请教2题 Prep 数学

luozhan

How many odd integers are greater than the integer x and less than the integer y?

(1) There are 12 even integers greater than x and less than y.

(2) There are 24 integers greater than x and less than y.

Answer: B

题目并没有说24个integers是连续的,所以多少个奇数并不确定?

Each employee of Company Z is an employee of either Division X or Division Y, but not both, If each division has some part-time employee, is the ratio of the number of full-time employees to the number of part-time employees greater for Division X than for Company Z?

(1) The ratio of the number of full-time employees to the number of part-time employess is less for Division Y than for Company Z.

(2) More than half of the full-time employees of company Z are employees of Division X, and more than half of the part-time employees of company Z are employees of Division Y.

Answer is D.

Can any one explain why (1) is sufficient?

Thanks.

[此贴子已经被作者于2008-3-10 12:46:04编辑过]

AlienX

For the first question, although the question doesn't mention whether those numbers are consecutive, C is indeed correct.

Condition #2 says:

Y>A1, A2, A3,...,A24>X

Condition #1 says that 12 of them(A1, A2, A3...A24) are even.

So 24 integers-number of even integer(which is 12)=12 odd integers.

luozhan

以下是引用AlienX在2008-3-10 11:00:00的发言：

For the first question, although the question doesn't mention whether those numbers are consecutive, C is indeed correct.

Condition #2 says:

Y>A1, A2, A3,...,A24>X

Condition #1 says that 12 of them(A1, A2, A3...A24) are even.

So 24 integers-number of even integer(which is 12)=12 odd integers.

Sorry, the official answer is B, and my answer is C. So your explaination is not right.

AlienX

hmm...I thought that the question didn't mean "24 consecutive #s".
I looked up online, and a guys said that "There are 24 integers greater than x and less than y"  means "There are 24 integers exactly 24 #s between integers x and y, and y>x", which implies that those 24 #'s have to be consecutive.  Hmm...never thought of interpeting the question this way.

AlienX

For your question #2, I am not too sure either.
Let me try:
Let A be the # of the full time employees in the company
Let B be the # of the part time employees in the company
Let C be the # of the full time employees in the Division Y
Let D be the # of the part time employees in the Division Y
Condition #1 says, A/B>C/D => C<AD/B -----------(a)
the
ratio of the # of the full time employees in the Division X to the # of
the part time employees in the Division X=(A-C)/(B-D)
<(A-AD/B)/(B-D)                    <----plug in (a), the numerator becomes bigger, then the positive fraction becomes bigger as well.
=A(1-D/B)(B-D)
=A[(B-D)/B]/(B-D)
=A/B
So it is sufficient.

[此贴子已经被作者于2008-3-10 16:38:03编辑过]

bigskings

楼主……

呵呵，