Data Sufficiency

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


pls explain to me esp. the 2nd statement

rent=R, Call 07's rent A, 08's rent B, and 09's rent C, then B=(1+x/100)*A and C=(1-y/100)B, find if C>A?
Assume A=1 --> B=(100+x)/100 and C=B(100-y)/100, C=(100-y)/100 * (100+x)/100 = (100-y)(100+x)/10,000
(10,000+100x-100y-xy)/10,000 = 1 + [100(x-y)-xy]/10,000
st(1) x>y, Not Sufficient as we don't know the value of y on which depends the value of x - also unknown;
st(2) xy/100<x-y, xy<100(x-y) OR 100(x-y)-xy>0 and we have 1 + [100(x-y)-xy]/10,000 is already more than 1 hence we can answer Yes C is greater than A, as C>1 Sufficient

IOM B, the annual rent collected by the corporation from the building in 1999 was more than that of 1997

beyondenim1 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


pls explain to me esp. the 2nd statement

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

b

Plug in 1997 rent = 100.
Increase in 1998 = (x/100)*100 = x.
Thus, rent in 1998 = 100+x.
Decrease in 1999 = y/100*(100+x) = y + xy/100
The problem asks whether the increase is greater than the decrease. Thus, the question can be rewritten as:

Is x > y + xy/100?

Statement 1: x > y
If x=20 and y=10, then y + xy/100 = 10 + (20*10)/100 = 12.
Is 20 > 12? Yes.

If x=90 and y=80, then y + xy/100 = 80 + (90*80)/100 = 152.
Is 90 > 152? No.
Since the answer can be both yes and no, insufficient.

Statement 2: x-y > xy/100
If x-y > xy/100, then x > y + xy/100.
Sufficient.

The correct answer is B.

It is helpful to be able to recognize the following formulas for repeated percent change:

If a value increases by x% and then by another y%, the total percent change = x + y + xy/100.
If a value increases by x% and then decreases by y%, the total percent change = x - y - xy/100.

GMATGuruNY 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

b

Plug in 1997 rent = 100.
Increase in 1998 = (x/100)*100 = x.
Thus, rent in 1998 = 100+x.
Decrease in 1999 = y/100*(100+x) = y + xy/100
The problem asks whether the increase is greater than the decrease. Thus, the question can be rewritten as:

Is x > y + xy/100?

Statement 1: x > y
If x=20 and y=10, then y + xy/100 = 10 + (20*10)/100 = 12.
Is 20 > 12? Yes.

If x=90 and y=80, then y + xy/100 = 80 + (90*80)/100 = 152.
Is 90 > 152? No.
Since the answer can be both yes and no, insufficient.

Statement 2: x-y > xy/100
If x-y > xy/100, then x > y + xy/100.
Sufficient.

The correct answer is B.

It is helpful to be able to recognize the following formulas for repeated percent change:

If a value increases by x% and then by another y%, the total change = x + y + xy/100.
If a value increases by x% and then decreases by y%, the total change = x - y - xy/100.

hello mitch

ur solution is splendid....just for clarification. if statement 1 states that x<Y and statement 2 remains the same then both statmenet would be true....and answer would be D

regards nafi

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

in 97, 100 rent
in 98, 100 + x
in 99,(100-y)(100+x)/100
thus we need to find (100-y)(100+x)/100 > 100
or 100x - 100y -xy>0
100(x-y)>xy??
x>y insufficient
b)xy<100(x-y)
Sufficient
IMo B