Problem Solving

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


OA after few posts.
Please explain the working

Total Books:

Botany: 50
Zoology: 65
geology: 50
physics: 90
chemistry : 110

If the books are removed randomly, following 'could' be a possible outcome of the first 323 draws:


Botany: 50
Zoology: 65
geology: 50
physics: 79
chemistry : 79

The next book would be either Physics or Chemistry making the total number 80. So, Answer is E

agoyal2 wrote:Total Books:

Botany: 50
Zoology: 65
geology: 50
physics: 90
chemistry : 110

If the books are removed randomly, following 'could' be a possible outcome of the first 323 draws:


Botany: 50
Zoology: 65
geology: 50
physics: 79
chemistry : 79

The next book would be either Physics or Chemistry making the total number 80. So, Answer is E

Anshul,

Could you please elaborate the explanation ?

Pranay

@agoyal2
I didn't get your explanation. Please elaborate.

The question asks how many books must be removed so that the 80 of the books removed are from the same science. So, you are removing books randomly with no selection criteria and you want to know after removing how many books, you will definitely have 80 books of the same subject.

So, when you start looking at the choices and suppose you just remove 81, they could be of botany and zoology. The library does not have 80 books on these subjects. Similarly if you pick say, 284, they could be Botany: 50,
Zoology: 65, geology: 50, physics: 60, chemistry : 59 (or any other combination), still you dont have 80 of the same subject.

Once you withdraw 324 books, you can be absolutely sure that you have 80 books from one subject. This is because there is no combination possible with 324 books where you can avoid putting the 80 in Physics or Chemistry.

Makes sense? I know this is a little confusion. If you still did not get it then I will request some of the experts in this forum to explain a better method of doing it.

Whats the OA?

The key-word of the question is "to ensure".

We should consider the most pessimistic case.

I didn't see the solution at a glance, but the process of agoyal2 seems to be the one.

OA?

I could see some light now.
Thanks agoyal2

OA is indeed E

agoyal2 wrote:The question asks how many books must be removed so that the 80 of the books removed are from the same science. So, you are removing books randomly with no selection criteria and you want to know after removing how many books, you will definitely have 80 books of the same subject.

So, when you start looking at the choices and suppose you just remove 81, they could be of botany and zoology. The library does not have 80 books on these subjects. Similarly if you pick say, 284, they could be Botany: 50,
Zoology: 65, geology: 50, physics: 60, chemistry : 59 (or any other combination), still you dont have 80 of the same subject.

Once you withdraw 324 books, you can be absolutely sure that you have 80 books from one subject. This is because there is no combination possible with 324 books where you can avoid putting the 80 in Physics or Chemistry.

Makes sense? I know this is a little confusion. If you still did not get it then I will request some of the experts in this forum to explain a better method of doing it.

Whats the OA?

agoyal2,
This is a nice explanation, but I still have question about why NOT [D]?
B=50 Z=65 P=90 G=50 C=110

285 randomly drawn, which means that (50+65+80+50+40) = 285 are drawn and as a result we can see that 80 books from one subject like that of Physics.

So this could also be a probable answer!