Problem Solving

BTGModeratorVI wrote: ↑

Tue Feb 18, 2020 10:58 am

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

Source: GMAT paper tests
Answer: E

Since 80 books must be of same science, they must be either from physics or chemistry.

Since this is a must be true question, we must ensure in all circumstances, we get 80 books of same science.

Say we get 50 books on botany, 65 books on zoology, 50 books on geology, 79 books on physics, and 79 books on chemistry. In this case, we would have removed 50 + 65 + 50 + 79*2 = 323 books.

The next book, be it physics or chemistry will make 80 books on the same science. So, 323 + 1 = 324 books must be removed to ensure that 80 of the books removed are on the same science

The correct answer: E

Hope this helps!

-Jay
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BTGModeratorVI wrote: ↑

Tue Feb 18, 2020 10:58 am

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

Source: GMAT paper tests
Answer: E

Let's see what happens when the following books are removed:
50 on botany
65 on zoology
79 on physics
50 on geology
79 on chemistry
TOTAL = 323

At this point, we do NOT have 80 of any one science topic.
However, if we remove one of the remaining books (which are either physics books or chemistry books), we will certainly have 80 books on one science topic.
In other words, if we remove 324 books, we can be certain of having 80 books on one science topic

Answer: E

Cheers,
Brent

BTGModeratorVI wrote: ↑

Tue Feb 18, 2020 10:58 am

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

Source: GMAT paper tests
Answer: E

Let’s assume the worst case scenario: all 50 botany, all 50 geology, and all 65 zoology books are removed, and 79 physics and 79 chemistry books are removed. We see that we have 50 x 2 + 65 + 79 x 2 = 323 books removed, but we still don’t have 80 books of one science removed. However, if we remove one more book, which must be either a physics book or a chemistry book, we will have 80 books of one science removed. Thus we need to remove 323 + 1 = 324 books.

Answer: E