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The annual rent collected by a corporation from a certain [#permalink ]
28 Aug 2004, 10:10

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The annual rent collected by a corporation from a certain building was x percent more in 1998 than in 1997 and y percent less in 1999 than in 1998.
Was the annual rent collected by the corporation from the building more in 1999 than in 1997?
(1)x > y
(2) xy/100 < x â€“ y
please explain, thank you.

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My guess is D..
if x > y then it should be yes
for 2nd statement.. its says the same thing x>y

VP

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Hi, all, first of all, let me speak my thought.
In question, we can get each year's annual rent.
1997 1998 1999
M (M+x%M) (M+x%M-[M+x%M]y%)
compare 1997 with 1999:
( M+x%M-[M+x%M]y%) - (M) = M (x-y-xy)%
If x-y-xy >0, then 1999's rent > 1997's rent, or otherwise.
But in (1) and (2), it seems to be not of help to answer the question.
Hence, I choose (E).
Any other ideas?
thank you

Last edited by

chunjuwu on 30 Aug 2004, 05:25, edited 1 time in total.

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Both statements by themselves are sufficient.
If the rent is n --- 1997
then the rent is (100+x)n --- 1998
and the rent is (100-y)(100+x)n = (100^2 + 100x - 100y -xy)n --- 1999
From (1), no matter how big or small the difference is between x and y, (100-y)(100+x) is always positive.
And so (100-y)(100+x)n > n
From (2), xy/100 < x - y
xy < 100x - 100y
also tells us (100^2 + 100x - 100y -xy)n is always positive.
So (100^2 + 100x - 100y -xy)n > n.
Therfore the answer should be (D)

Manager

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I would choose B
St.1
Consider when x = 20 and y = 10
1997 = 100
1999 = 108
Consider x = 50 and y = 49
1997 = 100
1999 = 76,5
St.2
xy/100 < x - y
x must be greater than y and x = 50 and y = 49 won't work.
My explanation might be not very well, but I think B is the answer.
Correct me if I am wrong.
Regards,
Alex

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chunjuwu wrote:

The annual rent collected by a corporation from a certain building was x percent more in 1998 than in 1997 and y percent less in 1999 than in 1998. Was the annual rent collected by the corporation from the building more in 1999 than in 1997? (1)x > y (2) xy/100 < x â€“ y

I'll go for e.

1) let's say in 97' was 100, let x =10, and y=9.9

98' it was 110, and 99' it was 110(.901)= 99.11

another scenario, x=10, y=5, and 99' > 98

insufficient

2) tells you essentially the same thing, so insufficient

D does not elicit any new info, hence it's E

I think the key here is to test extreme values for % changes

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Answer is E.
If X is the amount perceived in 97, income in 99 is equal to X(1+x)(1-y)
id est is (1+x)(1-y) <> 1 <=> 1 +x-y -xy <> 1
1)x>y does not provide the answer
2)xy/100<x-y neither as it is not enough precise xy>xy/100 and x-y >xy/100
1+2) does not change anything

VP

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Sorry, let me revise my talk
1997 1998 1999
M (M+x%M) (M+x%M-[M+x%M]y%)
Hence, in 1999, the rent would be
(M+x%M-[M+x%M]y%) = M(1+x%-y%-xy%%)
I think this is a little tricky, it should be xy%% instead of xy%
compare 1999' with 1997'
we get [M(1+x%-y%-xy%%)] - M = M(x%-y%-xy%%) = 1/10000(100x-100y-xy)
if 100x-100y-xy > 0 then 1999' >1997' , or otherwise
in (1) x>y it always positive. so, sufficient.
in (2) xy /100 < x-y => 100x-100y-xy >0 it always positive, so sufficient.
Therefore, I go with (D).

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Chunjuwu,
Is there an official answer for this question.
Thanks.
Regards,
Alex

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ywilfred wrote:

Both statements by themselves are sufficient. If the rent is n --- 1997 then the rent is (100+x)n --- 1998 and the rent is (100-y)(100+x)n = (100^2 + 100x - 100y -xy)n --- 1999 From (1), no matter how big or small the difference is between x and y, (100-y)(100+x) is always positive. And so (100-y)(100+x)n > n From (2), xy/100 < x - y xy < 100x - 100y also tells us (100^2 + 100x - 100y -xy)n is always positive. So (100^2 + 100x - 100y -xy)n > n. Therfore the answer should be (D)

I don't agree with this, I think it should be:

If the rent is n --- 1997

then the rent is (100+x)

/100 * n --- 1998

and the rent is [(100-y)

/100 ] * [(100+x)

/100 ] *n --- 1999

[(100-y)

/100 ] * [(100+x)

/100 ] can be >100 or <100. Therefore insufficient

2. is the same as 1, so also insufficient

My answer: E

It would have been D if the rent in 99 were

y percent less than that of 97

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I will go with E on this one.
For 1., 2. and comnibed I used the following number.
X = 20
Y = 19
or
X = 20
Y = 10
Whats the OA?

VP

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The OA is E,
but I don't think so
thank you.