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 â€“ y
1997's annual rent = A
1998's annual rent = B
1999's annual rent = C
B = A*(1+X/100)
C = B*(1-Y/100)
C-A > 0 ?
C - A = B*(1-Y/100) - A = A*(1+X/100)*(1-Y/100) -A
C - A = A[(1+X/100)*(1-Y/100)-1]
(1+X/100)*(1-Y/100)-1 = (X/100-Y/100 -XY/10000) > 0?
if X = 100 and Y = 100, then (X/100-Y/100 - XY/10000) < 0
if X = 100 and Y = 10, then (X/100-Y/100 - XY/10000) > 0
S2. xy/100 < x â€“ y
divide by 100 both side
XY/10000 < (X-Y)/100
(X-Y)/100 - XY/10000 > 0
=> means C-A > 0 sufficient..
The only thing that matters is what you believe.