Question

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) $x>yxy$
(2) $\frac{xy}{100}<x-Y$

• 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.

Answer 1

The correct option is B Statement (2) alone is sufficient, but statement (1) alone is not sufficient.

• Let A be the annual rent collected in 1997. Then the annual rent collected in 1998 is and the annual rent collected in 1999 is . Determine if , or equivalently, if .

1. Given that x > y, , is possible by choosing x = 100 and y = 10, since and is possible by choosing x = 100 and y = 90, since ; NOT SUFFICIENT.
2. As shown below, the given inequality is equivalent to the desired inequality, , which can be justified by the following steps, where each step’s inequality is equivalent to the previous step’s inequality.
   

• ,divide both sides by 100.
  
• ,subtract from both sides.
  
• , add 1 to both sides.
  
• ,factor the right side; SUFFICIENT.
  
• The correct answer is B; statement 2 alone is sufficient.