The prompt needs to include the statement in red:
tulipz123 wrote:Jack has a total of b hardback and paperback books in his library. None of the hardback books are biographies. If the number of hardback books is 1/3 the number of paperback books, and 3/4 of the 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
Let the number of paperbacks = the LCM of 3 and 4 = 12.
Since the number of hardbacks is 1/3 the number of paperbacks, hardbacks = (1/3)(12) = 4.
Thus, b = paperbacks + hardbacks = 12+4 = 16.
Since 3/4 of the 12 paperbacks are biographies, biographies = (3/4)(12) = 9. This is our target.
Now plug b=16 into the answers to see which yields our target of 9.
Only
E works:
(9/16)b = (9/16)(16) = 9.
The correct answer is
E,
Last edited by
GMATGuruNY on Wed Nov 05, 2014 7:55 am, edited 1 time in total.
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