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26 May 2017, 04:41
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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
(1) 65 people borrowed either 1 or 2 books
(2) 120 people borrowed either 3 or 4 books
26 May 2017, 04:42
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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.
Answer: C
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.
Answer: C
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