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
A. Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.
B. Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.
C. BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.
D. EACH statement ALONE is sufficient.
E. Statements (1) and (2) TOGETHER are NOT sufficient.
\(r*((100+x)/100)*((100-y)/100)\) --> multiply together--->\(r*((10000 - 100y + 100x -xy)/10000)\), or you could just reorder the x and y value to give us \(r*((10000 + 100x - 100y -xy)/10000)\)
(1) Doesn't help us much because x can be 25%, while y is 20% to give us no change in percentage, or they could be other variables that can either increase or decrease the overall rent.
(2) \((xy/100) < x - y\) -----> \(xy < 100x - 100y\), meaning that \(0 < 100x - 100y - xy\), so this value is positive, which means that the value goes up. So when you look at this expression:
\(r*((10000 + 100x - 100y -xy)/10000)\) ----> r*(1 + positive increase), it means that the rent collected in 1999 is more than that in 1997. TRUE and SUFF.
Answer is B