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Percentage

by nehakhas1 » Fri May 22, 2009 11:51 pm
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

Correct ans C
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Source: — Data Sufficiency |
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by kyabe » Sat May 23, 2009 12:58 am
I think it should be B

This is how I came at soultion:

Lets in 1997 the rent was R
Then in 1998 the rent was R*(100+X)/100 (Since increase was for X%)
And in 1999 the rent was R*(100+X)/100 - R*Y*(100+X)/100 (Since decrease was for Y)
Simplifying the rent in 1999 gives (R/100)*(100 + X - 100Y - YX)

So we have to find wether Rent in 1999 than 1997
=> ((R/100)*(100 + X - 100Y - YX))/R > 1
or, (100 + X - 100Y - YX)/100 > 1
or, X - 100Y - YX > 0 ------------------ (i)


Now coming to Stmt I:

X > Y

Looking at 1 and X > Y we cant conclude anything.

Now taking Stmt II:

XY/100 < X - Y

or, XY < 100 (X-Y)

Lets suppose XY = 99(X - Y)

(i) becomes X - 100Y - 99(X-Y) > 0
=> X - 100Y - 99X + 99Y > 0
=> -98X - Y > 0
=> 98X + Y < 0

Which can never be possible since X and Y are both positive value .

So we can say (2) is sufficient..

Anybody please correct me if I am wrong :(
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B is the answer

by TryHarder » Sat May 23, 2009 11:03 am
The answer is B since statement 2 is sufficient. I dont know how you came up with C, let me know the source.

If you start with a 100 as the rent for 1997, the rent for 1998 would be
100 + (x-y) - xy/100

As long as (x-y) > xy/100 the rent for 1999 would be above 100 (which is the initial rent)

B it is!!

Would appreciate if you can site the source of this question.
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