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Can someone solve this problem using "Pick a Number&quo

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by tulipz123 » Mon Nov 03, 2014 6:44 pm
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 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
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by GMATGuruNY » Mon Nov 03, 2014 6:59 pm
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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by Mathsbuddy » Wed Nov 05, 2014 5:30 am
To ease the reading, I have used:
P = no. of Paperbacks
H = no.of Hardbacks
b = P + H -> H = b - P
B = no. of Biographies
f = fraction of hardbacks that are biographies

Therefore, the question becomes:
H = P/3 -> P = 3H
B = 3P/4 + fH
Find B/b (in terms of b).

As f is not given, surely the question is INSUFFICIENT?
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by ceilidh.erickson » Wed Nov 05, 2014 7:46 am
What is the source of this question?

As MathBuddy has indicated, the question tells us that we have hardbacks and paperbacks, and tells us the fraction of paperbacks that are biographies. It does NOT tell us, however, whether any of the hardbacks are biographies. As such, it is actually an impossible question!

If the question told us that the only biographies were paperbacks, or if the question had specified "how many paperback biographies, in terms of b, are in Jack's library?" then we could use Mitch's strategy to get E. As it is written, though, we can't actually get to an answer.
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