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705-805 (Hard)|   Remainders|      
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banksy
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There are less than 50 books are to be divided by students. 14 Feb 2011, 15:45
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75% (hard)

Question Stats:

51% (02:12) correct 49% (02:39) wrong based on 181 sessions

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There are less than 50 books are to be divided by students. If the books are divided by 7 students, one book will be left. Haw many books are there?

(1) If the books are divided by 9 students, 8 books will be left.
(2) If the books are divided by 5 students, 3 books will be left.
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Bunuel
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There are less than 50 books are to be divided by students. 14 Feb 2011, 15:57
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banksy
There are less than 50 books are to be divided by students. If the books are divided by 7 students, one book will be left. Haw many books are there?
(1) If the books are divided by 9 students, 8 books will be left.
(2) If the books are divided by 5 students, 3 books will be left.
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Guess the book are to be divided equally among the students.

You can solve this question algebraically with formulas though simple listing the possible values of the books would probably be easier and quicker.

If the books are divided by 7 students, one book will be left --> there could be 1, 8, 15, 22, 29, 36, or 43 book.

(1) If the books are divided by 9 students, 8 books will be left --> there are 8, 17, 26, 35, or 44 --> to satisfy the condition in the stem # of books could be 8 only. Sufficient.

(2) If the books are divided by 5 students, 3 books will be left --> 3, 8, 13, 18, 23, 28, 33, 38, 43, or 48 --> to satisfy the condition in the stem # of books could be 8 or 43. Not sufficient.

Answer: A.
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There are less than 50 books are to be divided by students. 14 Feb 2011, 16:22
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I still don't get it.How we can have answer 8, if the books are to be divided among 9 students and 8 books will be left after this division.We should have at least 17 books in thi case. Where am I wrong. Thank you.
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There are less than 50 books are to be divided by students. 14 Feb 2011, 16:28
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I still don't get it.How we can have answer 8, if the books are to be divided among 9 students and 8 books will be left after this division.We should have at least 17 books in thi case. Where am I wrong. Thank you.
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Positive integer \(a\) divided by positive integer \(d\) yields a reminder of \(r\) can always be expressed as \(a=qd+r\), where \(q\) is called a quotient and \(r\) is called a remainder, note here that \(0\leq{r}<d\) (remainder is non-negative integer and always less than divisor).

Remember quotient can be zero too. For example: 8 divided by 9 yields a reminder of 8 and a quotient of zero - 8=0*9+8.

So each student will get 0 books and 8 books will be left.
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There are less than 50 books are to be divided by students. 23 Feb 2011, 19:09
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Just curious. I am trying to come up with an algebraic solution for this problem and I'm not quite getting there.

So we have two equations:
X = 7A + 1 ---> from the stem where X is the number of books
X = 9B + 8 ---> from the first clue

Hence, 7A + 1 = 9B + 8

How am I to arrive at the fact that (A=1;B=0) is the only pair that satisfies the equation. Am I missing something?
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There are less than 50 books are to be divided by students. 24 Feb 2011, 04:37
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bugSniper
Just curious. I am trying to come up with an algebraic solution for this problem and I'm not quite getting there.

So we have two equations:
X = 7A + 1 ---> from the stem where X is the number of books
X = 9B + 8 ---> from the first clue

Hence, 7A + 1 = 9B + 8

How am I to arrive at the fact that (A=1;B=0) is the only pair that satisfies the equation. Am I missing something?
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Check this:
good-problem-90442.html#p723049
manhattan-remainder-problem-93752.html#p721341
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There are less than 50 books are to be divided by students. 16 Sep 2021, 02:39
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