H:F:R

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j_shreyans: Legendary Member; Posts: 510; Joined: Thu Aug 07, 2014 2:24 amFollowed by: 5 members; Thanked: 3 times

by j_shreyans » Wed Oct 01, 2014 3:43 am

Each book on a certain shelf is labeled by a single category. For every 2 history books, there are 7 fantasy books and for every 3 fantasy books, there are 5 reference books. If the proportion of history to reference books is doubled, while the proportion of fantasy to reference books is maintained, which of the following could be the number of history books if there are fewer than 60 fantasy books on the shelf after the changes?

Guys ,

Let History book be H same as F and R

H:F=2:7
F:R=3:5

so H:F:R=6:21:35 right?

after doubling history books the ratio will be

H:F:R=12:21:35

what next should i do?

Pls correct me if i am wrong.

Source: Beat The GMAT — Problem Solving | Wed Oct 01, 2014 3:43 am

GMATinsight: Legendary Member; Posts: 1100; Joined: Sat May 10, 2014 11:34 pmFollowed by: 24 members; Location: New Delhi, India; Thanked: 205 times

by GMATinsight » Wed Oct 01, 2014 4:20 am

The History Books could be 12 or 24

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GMATGuruNY: GMAT Instructor; Posts: 15539; Joined: Tue May 25, 2010 12:04 pmFollowed by: 1906 members; Location: New York, NY; Thanked: 13060 times; GMAT Score:790

by GMATGuruNY » Wed Oct 01, 2014 5:41 am

Each book on a certain shelf is labeled by a single category. For every 2 history books, there are 7 fantasy books and for every 3 fantasy books, there are 5 reference books. If the proportion of history to reference books is doubled, while the proportion of fantasy to reference books is maintained, which of the following could be the number of history books if there are fewer than 60 fantasy books on the shelf after the changes?

6
21
24
35
36

H/F = 2/7.
F/R = 3/5.

To combine the ratios, the COMMON ELEMENT -- F -- must be represented by the SAME VALUE in each ratio:
H/F = (2*3)/(7*3) = 6/21.
F/R = (3*7)/(5*7) = 21/35.
Combining the ratios, we get:
H/F/R = 6/21/35.

After H/R is doubled from 6/35 to 12/35, the new ratio is as follows:
H/F/R = 12/21/35.

Since the actual value of F is less than 60, only two cases are possible.
H/F/R = 12/21/35.
H/F/R = 24/42/70.

Thus, the value of H could be 12 or 24.

The correct answer is C.

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