A certain packing box contains books between 50 to 60. How many books exactly does that box contains?
1) If the books are counted by three, there will be one book left over.
2) If the books are counted by six, there will be one book left over.
The OA is B
Source: Economist GMAT
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A certain packing box contains books between 50 to 60. How
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Given: 50 < Number of books < 60swerve wrote:A certain packing box contains books between 50 to 60. How many books exactly does that box contains?
1) If the books are counted by three, there will be one book left over.
2) If the books are counted by six, there will be one book left over.
The OA is B
Source: Economist GMAT
We have to find out the number of books.
Let's take each statement one by one.
1) If the books are counted by three, there will be one book left over.
The statement means that the number of books divided by 3 will leave a remainder 1.
Thus, Number of books = 3k + 1, where k is a positive integer
=> 50 < 3k + 1 < 60
=> k = 17, 18 or 19
Thus, the number of books = 52, 55, or 58. No unique answer. Insufficient.
2) If the books are counted by six, there will be one book left over.
The statement means that the number of books divided by 6 will leave a remainder 1.
Thus, Number of books = 6p + 1, where k is a positive integer
=> 50 < 6p + 1 < 60
=> 9
Thus, the number of books = 55. A unique answer. Sufficient.
The correct answer: B
Hope this helps!
-Jay
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