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# Maths, Physics and chemistry books are stored on a library

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Maths, Physics and chemistry books are stored on a library [#permalink]

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26 May 2008, 11:01
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Maths, 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 maths books as physics books and the number of physics books is 4 greater than that of chemistry books. Among all the books, 12 books are soft cover and the remaining are hard-cover. If there are a total of 7 hard-cover books among the maths and physics books. What is the probability, that a book selected at random is either a hard cover book or a chemistry book?

A. 1/10
B. 3/20
C. 1/5
D. 1/4
E. 9/20

[Reveal] Spoiler:
We know that M = 2P
P = 4 + C
M = 8+2C

8 + 2c + 4 + c + c = 20
4c + 12 = 20
4c = 8
c = 2 , P = 6, M = 12

Please assist further. Thanks
[Reveal] Spoiler: OA

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Last edited by VeritasPrepKarishma on 02 Apr 2014, 21:09, edited 3 times in total.
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26 May 2008, 11:24
Maths, Physics and chemistry books are stored on a library shelf that can accomodate 25 books. Currently, 20% of the shelf spots remain empty. There are twice as many maths books as physics books and the number of physics books is 4 greater than that of chemistry books. Among all the books, 12 books are soft cover and the remaining are hard-cover. If there are a total of 4 hard-cover books among the maths and physics books. What is the prob, that a book selected at random is either a hard cover book or a chemistry book?

1/10
3/20
1/5
1/4
9/20

the shelf has the capacity of 25 books, 20% empty (5 books), the shelf has 20 books

Phys = 1x
Math = 2x
chem = x - 4

1x + 2x + (x - 4) = 20
4x - 4 = 20
4x = 24
x = 6
x - 4 = 2

So the shelf only has 12 math, 6 phys, 2 chem books

If there are 12 soft covers and 8 hard covers, and 4 hard covers are math/phys, then 4 hard cover must be chemistry, BUT there are only 2 chemistry books.
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02 Jan 2011, 11:19
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Maths, Physics and chemistry books are stored on a library shelf that can accomodate 25 books. Currently, 20% of the shelf spots remain empty. There are twice as many maths books as physics books and the number of physics books is 4 greater than that of chemistry books. Among all the books, 12 books are soft cover and the remaining are hard-cover. If there are a total of 7 hard-cover books among the maths and physics books. What is the prob, that a book selected at random is either a hard cover book or a chemistry book?

Chemistry books: 2
Physics books: 6
Math books: 12

Sum = 20

P(Chemistry) = 2/20 = 1/10
P(Hard cover) = 8/20 = 4/10 = 2/5

P(AuB) = P(A)+P(B)-P(AnB)

P(AnB) = P(A)*(B) = (1/10)*(2/5) = 2/50

P(AuB) = 5/50 + 20/50 - 2/50 = 23/50

P(AuB) - P(AnB) = 21/50 (since either means that we don't want both)

What is wrong here? (OA: 9/20)
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Re: Maths, Physics and chemistry books are stored on a library [#permalink]

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30 Mar 2014, 09:32
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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.

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.

With those numbers, you also know that there are 8 total hardcovers, 1 of which is chemistry. So if your goal is to get either a hardcover or a chemistry, there are 9 ways to "win" - either one of the 7 hardcovers that aren't chemistry or the two chemistry books. So out of the 20 total, 9 provide the desired outcome, making the answer E.

Note - a common trap answer here is A, as people forget that "2 chem + 8 hard" double counts the one book that is "both". Venn Diagram logic can be helpful to avoid that trap, or in cases like this with relatively small numbers it may be even more convenient to just write out the possibilities.
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30 Mar 2014, 18:44
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Mackieman wrote:

Maths, Physics and chemistry books are stored on a library shelf that can accomodate 25 books. Currently, 20% of the shelf spots remain empty. There are twice as many maths books as physics books and the number of physics books is 4 greater than that of chemistry books. Among all the books, 12 books are soft cover and the remaining are hard-cover. If there are a total of 7 hard-cover books among the maths and physics books. What is the prob, that a book selected at random is either a hard cover book or a chemistry book?

Chemistry books: 2
Physics books: 6
Math books: 12

Sum = 20

P(Chemistry) = 2/20 = 1/10
P(Hard cover) = 8/20 = 4/10 = 2/5

P(AuB) = P(A)+P(B)-P(AnB)

P(AnB) = P(A)*(B) = (1/10)*(2/5) = 2/50

P(AuB) = 5/50 + 20/50 - 2/50 = 23/50

P(AuB) - P(AnB) = 21/50 (since either means that we don't want both)

What is wrong here? (OA: 9/20)

Everything is correct except this: P(AnB) = P(A)*(B) = (1/10)*(2/5) = 2/50
P(AnB) is given by the product of individual probabilities when the events are independent.
How many Chemistry books are hardcover? There are total 8 hardcovers and 7 belong to Math and Physics. This means there is only 1 Chemistry hardcover book out of total 20 books.
So P(AnB) = 1/20

Now P(AuB) = 1/10 + 2/5 - 1/20 = 9/20
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Get started with Veritas Prep GMAT On Demand for $199 Veritas Prep Reviews Intern Joined: 27 Feb 2014 Posts: 13 Location: India Concentration: Entrepreneurship, International Business GMAT 1: 650 Q49 V30 GPA: 3.5 WE: Engineering (Computer Software) Followers: 0 Kudos [?]: 5 [0], given: 7 Re: Maths, Physics and chemistry books are stored on a library [#permalink] ### Show Tags 01 Apr 2014, 22:12 @GDR29, Thanks for the explanation but I have one doubt. We know that there are two chemistry books and there is no information like atleast each of Maths, Physics and Checmistry has to be either soft or hard covered. In such case, there will be two chemistry books which may be hard covered. Please advise. Intern Joined: 02 Apr 2014 Posts: 1 Followers: 0 Kudos [?]: 2 [2] , given: 0 Re: Maths, Physics and chemistry books are stored on a library [#permalink] ### Show Tags 02 Apr 2014, 06:22 2 This post received KUDOS Hi guys, After knowing there are 20 books on the shelve, I've just used the "Among all the books, 12 books are soft cover and the remaining are hard-cover" info. Using this info you get that 8/20 books are hard cover... and at least one book has to be chemestry, so the chances of getting either a hard cover book or a chemestry one have to be higher than 8/20 --- only alternative is E) 9/20 What do you think? Thanks! Veritas Prep GMAT Instructor Joined: 16 Oct 2010 Posts: 7119 Location: Pune, India Followers: 2132 Kudos [?]: 13632 [0], given: 222 Re: Maths, Physics and chemistry books are stored on a library [#permalink] ### Show Tags 02 Apr 2014, 21:09 nishant.1987 wrote: @GDR29, Thanks for the explanation but I have one doubt. We know that there are two chemistry books and there is no information like atleast each of Maths, Physics and Checmistry has to be either soft or hard covered. In such case, there will be two chemistry books which may be hard covered. Please advise. There is a typo in the question given. You are given that there are 12 softcover books (which means there are 8 hard cover books). You also given that 7 of the hardcover books are either Math or Physics. So there is only 1 Chemistry hard cover book. _________________ Karishma Veritas Prep | GMAT Instructor My Blog Get started with Veritas Prep GMAT On Demand for$199

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Re: Maths, Physics and chemistry books are stored on a library [#permalink]

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02 Apr 2014, 21:12
easycheesy wrote:
Hi guys,
After knowing there are 20 books on the shelve, I've just used the "Among all the books, 12 books are soft cover and the remaining are hard-cover" info. Using this info you get that 8/20 books are hard cover... and at least one book has to be chemestry, so the chances of getting either a hard cover book or a chemestry one have to be higher than 8/20 --- only alternative is E) 9/20
What do you think?
Thanks!

That's correct. Note that we do analyze the rest of the data to say that the required probability has to be greater than 8/20 since it is possible that all Chem books are hardcover and hence already a part of the 8 books. But, to say that the required probability is "greater than or equal to" 8/20, all we need is "Among all the books, 12 books are soft cover and the remaining are hard-cover".

There is only one option greater than or equal to 8/20.
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Get started with Veritas Prep GMAT On Demand for $199 Veritas Prep Reviews Intern Joined: 19 Sep 2013 Posts: 4 Location: India Concentration: Technology GRE 1: 323 Q161 V162 WE: Engineering (Computer Software) Followers: 0 Kudos [?]: 6 [0], given: 17 Re: Maths, Physics and chemistry books are stored on a library [#permalink] ### Show Tags 11 May 2014, 23:29 1 This post was BOOKMARKED alimad wrote: Maths, 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 maths books as physics books and the number of physics books is 4 greater than that of chemistry books. Among all the books, 12 books are soft cover and the remaining are hard-cover. If there are a total of 7 hard-cover books among the maths and physics books. What is the probability, that a book selected at random is either a hard cover book or a chemistry book? A. 1/10 B. 3/20 C. 1/5 D. 1/4 E. 9/20 [Reveal] Spoiler: We know that M = 2P P = 4 + C M = 8+2C 8 + 2c + 4 + c + c = 20 4c + 12 = 20 4c = 8 c = 2 , P = 6, M = 12 Please assist further. Thanks Hello I am not good at probability, but somehow got this answer right . Could you please explain if the approach used by me is correct or it was just a stroke of luck that i got it right.. Number of Math+Physics+Chemistry books= 25 - ((20/100)*25) = 20 Hence, since M=2P, P=4+C, (4+C)+C+2(4+C)=20 Therefore, M=12, C=2, P=6 Probability of getting a chemistry book = 2/20 = 1/10 Probability of getting a Hardcover book = P(getting a math or phy book) * P( getting a hardcover book from math or phy books) = (18/20 )*(7/18) = 7/20 Therefore, P(Getting chemistry or hardcover book) = (1/10)+(7/20) = 9/20 I am really doubtful about the red colored approach. Please guide. Math Expert Joined: 02 Sep 2009 Posts: 36540 Followers: 7074 Kudos [?]: 93058 [0], given: 10541 Re: Maths, Physics and chemistry books are stored on a library [#permalink] ### Show Tags 12 May 2014, 02:32 Expert's post 1 This post was BOOKMARKED khushboobhatia wrote: alimad wrote: Maths, 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 maths books as physics books and the number of physics books is 4 greater than that of chemistry books. Among all the books, 12 books are soft cover and the remaining are hard-cover. If there are a total of 7 hard-cover books among the maths and physics books. What is the probability, that a book selected at random is either a hard cover book or a chemistry book? A. 1/10 B. 3/20 C. 1/5 D. 1/4 E. 9/20 [Reveal] Spoiler: We know that M = 2P P = 4 + C M = 8+2C 8 + 2c + 4 + c + c = 20 4c + 12 = 20 4c = 8 c = 2 , P = 6, M = 12 Please assist further. Thanks Hello I am not good at probability, but somehow got this answer right . Could you please explain if the approach used by me is correct or it was just a stroke of luck that i got it right.. Number of Math+Physics+Chemistry books= 25 - ((20/100)*25) = 20 Hence, since M=2P, P=4+C, (4+C)+C+2(4+C)=20 Therefore, M=12, C=2, P=6 Probability of getting a chemistry book = 2/20 = 1/10 Probability of getting a Hardcover book = P(getting a math or phy book) * P( getting a hardcover book from math or phy books) = (18/20 )*(7/18) = 7/20 Therefore, P(Getting chemistry or hardcover book) = (1/10)+(7/20) = 9/20 I am really doubtful about the red colored approach. Please guide. Your approach is correct. Though the red part should be {the probability of getting a hardcover math or physics book}. _________________ Current Student Joined: 03 Jul 2013 Posts: 93 Schools: ISB '17 (A), IIMC (A) Followers: 3 Kudos [?]: 153 [0], given: 14 Re: Maths, Physics and chemistry books are stored on a library [#permalink] ### Show Tags 10 Oct 2014, 18:55 VeritasPrepKarishma wrote: Mackieman wrote: Please help me with this one. Maths, Physics and chemistry books are stored on a library shelf that can accomodate 25 books. Currently, 20% of the shelf spots remain empty. There are twice as many maths books as physics books and the number of physics books is 4 greater than that of chemistry books. Among all the books, 12 books are soft cover and the remaining are hard-cover. If there are a total of 7 hard-cover books among the maths and physics books. What is the prob, that a book selected at random is either a hard cover book or a chemistry book? Chemistry books: 2 Physics books: 6 Math books: 12 Sum = 20 P(Chemistry) = 2/20 = 1/10 P(Hard cover) = 8/20 = 4/10 = 2/5 P(AuB) = P(A)+P(B)-P(AnB) P(AnB) = P(A)*(B) = (1/10)*(2/5) = 2/50 P(AuB) = 5/50 + 20/50 - 2/50 = 23/50 P(AuB) - P(AnB) = 21/50 (since either means that we don't want both) What is wrong here? (OA: 9/20) Everything is correct except this: P(AnB) = P(A)*(B) = (1/10)*(2/5) = 2/50 P(AnB) is given by the product of individual probabilities when the events are independent. How many Chemistry books are hardcover? There are total 8 hardcovers and 7 belong to Math and Physics. This means there is only 1 Chemistry hardcover book out of total 20 books. So P(AnB) = 1/20 Now P(AuB) = 1/10 + 2/5 - 1/20 = 9/20 Hi Karishma. request you to please help me by explaining why the solution is also accounting for the book which is both chemistry and hard cover when the question stem clearly asks we need to select only books which are "Either" chem or hard cover. _________________ Sometimes standing still can be, the best move you ever make...... Veritas Prep GMAT Instructor Joined: 16 Oct 2010 Posts: 7119 Location: Pune, India Followers: 2132 Kudos [?]: 13632 [0], given: 222 Re: Maths, Physics and chemistry books are stored on a library [#permalink] ### Show Tags 12 Oct 2014, 19:57 aadikamagic wrote: Hi Karishma. request you to please help me by explaining why the solution is also accounting for the book which is both chemistry and hard cover when the question stem clearly asks we need to select only books which are "Either" chem or hard cover. In Math, 'either or' is interpreted a little differently - it includes the elements which lie in both sets too. "Either Chem or hardcover" means "Chemistry books or hardcover books or both". _________________ Karishma Veritas Prep | GMAT Instructor My Blog Get started with Veritas Prep GMAT On Demand for$199

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Re: Maths, Physics and chemistry books are stored on a library [#permalink]

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15 Aug 2015, 03:10
This is a brilliant way of thinking. I really need to develop such ability to get +750. Thanks for sharing easycheesy
Kudos sent

easycheesy wrote:
Hi guys,
After knowing there are 20 books on the shelve, I've just used the "Among all the books, 12 books are soft cover and the remaining are hard-cover" info. Using this info you get that 8/20 books are hard cover... and at least one book has to be chemestry, so the chances of getting either a hard cover book or a chemestry one have to be higher than 8/20 --- only alternative is E) 9/20
What do you think?
Thanks!
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# Maths, Physics and chemistry books are stored on a library

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