Knewton Brutal Challenge (Math Edition) – Week 19

by , Aug 11, 2010

Last week the challenge was verbal; this week Data Suffiency is back with a vengeance . Explain your answer in the comments for your chance to win the shirt!

When a club withx members conducts a membership drive using a certain recruitment plan, the club will have [pmath]x^2[/pmath] members at the end of the second week, [pmath]x^3[/pmath] members at the end of the third week, and [pmath]x^n[/pmath] members at the end of thenth week of the membership drive. If the Arachnology Club used this recruitment plan, starting withm members, and itsmembership drive lasteda weeks, wherea is an integer, and the Botany Club used this recruitment plan, starting with 2m members, andits membership drive lastedb weeks,whereb is an integer,how many more members did the Arachnology Club have at the end of its membership drive than the Botany Club had at the end of its membership drive?

1. The Arachnology Club had twice as many members when its drive ended as the Botany Club had when its drive ended.

2. If the Arachnology Club's drive had lasted one week less than three times its actual length, and the Botany Club's drive had lasted four times as long as its actual length, both drives would have been the exact same length.

(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.