题目

­A certain jar has a capacity of 1284 jelly beans. How many minutes will it take to fill the jar to capacity?

(1) A person can fill the jar at a rate of 2 Jelly beans per second.

(2) It takes 6 times as long to fill the jas as it does to empty it, and it takes a total of 12 minutes and 29 seconds to do both.

选项

A.

Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.


B.

Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.


C.

BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.


D.

EACH statement ALONE is sufficient.


E.

Statements (1) and (2) TOGETHER are NOT sufficient.

解析

某个罐子能容纳1284颗果冻豆。将罐子装满需要多少分钟? (1)一个人可以每秒填充2颗果冻豆。 (2)装满罐子所花的时间是清空它所花时间的6倍,而装满和清空总共需要12分29秒。 #### 对于陈述(1): - 只给了单人工作效率,但没有给出具体人数,不充分。 #### 对于陈述(2): - 设清空罐子需要\(x\)秒,那么装满罐子需要\(6x\)秒,总共需要\(x + 6x=7x\)秒。 - 已知装满和清空总共需要\(12\)分钟\(29\)秒,即\(12\times60 + 29 = 749\)秒。 - 所以\(7x=749\),解得\(x = 107\)秒,那么装满罐子需要\(6x = 6\times107 = 642\)秒,换算成分钟为\(\frac{642}{60}=10.7\)分钟。 - 所以陈述(2)单独也可以求出装满罐子所需的时间,是充分的。 综上,每个陈述单独都足够,答案是D。
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