Data Sufficiency

Guys,

Does anyone have an efficient strategy for attaching these types of questions? I am consistently getting them wrong. Please help.

The annual rent collected by a corporation from a certain building was x% more in 1998 than 1997 and y% less in 1999 than 1998. Was the annual rent collected by the corp from the building more in 1999 than 1997?

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


Please let me know of any strategies for attaching such question types. Thanks.

okigbo wrote:Guys,

Does anyone have an efficient strategy for attaching these types of questions? I am consistently getting them wrong. Please help.

The annual rent collected by a corporation from a certain building was x% more in 1998 than 1997 and y% less in 1999 than 1998. Was the annual rent collected by the corp from the building more in 1999 than 1997?

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


Please let me know of any strategies for attaching such question types. Thanks.

IMO the answer is D. What is OA?

I approached this by picking 100 as the annual rent in 1997 and then trying percentages like 10 and 20 and then trying other numbers.

For statement 1: x>y

so x = 20% and y = 10%

1997 = 100
1998 = 120
1999 = 108

Then I saw that in order to collect a rent that is equal to or less than 120 we would have to multiply by 83% which is higher than 20% and therefore contrary to statement 1.

I figured this by setting 120x = 100. The answer is 5/6 which is .83 & 1/3 or 83 and 1/3 percent. This will be the case for any number; in order to reduce a number to the original number or to a number lower than the original number the percentage reduced must be greater than the original percentage increased.

So A is sufficient because y% is not bigger than x% and cannot, therefore, reduce the second number to the original.

Then statement 2 says that xy < 100(x-y). I started just by picking some numbers then I realized that this statement is true only when x > y because if y > x then it is a negative number; xy is positive because percentages are always positive.

OA is B.

any intuitive way to prove statement (A) is insufficient other than plugging numbers ?

All we know is that it went up and then it went down. Plugging in simple numbers is the easiest way to think about it. If it went up 10% from 100 to 110, then knowing that it went down more than 10% is insufficient to determine if now we are less than 100 because if its only a small amount more, say 10.01%, then we are stll above 100, but if it went down a lot more, say, 20%, then we are under 100.

okigbo wrote:Guys,

Does anyone have an efficient strategy for attaching these types of questions? I am consistently getting them wrong. Please help.

The annual rent collected by a corporation from a certain building was x% more in 1998 than 1997 and y% less in 1999 than 1998. Was the annual rent collected by the corp from the building more in 1999 than 1997?

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


Please let me know of any strategies for attaching such question types. Thanks.

Here algebra works well!

Suppose the rent in 1997 was r. In 1998 it was x percent higher than in 1997, i.e. r (1 + x/100)
In 1999 it was y% lower than in 1998, i.e. r (1 + x/100)(1 - y/100)

1999 rent higher than 1997 rent if and only if (1 +x/100)(1 - y/100) > 1

In other words, expanding, is 1 + (x - y)/100 - xy/10000 > 1 ?

Simplifying, x - y - xy/100 > 0 ?

Hi Kevin,

Can you please explain on the step

1999 rent higher than 1997 rent if and only if (1 +x/100)(1 - y/100) > 1

How did u arrive at (1 +x/100)(1 - y/100) is 'greater than 1'

I am not able to understand.

Thank you.

sorry...got it...

1997: rx1
1999: r (1 + x/100)(1 - y/100)

-> annual rent in 1997 = annual rent in 1998 <=> 1 + x/100)(1 - y/100) = 1
-> annual rent in 1997< annual rent in 1998 <=> 1 + x/100)(1 - y/100) > 1