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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GMATGuruNY
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The prompt needs to include the statement in red:
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,
Let the number of paperbacks = the LCM of 3 and 4 = 12.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
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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Mathsbuddy
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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?
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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ceilidh.erickson
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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.
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.
Ceilidh Erickson
EdM in Mind, Brain, and Education
Harvard Graduate School of Education
EdM in Mind, Brain, and Education
Harvard Graduate School of Education
