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# The annual rent collected by a corporation from a certain

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Joined: 28 Dec 2004
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The annual rent collected by a corporation from a certain [#permalink]  20 May 2008, 10:53
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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) 100xy < x – y
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

i dont agree with the OA..

btw i get B
Director
Joined: 23 Sep 2007
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Re: DS-Rent [#permalink]  20 May 2008, 17:09
My guess is E

I have not proven it yet
Manager
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Re: DS-Rent [#permalink]  20 May 2008, 20:12
fresinha12 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) 100xy < x – y
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

i dont agree with the OA..

btw i get B

Lets try this out-

annual rent collected

In 1997: Assume its R
In 1998 : ((100+x)/100)R
In 1999 : ((100+x)/100)((100-y)/100)R

Simplifying
1999=
((10000+100(x-y)-xy)R)/10000

so we have to prove whether 100(x-y) is greater or less than xy
From 1:x > y but we dont know whether if x=11 and y =10 then 100(x-y) < xy
but when x=4 and y=3 then 100(x-y) >xy

So insuff

From 2: 100xy < x – y re writing the equation
((10000+100(x-y)-xy)R)/10000
is 1+((x-y)/100)-(xy/10000)

and 100xy < x – y is xy< ((x-y)/100)
as xy< ((x-y)/100) we can say
(xy/10000)<((x-y)/100)/10000
(xy/10000)<((x-y)/100)

so its sufficient

i think that the ans is b
Intern
Joined: 14 Apr 2008
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Re: DS-Rent [#permalink]  21 May 2008, 01:59
It's B for me also.

Explanation as follows:

1997: R
1998: R+100xR
1999: R+100xR-100y(R+100xR)

whether 1999 rent is higher than 1997 rent comes to whether 1999 rent - 1997 rent > 0 or not.

1999 - 1997 = R+100xR-100y(R+100xR) - R
= 100R(x-y) - 100x.100y.R
= 100R [(x-y) - 100xy]

A - not sufficient
B: x-y>100xy -> x-y - 100y > 0 -> sufficient.
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Re: DS-Rent [#permalink]  22 May 2008, 18:19
fresinha12 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) 100xy < x – y

B. if (x - y) > 100xy, then it is obviously x > y since x-y is +ve. so A is not necessary here if B answers the question..
100xy can never be 0 if x and y are +ve. per the question, x and y cannot be zeros. in that case, if (x-y) > 100xy, then 1999 rent is always greater than 1997 rent.

suppose if x = 20% and y = 15%, 100xy = 3% and x-y = 5%. so in this case, 1999 rent > 1997 rent.
suppose if x = 20% and y = 16.5%, 100xy = 3.3% and x-y = 2.5%. so in this case, 1999 rent < 1997 rent.

so B is sufficient.
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Joined: 11 Apr 2008
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Schools: Kellogg(A), Wharton(W), Columbia(D)
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Re: DS-Rent [#permalink]  23 May 2008, 01:22
2
KUDOS
It's B for me also.

Explanation as follows:

1997: R
1998: R+100xR
1999: R+100xR-100y(R+100xR)

whether 1999 rent is higher than 1997 rent comes to whether 1999 rent - 1997 rent > 0 or not.

1999 - 1997 = R+100xR-100y(R+100xR) - R
= 100R(x-y) - 100x.100y.R
= 100R [(x-y) - 100xy]

I don't understand the explantion too well -
here,
1998: R+100xR

According to the question,

...was x percent more in 1998 than in 1997...
Thus 1998 rent should be (100+x)/100 * R , and not 100xR.
e.g.
...was 12 percent more in 1998 than in 1997...
then,
1998 rent should be (100+12)/100 * R , and not 100*12*R.

Pls correct me if I am wrong !!
Re: DS-Rent   [#permalink] 23 May 2008, 01:22
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# The annual rent collected by a corporation from a certain

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