If n is the greatest positive integer for which 2ⁿ is a factor of 10!, then n =

A rectangular picture is surrounded by a boarder, as shown in the figure above.  Without the boarder the length of the picture is twice its width.  If the area of the boarder is 196 square inches, what is the length, in inches, of the picture, excluding the boarder?

In the figure above, the area of square region PRTV is 81, and the ratio of the area of square region XSTU to the area of square region PQXW is 1 to 4.  What is the length of segment RS?

A certain university will select 1 of 7 candidates eligible to fill a position in the mathematics department and 2 of 10 candidates eligible to fill 2 identical positions in the computer science department.  If none of the candidates is eligible for a position in both departments, how many different sets of 3 candidates are there to fill the 3 positions?

What is the greatest prime factor of 2¹⁰⁰ - 2⁹⁶?

Pat, Kate, and Mark charged a total of 162 hours to a certain project.  If Pat charged twice as much time to the project as Kate and ~$\frac{1}{3}$~ as much time as Mark, how many more hours did Mark charge to the project than Kate?

A certain company’s profit in 1996 was 15 percent greater than its profit in 1995, and its profit in 1997 was 20 percent greater than its profit in 1996.  The company’s profit in 1997 was what percent greater than its profit in 1995?

Of the families in City X in 1994, 40 percent owned a personal computer.  The number of families in City X owning a computer in 1998 was 30 percent greater than it was in 1994, and the total number of families in City X was 4 percent greater in 1998 than it was in 1994.  What percent of the families in City X owned a personal computer in 1998?

The operation ○ is defined by the equation x ○ y = (x-y)/(x+y), where y ≠ -x.  If 3 ○ y = 5 ○ 4, then y =

Enrollment in City College in 1980 was ~$83\frac{1}{3}$~ percent of enrollment in 1990.  What was the percent increase in the college’s enrollment from 1980 to 1990?