A certain scholarship committeeawarded scholarships in the amounts of $1,250, $2,500, and $4,000. The committee awarded twice as many $2,500scholarships as $4,000 scholarships, and it awarded three times as many $1,250scholarships as $2,500 scholarships. If a total of $37,500 was awarded in$1,250 scholarships, how many $4,000 scholarships were awarded?

In 1990 the budgets for projects Q and V were $660,000 and $780,000, respectively. In each of the next 10 years, the budget for Q was increased by $30,000 and the budget for V was decreased by $10,000. In which year was the budget for Q equal to the budget for V ?

Ifn and y are positive integers and ~$450y=n^{3}$~, whichof the following must be an integer?

I. ~$\frac{y}{3\ast 2^{2}\ast 5}$~

II. ~$\frac{y}{3^{2}\ast 2\ast 5}$~

III. ~$\frac{y}{3\ast 2\ast5 ^{2}}$~

Which of the following mustbe equal to ~$x^{6}x^{4}$~ ?

Committee X has 4 members,committee Y has 5 members, and these committees have no members in common. If a task force is to be formed consisting ofone member of X and one member of Y, how many different task forces arepossible?

At a repair shop, the totalcost of a repair consists of the charge for parts and a charge of $22.00 perhour for labor. If the total cost of acertain repair at the shop was $249.75 and the charge for parts was $150.75,then the labor charge was for how many hours of labor?

The perimeter of a certain isosceles right triangle is ~$16+16\sqrt{2}$~. What is the length of the hypotenuse of the triangle?

To furnish a room in amodel home, an interior decorator is to select 2 chairs and 2 tables from acollection of chairs and tables in a warehouse that are all different from eachother. If there are 5 chairs in thewarehouse and if 150 different combinations are possible, how many tables arein the warehouse?

If a, b, c, and d areconsecutive even integers and a < b < c < d, then a + b is how muchless than c + d ?

If ~$2^{x}-2^{x-2}=3\left ( 2^{13} \right )$~, what is the value of x ?