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

Question

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

chetan2u · Answer

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

KrishnakumarKA1 · Answer

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

Nunuboy1994 · Answer

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.

BillyZ · Answer

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.

VodkaHelps · Answer

https://preview.ibb.co/dUs4By/Capture.jpg

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?

CounterSniper · Answer

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

VodkaHelps · Answer

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.

VodkaHelps · Answer

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.

bumpbot · Answer

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