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There are 1,280 books at a library. Everyone borrows these books at le

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There are 1,280 books at a library. Everyone borrows these books at le  [#permalink]

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New post 13 Mar 2017, 22:25
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There are 1,280 books at a library. Everyone borrows these books at least one, and maximum 10. If all books were borrowed, is the number of people who borrowed greater than 240?

1) 65 people borrowed either 1 or 2 books

2) 120 people borrowed either 3 or 4 books

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Re: There are 1,280 books at a library. Everyone borrows these books at le  [#permalink]

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New post 14 Mar 2017, 00:50
ziyuen wrote:
There are 1,280 books at a library. Everyone borrows these books at least one, and maximum 10. If all books were borrowed, is the number of people who borrowed greater than 240?

1) 65 people borrowed either 1 or 2 books

2) 120 people borrowed either 3 or 4 books



Hi

If we don't have any restrictions, then the minimum number is when all buy 10, so 1280/10=128...
MAX will be when all buy 1, then 1280/1=1280...


Let's see the statements and restrictions..

1) 65 people borrowed either 1 or 2 books
let each one borrow 65*2=130...
So remaining 1280-130=1150..
This can be by min 1150/10 or 115 to max 1150/3~383..
So total can be 115+65=170 to any number 383+65...
So insufficient


2) 120 people borrowed either 3 or 4 books
let each one borrow 120*4=480...
So remaining 1280-480=800..
This can be by min 800/10 or 80 to max 800/1=800..
So total can be 110+80=200 to any number 800+80=880...
So insufficient


Combined
LEAST number
65*2 +120*4=610..
So remaining 1280-610=670..
This can be by 670/10 or 67 to 670/5 or 134.. 1,2,3 or 4 have already been addressed by the two statements, so rest will be 5 to 10
So total can be 120+67+65, which is >240 to any number 120+134+65...
YES always, so sufficient

C
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Re: There are 1,280 books at a library. Everyone borrows these books at le  [#permalink]

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New post 15 Mar 2017, 05:05
for minimum number of people, we will maximize the the number of books taken by each person

St 1: let 65 people borrow 2 books each. total books borrowed = 1280-130 = 1150. let rest of the people borrow 10 books each. therefore total number of people borrowing 115. therefore the minimum people will be 115 +65 = 180. SO cannot be said if the number of people will be greater than 240 or not. INSUFFICIENT

St 2: let 120 people borrow 4 books each. total books borrowed = 1280-480 = 800. let rest of the people borrow 10 books each. therefore total number of people borrowing 80. therefore the minimum people will be 120 +80 = 200. SO cannot be said if the number of people will be greater than 240 or not. INSUFFICIENT

St 1 & St 2: let 65 people borrow 2 books each and 120 borrow 4 books each. total books borrowed = 1280-130-480 = 670. let rest of the people borrow 10 books each. therefore total number of people borrowing 67. therefore the minimum people will be 67+120+65 = 252. therefore the total number of people will be minimum of 252, which is greater than 240. ANSWER

option C
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Re: There are 1,280 books at a library. Everyone borrows these books at le  [#permalink]

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New post 23 Mar 2017, 14:08
ziyuen wrote:
There are 1,280 books at a library. Everyone borrows these books at least one, and maximum 10. If all books were borrowed, is the number of people who borrowed greater than 240?

1) 65 people borrowed either 1 or 2 books

2) 120 people borrowed either 3 or 4 books


In order to solve this question we need to minimize the set- if 65 people borrowed 1 set and 120 people borrowed 3 books then the number of people would exceed 240- this can be extrapolated from using the information in both statements. Hence, 1 and 2 are sufficient.
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There are 1,280 books at a library. Everyone borrows these books at le  [#permalink]

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New post 27 Mar 2017, 17:15
ziyuen wrote:
There are 1,280 books at a library. Everyone borrows these books at least one, and maximum 10. If all books were borrowed, is the number of people who borrowed greater than 240?

1) 65 people borrowed either 1 or 2 books

2) 120 people borrowed either 3 or 4 books


OFFICIAL SOLUTION



In the original condition, you must know the number of people who borrow each book, so there are many variables. Hence, C is most likely to be the answer. If the question is about “greater than”, you have to find“ the least value”. In other words, you have to find the minimum value of those people who borrowed the books. By solving con 1) & con 2), \(65*2=130\), \(120*4=480\), \(\frac{(1280-480-130)}{10}+120+65 = 252>240\), and the question is mainly about the number of people, which is an integer, so “CMT 4 (A: if you get C too easily, consider A or B)”can be applied.

In the case of 1), 1,200 people borrow 1 book each, and 40 people borrow 2 books each, and the condition is yes, and \(\frac{(1280 - 130)}{10}+ 65=180<240\) NO, hence it is not sufficient. 

In the case of 2), 120 people borrow 3 books each, and 920 people borrow 1 book each, the condition is yes, and  \(\frac{(1280 - 480)}{10} + 120=200<240\) NO, hence it is not sufficient. Therefore, the answer is C.
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There are 1,280 books at a library. Everyone borrows these books...  [#permalink]

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New post 20 Jul 2018, 02:47
There are 1,280 books at a library. Everyone borrows these books at least one, and maximum 10. If all books were borrowed, is the number of people who borrowed greater than 240?

1) 65 people borrowed either 1 or 2 books

2) 120 people borrowed either 3 or 4 books
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There are 1,280 books at a library. Everyone borrows these books...  [#permalink]

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New post 20 Jul 2018, 02:52
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I dont think this is a good solution as:

The first condition which 65 people borrowed either 1 or 2 books indicates that there are only 65 people that borrowed 1 or 2 books. However, the solution gives the following example for the 1st condition: 1,200 people borrow 1 book each and 40 people borrow 2, this contradicts the given condition which limits number of people who borrowed 1 or 2 books to only 65.

What do you guys think?
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There are 1,280 books at a library. Everyone borrows these books...  [#permalink]

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New post Updated on: 20 Jul 2018, 04:16
alexlearning17 wrote:
There are 1,280 books at a library. Everyone borrows these books at least one, and maximum 10. If all books were borrowed, is the number of people who borrowed greater than 240?

1) 65 people borrowed either 1 or 2 books

2) 120 people borrowed either 3 or 4 books


we would want to minimize the number of people such that the minimum possible value is greater than 240
1) 65 people borrowed either 1 or 2 books
say 65 people borrowed 1 book
remaining books 1215
minimum no of people required = 121+1
the + 1 will take 5 books
total no of people =122+65=187 < 240 so no
if the remaining people will borrow 3 books then yes > 240
insufficient

2) 120 people borrowed either 3 or 4 books
similarly ,
say 120 people borrowed 3 books = 360 books
remaining books
920
minimum no of people required = 92
total 120+92=212 < 240 so no
again if the remaining no of people borrow 1 book then yes > 240


combining both

65 people borrow 1 book, and 120 people borrow 3 books
books remaining 855
minimum no of people required = 85+1
total 65+120+86=271 >240 so yes

C

Originally posted by CounterSniper on 20 Jul 2018, 03:52.
Last edited by CounterSniper on 20 Jul 2018, 04:16, edited 1 time in total.
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Re: There are 1,280 books at a library. Everyone borrows these books...  [#permalink]

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New post 20 Jul 2018, 04:07
CounterSniper wrote:
alexlearning17 wrote:
There are 1,280 books at a library. Everyone borrows these books at least one, and maximum 10. If all books were borrowed, is the number of people who borrowed greater than 240?

1) 65 people borrowed either 1 or 2 books

2) 120 people borrowed either 3 or 4 books


we would want to minimize the number of people such that the minimum possible value is greater than 240
1) 65 people borrowed either 1 or 2 books
say 65 people borrowed 1 book
remaining books 1215
minimum no of people required = 121+1
the + 1 will take 5 books
total no of people =122+65=187 < 240 so no
if the remaining people will borrow 1 book then yes > 240
insufficient

2) 120 people borrowed either 3 or 4 books
similarly ,
say 120 people borrowed 3 books = 360 books
remaining books
920
minimum no of people required = 92
total 120+92=212 < 240 so no
again if the remaining no of people borrow 1 book then yes > 240


combining both

65 people borrow 1 book, and 120 people borrow 3 books
books remaining 855
minimum no of people required = 85+1
total 65+120+86=271 >240 so yes

C


For the condition 1), I dont think you can use another set of people that borrowed just 1 book because the condition already limited number of people who borrowed 1 or 2 books to just 65 people.
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Re: There are 1,280 books at a library. Everyone borrows these books...  [#permalink]

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New post 20 Jul 2018, 04:17
alexlearning17 wrote:
CounterSniper wrote:
alexlearning17 wrote:
There are 1,280 books at a library. Everyone borrows these books at least one, and maximum 10. If all books were borrowed, is the number of people who borrowed greater than 240?

1) 65 people borrowed either 1 or 2 books

2) 120 people borrowed either 3 or 4 books


we would want to minimize the number of people such that the minimum possible value is greater than 240
1) 65 people borrowed either 1 or 2 books
say 65 people borrowed 1 book
remaining books 1215
minimum no of people required = 121+1
the + 1 will take 5 books
total no of people =122+65=187 < 240 so no
if the remaining people will borrow 1 book then yes > 240
insufficient

2) 120 people borrowed either 3 or 4 books
similarly ,
say 120 people borrowed 3 books = 360 books
remaining books
920
minimum no of people required = 92
total 120+92=212 < 240 so no
again if the remaining no of people borrow 1 book then yes > 240


combining both

65 people borrow 1 book, and 120 people borrow 3 books
books remaining 855
minimum no of people required = 85+1
total 65+120+86=271 >240 so yes

C


For the condition 1), I dont think you can use another set of people that borrowed just 1 book because the condition already limited number of people who borrowed 1 or 2 books to just 65 people.


Corrected !!
Thanks !!
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There are 1,280 books at a library. Everyone borrows these books...  [#permalink]

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New post 20 Jul 2018, 04:58
Quote:
There are 1,280 books at a library. Everyone borrows these books at least one, and maximum 10. If all books were borrowed, is the number of people who borrowed greater than 240?

1) 65 people borrowed either 1 or 2 books

2) 120 people borrowed either 3 or 4 books

we would want to minimize the number of people such that the minimum possible value is greater than 240
1) 65 people borrowed either 1 or 2 books
say 65 people borrowed 1 book
remaining books 1215
minimum no of people required = 121+1
the + 1 will take 5 books
total no of people =122+65=187 < 240 so no
if the remaining people will borrow 1 book then yes > 240
insufficient

2) 120 people borrowed either 3 or 4 books
similarly ,
say 120 people borrowed 3 books = 360 books
remaining books
920
minimum no of people required = 92
total 120+92=212 < 240 so no
again if the remaining no of people borrow 1 book then yes > 240


combining both

65 people borrow 1 book, and 120 people borrow 3 books
books remaining 855
minimum no of people required = 85+1
total 65+120+86=271 >240 so yes

C

For the condition 1), I dont think you can use another set of people that borrowed just 1 book because the condition already limited number of people who borrowed 1 or 2 books to just 65 people.

Corrected !!
Thanks !!


Yeah. Because in the solution provided by MathRevolution, they also considered that same way and I believed it was a wrong way to do it.
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Re: There are 1,280 books at a library. Everyone borrows these books at le  [#permalink]

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New post 20 Jul 2018, 09:24
alexlearning17 wrote:
There are 1,280 books at a library. Everyone borrows these books at least one, and maximum 10. If all books were borrowed, is the number of people who borrowed greater than 240?

1) 65 people borrowed either 1 or 2 books

2) 120 people borrowed either 3 or 4 books


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Re: There are 1,280 books at a library. Everyone borrows these books at le &nbs [#permalink] 20 Jul 2018, 09:24
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