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The operation @ is defined for all numbers $$x$$ and $$y$$ by the equation $$x@y=x^2+y$$.

Quantity A

($$\frac{2}{3}$$@$$\frac{2}{3}$$)@$$\frac{2}{3}$$

Quantity B

$$\frac{2}{3}$$@($$\frac{2}{3}$$@$$\frac{2}{3}$$)


The leg of isosceles triangle A is 8, while the leg of isosceles triangle B is 10.

Quantity A

The area of isosceles triangle A

Quantity B

The area of isosceles triangle B




The figure represents a 5-foot-wide circular walkway that is bounded by two concentric circles. The outer boundary of the walkway is approximately how many feet longer than the inner boundary of the walkway?


The figure above shows five congruent circles each with radius 2 such that each of the five circles is tangent to two other congruent circles and to a smaller inner circle. The perimeter of the figure is composed of 5 line segments of length x and 5 circular arcs of length y. What is the perimeter of the figure?
If $$a$$ and $$b$$ are integers satisfying the equation $$a^{2}+b^{2}=145$$, which of the following could be the value of $$a+b$$?

Indicate all such values.

$$x=y$$

BD∥AE

Quantity A

The area of △ACE

Quantity B

The area of △BDF



In the figure, the perimeter of quadrilateral RSTW is 34. What is the perimeter of triangle STW?
If 12 percent of the books in a library are reference books, then the ratio of the number of reference books to the number of nonreference books is closest to which of the following?
$$x \lt y$$

The median of $$x$$, $$y$$ and $$120$$ is $$100$$

Quantity A

$$x$$

Quantity B

$$90$$


Which of the following number has more even divisors than odd divisors?
If the ones digit of $$7^{n}$$ is 9, which of the following could be the value of $$n$$?

Indicate all such values.
How many integer values of n satisfy the inequality | 3-n | ≤ 4 ?
A family paid 12 percent of its annual after-tax income on food last year. This amount was equal to 10 percent of its annual before-tax income last year. Which of the following is closest to the percent of the family's annual before-tax income that was paid for taxes last year?
How many integers from 1 to 2,000, inclusive, are both the square of an integer and the cube of an integer?
Sequence $$S$$: $$a_{1}, a_{2}, a_{3},......,a_{n}$$........

In sequence $$S$$, $$a_{1}$$ is an integer and $$a_{n}=2a_{n-1}$$ for all integers n greater than 1. If no term of sequence S is a multiple of 100, which of the following could be the value of $$a_{1}$$?

Indicate all such values.
Which of the following values of $$x$$ satisfies the equation $$\frac{x}{2}=n!$$ for some positive integer $$n$$?

The figure above shows a rectangle inscribed in a large circle. Inside the rectangle is a small circle of radius 2 that is tangent to two sides of the rectangle. If the length of the rectangle is twice its width, what is the area of the large circle?
List S contains 500 numbers. The range of the numbers in list S is 10.

Quantity A

The average (arithmetic mean) of the greatest number and the least number in list S

Quantity B

5 more than the least number in list S


What is the tens digit of $$\frac{39!}{29!}$$?


In the sum above, if X and Y each denote one of the digits from 0 to 9, inclusive, then X=?

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