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805+ Level|   Algebra|      
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There are 1,280 books at a library. Everyone borrows these books at le Updated on: 07 Oct 2018, 06:56
Originally posted by GMATBusters on 06 Oct 2018, 10:17.
Last edited by GMATBusters on 07 Oct 2018, 06:56, edited 2 times in total.
Renamed the topic and edited the question.
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C
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95% (hard)

Question Stats:

45% (03:14) correct 55% (02:16) wrong based on 81 sessions

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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 book


Weekly Quant Quiz #3 Question No 4

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C
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There are 1,280 books at a library. Everyone borrows these books at le 06 Oct 2018, 10:23
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65 borrowed once or twice ...so maximum = 65*2= 130

But rest of the books = 1280-130 = 1150

considering max books lent min number = 1150/10= 115 so total becomes 115+65= 190

but option A is not sufficient to prove as maximum case was considered, for limiting case it may be >240 or less than

option B: 120 people borrowed either 3 or 4 book
so considering max = 120*4= 480
rest = 1280-480=800
so min = 800/10= 80
so total becomes 120+80= 200
considering only 3 books it may be more
so not sufficient

if we consider both ...120*4= 480 and 65*2= 130
so rest = 1280- 610= 670 so min = 67
so total = 120+65+67 =.252


Hence C is the answer
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There are 1,280 books at a library. Everyone borrows these books at le 06 Oct 2018, 10:24
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Answer should be C, please find solution images attached.

Best,
G
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There are 1,280 books at a library. Everyone borrows these books at le 06 Oct 2018, 10:28
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A:
statement one: if 65 people borrowed a max of 2 books each then a total of 130 books are borrowed
this leaves 1150 books and if everyone borrows a max of 10 books each then thats an additional 115 people. giving a total of 245

statment 2: not sufficient if 120 people borrowed 4 books (we take the greater of the 2) then that leaves 800 books left to be borrowed. which could be a minimum of 80 people which only adds up to 200. thus not sufficient
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There are 1,280 books at a library. Everyone borrows these books at le Updated on: 06 Oct 2018, 11:00
Originally posted by MsInvBanker on 06 Oct 2018, 10:39.
Last edited by MsInvBanker on 06 Oct 2018, 11:00, edited 1 time in total.
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I believe it is E.

(1) If all 65 people are borrowing 2 books, that is 130 books. And everyone else is borrowing 10 each, there are 1,150 books. Thus, 115 people. Total number of people will be 180 but it can be more than that too if people borrowed less number of books.

If all 65 people are borrowing 1 book, that is 65 books. And everyone else is borrowing 10 each (and one person, 5), there are 1,215 books. Thus, 122 people. Total number of people will be 187 but it can be more than that too if people borrowed less number of books.

(2) If all 120 people are borrowing 4 books, that is 480 books. And everyone else is borrowing 10 each, there are 800 books. Thus, 80 people. Total number of people will be 200 but it can be more than that too if people borrowed less number of books.

If all 120 people are borrowing 3 books, that is 360 books. And everyone else is borrowing 10 each, there are 920 books. Thus, 92 people. Total number of people will be 222 but it can be more than that too if people borrowed less number of books.

Even put together there will be ambiguity. Therefore, E.
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There are 1,280 books at a library. Everyone borrows these books at le 06 Oct 2018, 10:40
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1) ns 2) ns

1+2) is 65*1 + 120 * 3 . then 755/55 GT 10 not a feasible case
if 65*2 + 120*4; then 670/55 GT 10 ... not a ffeasible case ...thus Suff....... Ans C
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There are 1,280 books at a library. Everyone borrows these books at le 06 Oct 2018, 10:41
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1) 65 people borrowed either 1 or 2 books

If 65 people borrowed just 1 book each, then there are 1215 books remaining.

Those 1215 books COULD have been borrowed by 400 people (borrowing 3-4 books each), so the total number of people would have been 65 + 400 = 465

and the answer to the question would be YES.

Those 1215 books COULD have been borrowed by 122 people (borrowing 9-10 books each), so the total number of people would have been 65 + 122 = 187

and the answer to the question would be NO.

Statement 1 is INSUFFICIENT

2) 120 people borrowed either 3 or 4 books

IF 120 people borrowed 3 books each, then there are 920 books remaining.

Those 920 books COULD have been borrowed by 920 people (borrowing 1 book each), so the total number of people would have been 120 + 920 = 1040

and the answer to the question would be YES.

Those 920 books COULD have been borrowed by 92 people (borrowing 10 books each), so the total number of people would have been 120 + 92 = 212
and the answer to the question would be NO.

Statement 2 is INSUFFICIENT

Combined, we know,

65 people borrowed either 1 or 2 books
120 people borrowed either 3 or 4 books

After we consider the above 185 people, everyone else would have borrowed 5-10 books each.

MINIMUM:
(65 people)(1 book each) = 65 books
(120 people)(3 books each) = 360 books

So those 185 people borrowed 425 books - at the minimum - before we consider anyone else. That leaves 855 books for the other people. This means AT LEAST 86 additional people borrowed books - since (85)(10) = 850 and that isn't enough books. 65+120+86 = 271 people and the answer to the question is YES.

MAXIMUM:
(65 people)(2 books each) = 130 books
(120 people)(4 books each) = 480 books

So those 185 people borrowed 610 books - at the maximum - before we consider anyone else. That leaves 670 books for the other people. This means AT LEAST 67 additional people borrowed books - since (67)(10) = 670. 65+120+67 = 252 people and the answer to the question is YES.

Thus, in all possibilities, there would be MORE than 240 people, so the answer to the question is ALWAYS YES.

Final Answer: C
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There are 1,280 books at a library. Everyone borrows these books at le 06 Oct 2018, 11:02
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Using St 1 we can see that no of people can be less than 240 with the given condition

Using st 2 we can see that no of people can be less than 240 with given condition

Combining both and taking extreme scenarios (books borrowed as 2 and 4) we get that maximum number of people for remaining books takes total number beyond 240 even in worst case scenario (65 take 2, 120 take 4 and remaining take 10)

C
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