Knewton Brutal Math Challenge - Week 9

by , May 20, 2010

The shirt is once again in play. Find the answer in the crosshairs, and bring it home.

When exactly [pmath]n[/pmath] years have passed since the day on which a certain car was purchased, the value of the car has decreased by [pmath]a_n%[/pmath] from its value one year previously, where [pmath]n[/pmath] is a positive integer. If [pmath]a_1 = 10[/pmath], and for each [pmath]n > 1[/pmath], [pmath]a_n[/pmath] - [pmath]a_{n-1} = k[/pmath], for some constant positive integer [pmath]k[/pmath], what is the value of the car after exactly 5 years?

1. The value of the car decreases more during the year immediately after the purchase of the car than it does during the next year, and the value of the car after exactly 3 years is $7,048.80.
2. The value of the car after exactly 4 years is $6,132.46.

(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.