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A certain carton holds fewer than 50 books. What is the number of book

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nilesh376
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A certain carton holds fewer than 50 books. What is the number of book [#permalink] New post   17 Apr 2010, 01:52
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A certain carton holds fewer than 50 books. What is the number of books in the carton?

(1) The books in the carton can be divided into 3 stacks of X books each, with 2 books lefts over.

(2) The books in the carton can be divided into Y stacks of 7 books each , with 2 books left over.
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Re: A certain carton holds fewer than 50 books. What is the number of book [#permalink] New post   17 Apr 2010, 05:16
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nilesh376 wrote:
A certain carton holds fewer than 50 books. What is the number of books in the carton?

1. The books in the carton can be divided into 3 stacks of X books each, with 2 books lefts over.

2. The books in the carton can be divided into Y stacks of 7 books each , with 2 books left over.


Please provide ur answer with explanation??



(1) Basically statement tells that the number of books divided by 3 gives remainder of 2 --> \(n=3x+2<50\) --> multiple values of \(n\) are possible. Not sufficient.

(2) Basically statement tells that the number of books divided by 7 gives remainder of 2 --> \(n=7y+2<50\) --> multiple values of \(n\) are possible. Not sufficient.

(1)+(2) \(n=21k+2<50\) --> \(k=1\), \(n=23<50\) or \(k=2\), \(n=44<50\). Not sufficient.

Answer: E.
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Re: A certain carton holds fewer than 50 books. What is the number of book [#permalink] New post   17 Apr 2010, 02:42
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44 also satisfy the given statements...

so ans should be E
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Re: A certain carton holds fewer than 50 books. What is the number of book [#permalink] New post   17 Apr 2010, 02:21
IMO C.

Total books < 50.
1. The books in the carton can be divided into 3 stacks of X books each, with 2 books lefts over. [Insuff]
If the no. of books = 5 and per stack 1 book
If the no. of books = 8 and per stack 2 book, and so on.

2. The books in the carton can be divided into Y stacks of 7 books each , with 2 books left over.
Let Y = 2 the total books = 16
Let Y = 3 the total books = 23. [Insuff]

On combining 1) and 2):
3 stacks each with 7 books
So total books can be 23.
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Re: A certain carton holds fewer than 50 books. What is the number of book [#permalink] New post   17 Apr 2010, 03:32
OA is 'E' even missed it cud be 44. The Q says can be.. it cud tk 6 stacks (<50) or 14 books ( >50)
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Re: A certain carton holds fewer than 50 books. What is the number of book [#permalink] New post   17 Apr 2010, 04:08
Can u explain more?

It's true that 44 can be the number but we can have 3 stacks and 7 books from statements 1 and 2.
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Re: A certain carton holds fewer than 50 books. What is the number of book [#permalink] New post   17 Apr 2010, 04:10
nilesh376 wrote:
A certain carton holds fewer than 50 books. What is the number of books in the carton?

1. The books in the carton can be divided into 3 stacks of X books each, with 2 books lefts over.

2. The books in the carton can be divided into Y stacks of 7 books each , with 2 books left over.


Please provide ur answer with explanation??


answer is E, no common multiple seems possible
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Re: A certain carton holds fewer than 50 books. What is the number of book [#permalink] New post   17 Apr 2010, 11:09
Good explanation.

+1.
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Re: A certain carton holds fewer than 50 books. What is the number of book [#permalink] New post   05 Oct 2016, 20:13
Does (1)+(2) indicate that carton only can be divided into 3 stacks of 7 books each?
So book number is (3*7)+2=23. 44 is not possible.

Ans C?
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Re: A certain carton holds fewer than 50 books. What is the number of book [#permalink] New post   06 Oct 2016, 00:52
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vvvvvbio wrote:
Does (1)+(2) indicate that carton only can be divided into 3 stacks of 7 books each?
So book number is (3*7)+2=23. 44 is not possible.

Ans C?


The OA is E: a-certain-carton-holds-fewer-than-50-books-what-is-the-number-of-book-92810.html#p714592
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Re: A certain carton holds fewer than 50 books. What is the number of book [#permalink] New post   06 Oct 2016, 01:29
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vvvvvbio wrote:
Does (1)+(2) indicate that carton only can be divided into 3 stacks of 7 books each?
So book number is (3*7)+2=23. 44 is not possible.

Ans C?


Both 23 and 44 are possible answers.

(1) The books in the carton can be divided into 3 stacks of X books each, with 2 books lefts over:
(2) The books in the carton can be divided into Y stacks of 7 books each, with 2 books left over.

If x = 7 and y = 3, then 23 is OK.
If x = 14 and y = 6, then 44 is OK.
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Re: A certain carton holds fewer than 50 books. What is the number of book [#permalink]
06 Oct 2016, 01:29
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