There is a typo in the posted problem: the total number of hard-cover books should be 7.
Also, the wording of the question stem is ambiguous: it is not crystal clear whether
either a hard-cover book or a chemistry book is meant to exclude any books that are BOTH hard-cover AND chemistry.
I believe that the following reflects the intent of the problem:
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. For her new class, Mary wants a hard-cover chemistry book. If her friend John randomly selects one of the books on the shelf, what is the probability that the book John selects will have at least one of the two features Mary wants?
A. 1/10
B. 3/20
C. 1/5
D. 1/4
E. 9/20
P = good/total.
Here, a GOOD book is either hard-cover, chemistry, or both.
This is an EITHER/OR group problem.
Every book is EITHER chemistry OR a math/physics.
Every book is EITHER hard-cover OR soft-cover.
Use a GROUP GRID (also known as a double-matrix) to organize the data:
In the grid above, the entries in any given row or column must add up to the TOTAL of that row or column:
In the top row, hard-cover chemistry + hard-cover math/physics = total hard-cover.
In the middle column, hard-cover math/physics + soft-cover math/physics = total math/physics
.
A library shelf that can accommodate 25 b
ooks. Currently, 20% of the shelf spots remain empty.
Empty spots = (20/100)(25) = 5.
Thus, the total number of books on the shelf = 25-5 = 20.
Enter this information in the grid:
The number of physics books is 4 greater than that of chemistry books.
There are twice as many math books as physics books.
Case 1: C=1
Since there are 4 more physics books, P = C+4 = 1+4 = 5.
Since there are twice as many math books as physics books, M = 2P = 2*5 = 10.
Total = C+P+M = 1+5+10 = 16.
Too small:
The total number of books must be 20.
Case 2: C=2
Since there are 4 more physics books, P = C+4 = 2+4 = 6.
Since there are twice as many math books as physics books, M = 2P = 2*6 = 12.
Total = C+P+M = 2+6+12 = 20.
This works.
Thus, C=2 and M+P = 18.
Enter this information in the grid:
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.
Enter this information in the grid:
Complete the grid:
Resulting values:
Hard-cover chemistry books = 1.
Soft-cover chemistry books = 1.
Hard-cover math or physics books = 7.
Total number of good books = 1+1+7 = 9.
P = good/total = 9/20.
The correct answer is
E.
Private tutor exclusively for the GMAT and GRE, with over 20 years of experience.
Followed here and elsewhere by over 1900 test-takers.
I have worked with students based in the US, Australia, Taiwan, China, Tajikistan, Kuwait, Saudi Arabia -- a long list of countries.
My students have been admitted to HBS, CBS, Tuck, Yale, Stern, Fuqua -- a long list of top programs.
As a tutor, I don't simply teach you how I would approach problems.
I unlock the best way for YOU to solve problems.
For more information, please email me (Mitch Hunt) at
[email protected].
Student Review #1
Student Review #2
Student Review #3
