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The annual rent collected by a corporation from a certain

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The annual rent collected by a corporation from a certain [#permalink] New post 05 Aug 2006, 07:10
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 – y
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Re: The annual rent [#permalink] New post 05 Aug 2006, 10:11
ong 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 – y

1997=>x%increase=>1998=>y%decrease=>1999
Let
1997's annual rent = A
1998's annual rent = B
1999's annual rent = C

B = A*(1+X/100)
C = B*(1-Y/100)

C-A > 0 ?
C - A = B*(1-Y/100) - A = A*(1+X/100)*(1-Y/100) -A
C - A = A[(1+X/100)*(1-Y/100)-1]
(1+X/100)*(1-Y/100)-1 = (X/100-Y/100 -XY/10000) > 0?

S1. x>y
insufficient
if X = 100 and Y = 100, then (X/100-Y/100 - XY/10000) < 0
if X = 100 and Y = 10, then (X/100-Y/100 - XY/10000) > 0

S2. xy/100 < x – y

divide by 100 both side
XY/10000 < (X-Y)/100
(X-Y)/100 - XY/10000 > 0 => means C-A > 0 sufficient..

Hence, B
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Senior Manager
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 [#permalink] New post 05 Aug 2006, 19:23
only B is sufficient
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Re: The annual rent [#permalink] New post 05 Aug 2006, 21:16
freetheking wrote:
ong 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 – y

1997=>x%increase=>1998=>y%decrease=>1999
Let
1997's annual rent = A
1998's annual rent = B
1999's annual rent = C

B = A*(1+X/100)
C = B*(1-Y/100)

C-A > 0 ?
C - A = B*(1-Y/100) - A = A*(1+X/100)*(1-Y/100) -A
C - A = A[(1+X/100)*(1-Y/100)-1]
(1+X/100)*(1-Y/100)-1 = (X/100-Y/100 -XY/10000) > 0?

S1. x>y
insufficient
if X = 100 and Y = 100, then (X/100-Y/100 - XY/10000) < 0
if X = 100 and Y = 10, then (X/100-Y/100 - XY/10000) > 0

S2. xy/100 < x – y

divide by 100 both side
XY/10000 < (X-Y)/100
(X-Y)/100 - XY/10000 > 0 => means C-A > 0 sufficient..

Hence, B


Could u explain me more this
How it come?

(1+X/100)*(1-Y/100)-1 = (X/100-Y/100 -XY/10000) > 0?
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Re: The annual rent [#permalink] New post 05 Aug 2006, 22:07
ong wrote:
Could u explain me more this
How it come?

(1+X/100)*(1-Y/100)-1 = (X/100-Y/100 -XY/10000) > 0?


Given...
C-A > 0 ? => being asked : Was the annual rent collected by the corporation from the building more in 1999 than in 1997
C - A = A[(1+X/100)*(1-Y/100)-1]
(1+X/100)*(1-Y/100)-1 = (X/100-Y/100 -XY/10000) > 0?

Since A is a positive number, you only need to consider [].
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 [#permalink] New post 06 Aug 2006, 00:03
B
1997 = R
1998 = R (1+x/100)
1999 = R (1+x/100) (1-y/100) = R[1+ (1/100)*((x-y) - xy/100)]

St1: Clearly INSUFF

St2: If xy/100 is less than (x-y) then ((x-y) - xy/100) will be +ve and hence rent in 1999 will be more.
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  [#permalink] 06 Aug 2006, 00:03
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