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# The annual rent collected by a company from a certain

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Senior Manager
Joined: 12 Mar 2009
Posts: 307
The annual rent collected by a company from a certain [#permalink]

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12 May 2009, 12:04
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The annual rent collected by a company 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 company more in 1999 than in 1997?

1. x > y
2. (xy)/100 < (x-y)

OA is
b
Director
Joined: 23 May 2008
Posts: 760
Re: rent by the company [#permalink]

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12 May 2009, 17:32
im getting D

let a=1997 rent
let b=1998 rent
let c=1999 rent

(1+x%)a=b

(1-y%)b=c , b=c/(1-y%)

(1+x%)a = c/(1-y%)

is c>a?

1) x>y

let x=10 and y=5
1.10a=c/.95
1.05a=c...yes c>a

let x=3 and y=2
1.03a=c/.98
1.0094a=c...yes c>a

whenever x>y, c>a...sufficient

2) xy/100 < x-y
xy < (x-y)100

let x=10 and y=5

50 < (5)100

let x=3 and y=2
6< 100

x has to be > y to make statement 2 true, so sufficient
Manager
Joined: 15 Apr 2008
Posts: 50
Location: Moscow
Re: rent by the company [#permalink]

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13 May 2009, 02:03
B for me.
Let the rent in 1997 be A, then in 1998 it will become A * (1 + x/100) and in 1999 it will be A * (1 + x/100) * (1 - y/100). We need to know whether (1 + x/100) * (1 - y/100) is bigger than 1:
(1 + x/100) * (1 - y/100) >? 1
(100 + x)/100 * (100 + y)/100 >? 1
[(100 + x) * (100 + y)] / 10000 >? 1
(10000 + 100x - 100y - xy) / 10000 >? 1
1 + (x-y)/100 - xy/10000 >? 1
(x-y)/100 - xy/10000 >? 0
(x-y) - xy/100 >? 0
(x-y) >? xy/100 (since xy is positive)

1. doesn't give us anything, not suff.
2. clearly gives us the answer, suff
Senior Manager
Joined: 08 Jan 2009
Posts: 317
Re: rent by the company [#permalink]

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13 May 2009, 05:52
let a=1997 rent
let b=1998 rent
let c=1999 rent
is c> a ?

Stmt 1 : x > y
if x = 20 % and y = 10 % and a =100
then b = 120 and c = 108 so c > a .
if y = 18 % then c = 98.4 so c < a . Insufficient.

stmt 2 : x - y > x y / 100.
Put same x and y values. if x = 20 % and y = 10 % the condition will remain true. C > a
when y = 18 % the condition will turn false.
Sufficient.

Hence B.
Manager
Joined: 29 May 2008
Posts: 110
Re: rent by the company [#permalink]

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13 May 2009, 08:36
I like the last explanation, but you know it is difficult for me to think about this problem in only 2 minutes aprox, any ideas to become faster?
Director
Joined: 23 May 2008
Posts: 760
Re: rent by the company [#permalink]

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13 May 2009, 09:45
tkarthi4u wrote:
let a=1997 rent
let b=1998 rent
let c=1999 rent
is c> a ?

Stmt 1 : x > y
if x = 20 % and y = 10 % and a =100
then b = 120 and c = 108 so c > a .
if y = 18 % then c = 98.4 so c < a . Insufficient.

stmt 2 : x - y > x y / 100.
Put same x and y values. if x = 20 % and y = 10 % the condition will remain true. C > a
when y = 18 % the condition will turn false.

Hence B.

yeah you are correct, I didnt plug in enough numbers. Ans is B
SVP
Joined: 07 Nov 2007
Posts: 1765
Location: New York
Re: rent by the company [#permalink]

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13 May 2009, 10:14
vaivish1723 wrote:
The annual rent collected by a company 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 company more in 1999 than in 1997?

1. x > y
2. (xy)/100 < (x-y)

OA is
b

1997 rent = 100
1998 rent = 100(1+x/100)
1999 rent = 100(1+x/100) (1-y/100)

Question is asking 100(1+x/100) (1-y/100) > 100
i.e Is (1+x/100) (1-y/100)>1
1+xy/(100*100 )+(x-y)/100 >1

option B says (x-y) >(xy)/100( as you know x and y are potive)
x-y is +ve

1+xy/(100*100 )+(x-y)/100 definitely >1 (We need not to solve completely

_________________

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Senior Manager
Joined: 08 Jan 2009
Posts: 317
Re: rent by the company [#permalink]

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13 May 2009, 22:40
I came across a formula i thought i can share.

If some value is raised by x % and then decrease by y% then the total gain/Loss in the whole transaction is given by :
(x - y - xy/100).

so if x- y > xy/100 then u can see gain in transaction so final amt > initial amt. So we can prove the Stmt 2 immediately instead of substitution.
Re: rent by the company   [#permalink] 13 May 2009, 22:40
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