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Manager  Joined: 25 Apr 2014
Posts: 105
Mathematics, physics, and chemistry books are stored on a li  [#permalink]

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5 00:00

Difficulty:   75% (hard)

Question Stats: 54% (02:39) correct 46% (03:07) wrong based on 99 sessions

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Mathematics, physics, and chemistry books are stored on a library shelf that can accommodate 25 books. Currently, 20% of the shelf spots remain empty. There are twice as many mathematics books as physics books and the number of physics books is 4 greater than that of the chemistry books. Ricardo selects 1 book at random from the shelf, reads it in the library, and then returns it to the shelf. Then he again chooses 1 book at random from the shelf and checks it out in order to read at home. What is the probability Ricardo reads 1 book on mathematics and 1 on chemistry?

A) 3%
B) 6%
C) 12%
D) 20%
E) 24%
Veritas Prep GMAT Instructor D
Joined: 16 Oct 2010
Posts: 9238
Location: Pune, India
Re: Mathematics, physics, and chemistry books are stored on a li  [#permalink]

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2
1
maggie27 wrote:
Mathematics, physics, and chemistry books are stored on a library shelf that can accommodate 25 books. Currently, 20% of the shelf spots remain empty. There are twice as many mathematics books as physics books and the number of physics books is 4 greater than that of the chemistry books. Ricardo selects 1 book at random from the shelf, reads it in the library, and then returns it to the shelf. Then he again chooses 1 book at random from the shelf and checks it out in order to read at home. What is the probability Ricardo reads 1 book on mathematics and 1 on chemistry?

A) 3%
B) 6%
C) 12%
D) 20%
E) 24%

Shelf can accomodate 25 books but 20% of it is empty so there are in all 20 books.
If no of Chem books = x, number of Physics book = x+4, number of Math books = 2(x+4)

x + x+4 + 2(x+4) = 4x + 12 = 20
x = 2

Chem books = 2, Phy books = 6, Math books = 12

Probability of picking a Math book = 12/20
Probability of picking a Chem book = 2/20

Total Probability = Pick Math first and then Chem + Pick Chem first and then Math
= (12/20) * (2/20) + (2/20) * (12/20) = 12/100 = 12%
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Math Expert V
Joined: 02 Sep 2009
Posts: 55271
Re: Mathematics, physics, and chemistry books are stored on a li  [#permalink]

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maggie27 wrote:
Mathematics, physics, and chemistry books are stored on a library shelf that can accommodate 25 books. Currently, 20% of the shelf spots remain empty. There are twice as many mathematics books as physics books and the number of physics books is 4 greater than that of the chemistry books. Ricardo selects 1 book at random from the shelf, reads it in the library, and then returns it to the shelf. Then he again chooses 1 book at random from the shelf and checks it out in order to read at home. What is the probability Ricardo reads 1 book on mathematics and 1 on chemistry?

A) 3%
B) 6%
C) 12%
D) 20%
E) 24%

VERITAS PREP OFFICIAL SOLUTION:

The first phase of this problem requires you to determine how many mathematics and chemistry books are even on the shelf. To do so, you have the equations:

m + p + c = 20 (since 4/5 of the 25 spots are full of books)

m = 2p

p = 4 + c

From that, you can use Substitution to get everything down to one variable (and since all three equations include p, that's probably the easiest to work on). If

c = p - 4

m = 2p

p = p

Then (p - 4) + 2p + p = 20, so 4p = 24 and p = 6. That means that there are 12 math, 6 physics, and 2 chemistry books on the shelf.

Here's where this becomes a probability problem: the probability of reading math, then chemistry is (12/20)(2/20), which simplifies to 6/100. That makes B a tempting answer, but keep in mind that Ricardo could read them in the opposite order, chemistry then math. In that case, the probability works out to the same, but since 6% of the time he reads C then M and 6% of the time he reads M then C, then 12% of the time his outcome is that he reads one of each, so the answer is C.
_________________ Re: Mathematics, physics, and chemistry books are stored on a li   [#permalink] 30 Dec 2017, 01:12
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# Mathematics, physics, and chemistry books are stored on a li

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