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08 May 2022, 02:13
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D
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Each book in a certain library is classified in one of three categories: fiction, nonfiction, or biography. The ratio of the number of fiction books to the number of nonfiction books is 4 to 3, and the ratio of the number of nonfiction books to the number of biographies is 3 to 2. If there are at least 10,000 books in the library, what is the least number of books that could be in the library?
A. 10,000
B. 10,002
C. 10,005
D. 10,008
E. 10,009
Source: Skills Insight
A. 10,000
B. 10,002
C. 10,005
D. 10,008
E. 10,009
Source: Skills Insight
27 Jun 2022, 08:38
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Bunuel
Each book in a certain library is classified in one of three categories: fiction, nonfiction, or biography. The ratio of the number of fiction books to the number of nonfiction books is 4 to 3, and the ratio of the number of nonfiction books to the number of biographies is 3 to 2. If there are at least 10,000 books in the library, what is the least number of books that could be in the library?
A. 10,000
B. 10,002
C. 10,005
D. 10,008
E. 10,009
Source: Skills Insight
A. 10,000
B. 10,002
C. 10,005
D. 10,008
E. 10,009
Source: Skills Insight
The ratio of the number of fiction books (F) to the number of nonfiction books (N) is 4 to 3
We can write: F : N = 4 : 3
The ratio of the number of nonfiction books (N) to the number of biographies (B) is 3 to 2
We can write: N : B = 3 : 2
Since we have the same value for B in both ratios, we can combine them to get: F : N : B = 4 : 3 : 2
4 + 3 + 2 = 9, which means of the total number of books must be a multiple of 9.
Useful property: If a number is divisible by 9, the sum of its digits must be divisible by 9
Check the answer choices....D (10,008) is divisible by 9 (since 1 + 0 + 0 + 0 + 8 = 9, and 9 is divisible by 9)
Answer: D
General Discussion
05 Jun 2022, 06:49
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Fiction : Non-Fiction : Biography => 4:3:2
Total number of books = 4k+3k+2k = 9k
There are atleast 10,000 books: 9k>10,000
k>1111.1
we need the minimum possible number so k=1112
Plugging in the value of k:
Minimum number of books = 9*1112 = 10008
Ans. D
Total number of books = 4k+3k+2k = 9k
There are atleast 10,000 books: 9k>10,000
k>1111.1
we need the minimum possible number so k=1112
Plugging in the value of k:
Minimum number of books = 9*1112 = 10008
Ans. D
