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100 points for $49 worth of Veritas practice GMATs FREE VERITAS PRACTICE GMAT EXAMS Earn 10 Points Per Post Earn 10 Points Per Thanks Earn 10 Points Per Upvote ## Jack has a total of b hardback and paperback books in his... tagged by: BTGmoderatorLU ##### This topic has 3 expert replies and 0 member replies ### Top Member ## Jack has a total of b hardback and paperback books in his... Jack has a total of b hardback and paperback books in his library. If the number of hardback books is 1/3 the number of paperback books, and 3/4 of the paperback books are biographies, how many biographies, in terms of b, are in Jack's library? A) (1/9)b B) (3/20)b C) (3/16)b D) (1/3)b E) (9/16)b The OA is E. I'm really confused by this PS question. Experts, any suggestion about how can I solve it? I don't understand it. Thanks in advance. ### GMAT/MBA Expert Legendary Member Joined 14 Jan 2015 Posted: 2667 messages Followed by: 122 members Upvotes: 1153 GMAT Score: 770 LUANDATO wrote: Jack has a total of b hardback and paperback books in his library. If the number of hardback books is 1/3 the number of paperback books, and 3/4 of the paperback books are biographies, how many biographies, in terms of b, are in Jack's library? A) (1/9)b B) (3/20)b C) (3/16)b D) (1/3)b E) (9/16)b The OA is E. I'm really confused by this PS question. Experts, any suggestion about how can I solve it? I don't understand it. Thanks in advance. Call the number of paperbacks 12. (A multiple of the denominators in the given fractions.) Hardbacks: 1/3 of 12 = 4 b: 12 + 4 = 16 Paperback biographies: (3/4) * 12 = 9 --> this is our target. (Presumably, there are no hardback biographies. The prompt could have been a little clearer on this point.) So now we want plug in 16 in place of b in the answer choices until we find a value equal to 9. Answer Choice E: (9/16) * 16 = 9. _________________ Veritas Prep | GMAT Instructor Veritas Prep Reviews Save$100 off any live Veritas Prep GMAT Course

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LUANDATO wrote:
Jack has a total of b hardback and paperback books in his library. If the number of hardback books is 1/3 the number of paperback books, and 3/4 of the paperback books are biographies, how many biographies, in terms of b, are in Jack's library?

A) (1/9)b
B) (3/20)b
C) (3/16)b
D) (1/3)b
E) (9/16)b

The OA is E.

I'm really confused by this PS question. Experts, any suggestion about how can I solve it? I don't understand it. Thanks in advance.
Algebraically:

If there are three times as many paperbacks as hardbacks, then 3/4 of the books will be paperback and 1/4 of the books will be hardbacks. (3/4 is three times the value of 1/4.)
Paperbacks: (3/4)b
Paperback biographies: (3/4)*(3/4) b = (9/16)b. E is the correct answer.

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Save $100 off any live Veritas Prep GMAT Course Enroll in a Veritas Prep GMAT class completely for FREE. Wondering if a GMAT course is right for you? Attend the first class session of an actual GMAT course, either in-person or live online, and see for yourself why so many students choose to work with Veritas Prep. Find a class now! ### GMAT/MBA Expert GMAT Instructor Joined 25 Apr 2015 Posted: 2801 messages Followed by: 18 members Upvotes: 43 LUANDATO wrote: Jack has a total of b hardback and paperback books in his library. If the number of hardback books is 1/3 the number of paperback books, and 3/4 of the paperback books are biographies, how many biographies, in terms of b, are in Jack's library? A) (1/9)b B) (3/20)b C) (3/16)b D) (1/3)b E) (9/16)b We are given that Jack has a total of b hardback and paperback books in his library. We can let h = the number of hardback books and p = the number of paperback books, and thus h + p = b. We know that the number of hardback books is 1/3 the number of paperback books, and thus: h = (1/3)p We can now substitute (1/3)p for h in the equation h + p = b: (1/3)p + p = b Multiplying the entire equation by 3, we have: p + 3p = 3b 4p = 3b p = 3b/4 Finally, we are given that 3/4 of the paperback books are biographies. Since p = 3b/4, we have: (3/4)(3b/4) = biographies 9b/16 = biographies Answer: E _________________ Scott Woodbury-Stewart Founder and CEO scott@targettestprep.com See why Target Test Prep is rated 5 out of 5 stars on BEAT the GMAT. Read our reviews • Award-winning private GMAT tutoring Register now and save up to$200

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