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06 Mar 2020, 05:06
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B
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76% (01:46) correct
24%
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Two libraries are planning to combine a portion of their collections in one new space. The new space will house 1/3 of the books from Library A, along with 1/4 of the books from Library B. If there are twice as many books in Library B as in Library A, what proportion of the books in the new space will have come from Library A?
A. 1/3
B. 2/5
C. 1/2
D. 7/12
E. 3/5
A. 1/3
B. 2/5
C. 1/2
D. 7/12
E. 3/5
06 Mar 2020, 05:24
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Bunuel
Assume total books in Library A & B combined = \(3x\)
If there are twice as many books in Library B as in Library A
--> Number of books in Library A = \(x\) & in Library B = \(2x\)
The new space will house \(\frac{1}{3}\) of the books from Library A, along with \(\frac{1}{4}\) of the books from Library B
--> Number of books in new space = \(\frac{1}{3}*x + \frac{1}{4}*2x = \frac{5x}{6}\)
Proportion of books from Library A = \(\frac{x}{3}/\frac{5x}{6} = \frac{2}{5}\)
Option B
Archit3110
06 Mar 2020, 09:21
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let books of library A = x and B = 2x
so new library will have x/3 of A and x/2 of B
total books in new library ; x/3+x/2 = 5x/6
and proportion of A library ; x/3 * 6/5x = 2/5
IMO B
so new library will have x/3 of A and x/2 of B
total books in new library ; x/3+x/2 = 5x/6
and proportion of A library ; x/3 * 6/5x = 2/5
IMO B
Bunuel
