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OG: DS #120

by tonebeeze » Sun Dec 26, 2010 1:11 pm
Hello all,

I had trouble with the DS question. What is the best approach to solve these types of problems? Thanks!

120. 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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Source: — Data Sufficiency |

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by Anurag@Gurome » Sun Dec 26, 2010 1:35 pm
Say annual rent in 1997 = A
=> Annual rent in 1998, B = A + x% of A = A + Ax/100 = A(1 + x/100)
=> Annual rent in 1999, C = B - y% of B = B - By/100 = B(1 - y/100) = A(1 + x/100)(1 - y/100)

We have to determine whether C is greater than A or not.
Let's assume C is greater than A.
=> C > A
=> A(1 + x/100)(1 - y/100) > A
=> (1 + x/100)(1 - y/100) > 1
=> (1 + x/100 - y/100 - xy/10000) > 1
=> (x/100 - y/100 - xy/10000) > 0
=> (x/100 - y/100) > xy/10000
=> (x - y) > xy/100

Thus only if (x - y) is greater than xy/100 then C will be greater than A.

Statement 1: x > y
This doesn't ensure the required condition.

Not sufficient.

Statement 2: xy/100 < (x - y)
This is exactly what we need!

Sufficient

The correct answer is B.
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by anshumishra » Sun Dec 26, 2010 1:38 pm
tonebeeze wrote:Hello all,

I had trouble with the DS question. What is the best approach to solve these types of problems? Thanks!

120. 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
Let "r" be the rent in 1997.

1997 -> r
1998 -> r*(100+x)/100
1999 -> r*(100+x)*(100-y)/(100*100) = r*(10000-100y+100x-xy)/10000 > r ?


Statement 1 :
x>y
We can't conclude , as for different values of x and y (x>y) the value of [r*(10000-100y+100x-xy)/10000] could be equal or lesser. Example : It could be equal (x=50,y=40) or less (x=50,Y=45).

- NOT SUFFICIENT

Statement 2:

xy/100 < x-y => xy < 100x - 100y => -100y + 100x -xy > 0

So, [r*(10000-100y+100x-xy)/10000] = r*(10000+some positive value)/10000 > r --- SUFFICIENT

Hence Answer is B.
Thanks
Anshu

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