Thanks for your help!

Vasudha wrote:Dear friends,

This is a question which I have not been able to solve.....



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

Thanks for your help!

For such a q u need to think of the worst case scenario..... so what is the worst case scenario here.... it will be something like this... i first pick the 50 books of botany, then i pick the next 65 zoology books, then i pick the 50 books of geology..... so these add up to 165..... then i pick 79 physics books and another 79 books on chemistry.... the sum uptil now is 323... the next book i pick up will ensure that there are 80 books on the same science ( it doesnt matter which book i pick up physics or chemistry )... so the answer is 324...

now it need not be that u pick the book in the order i mentioned it culd be in any order or they culd also be mixed together... the only thing that matters is bfor the last book is picked, i pick all the books on botany,geology and zoology and 79 books each on physics and chemistry...

i hope u understand the explanation ... i am very bad at explaining things..

Thanks Gabriel


You are right. That is the right answer. I understand your explanation. It seems a lot easier now. Thanks

I used the process of elimination to find the answer.....


Consider that you keep on moving books without moving 80 from the same group. Since subjects Botany, Zoology and Geology don't even have 80 books - consider that you move them first.

Hence you move 50+65+50 = 165 books. So you've moved 165 without 80 from 1 group. Thus rule our choices A, B and C. Now consider that you move 285 - 165 i.e. 120 more books. Even here you could have moved 50 from physics and say 70 from chemistry. Hence still we have no gurantee. So even Choice D is out.

Thus by Process of Elimination its Choice E.

Hi,

I would like to know why you picked 79 books on physics and chemistry....


the only thing that matters is bfor the last book is picked, i pick all the books on botany,geology and zoology and 79 books each on physics and chemistry...