Box A contains twice as many books as Box B. In Box A, there

Question

Box A contains twice as many books as Box B. In Box A, there are three times as many hardcover books as softcover books. Overall, the two boxes contain 7 hardcover books for every 2 softcover books. What fraction of the books in Box B are hardcover?

(A) \(3/4\)
(B) \(7/9\)
(C) \(4/5\)
(D) \(5/6\)
(E) \(7/8\)

Show Answer

Official Answer

D

(A)  3/4 
(B)  7/9 
(C)  4/5 
(D)  5/6 
(E)  7/8

kevincan · Answer

Let the number of books in Box B be x. Then Box A contains 2x books.

Since Box A has three times as many hardcover books as softcover books, 3/4 of the books in Box A are hardcover and the other 1/4 are softcover. Thus:

Hardcover books in Box A = (3/4)(2x) = 3x/2

Softcover books in Box A = (1/4)(2x) = x/2

Let f be the fraction of the books in Box B that are hardcover. Then Box B contains fx hardcover books and (1 − f)x softcover books.

Since the overall ratio of hardcover to softcover books is 7:2,

(3x/2 + fx) / (x/2 + (1 − f)x) = 7/2

Dividing numerator and denominator by x gives

(3/2 + f) / (3/2 − f) = 7/2

Cross-multiplying,

2(3/2 + f) = 7(3/2 − f)

3 + 2f = 21/2 − 7f

9f = 15/2

f = 5/6

kevincan · Answer

Who would use a matrix for this question instead of so many variables ?

Radhika29 · Answer

A=2B, so total is A+B=3B
3B has books in the ratio of 7:2 (hardcover to softcover).. taking a multiple of 9 helps here, 3B=18, so B is 6 and A becomes 12.
When we simply distribute we get B has books in the ratio of 5:1, 5/6 is the answer

Saviooo · Answer

can we solve this using numbers faster than using variables

kevincan · Answer

........hard ......soft...... total 
 A.......3...........1............4
..B......x...........2- x........2
A&B...3+x.......3-x.........6

2(3+x)=7(3-x)

9x = 15
X = 5/3

X/2 = 5/6

FerociousStorm · Answer

No of books -
box A = 200
box B = 100

A has 3 hardcover books for every 1 softcover book which is 75 in percentage, thus it has 150 of HC books. When we add HC books from B to this we get-

(150 + B) / 300 = 7/9

Solve to get 0.83. Therefore 83 percent of books in B are HC, which is option D -> 5/6

HarshavardhanR · Answer

https://gmatclub.com/forum/download/file.php?id=89418 --- Harsha GMAT-Club-Forum-my36ldjv.png

Genius001 · Answer

Let Box B contain x books. Then Box A contains 2x books.

Since the hardcover-to-softcover ratio in Box A is 3:1, we have:

Hardcover in A = 3x/2
Softcover in A = x/2

Let h be the number of hardcover books in Box B. Then Box B has x − h softcover books.

Using the overall hardcover-to-softcover ratio of 7:2:

(3x/2 + h) / (x/2 + x − h) = 7/2

⇒ (3x/2 + h) / (3x/2 − h) = 7/2

Cross-multiplying:

2(3x/2 + h) = 7(3x/2 − h)

3x + 2h = 21x/2 − 7h

9h = 15x/2

h = 5x/6

Therefore, the fraction of books in Box B that are hardcover is:

h/x = 5/6

Answer: D (5/6)

Box A contains twice as many books as Box B. In Box A, there

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Box A contains twice as many books as Box B. In Box A, there

Prep Toolkit

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

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My Rewards