Geometry

Is the area of the triangular region above less than 20? (1) x^2 + y^2≠ z^2 (2) x + y < 13

If each side of parallelogram P has length 1, what is the area of P ? (1) One angle of P measures 45 degrees. (2) The altitude of P is 2 √ 2 2 2 .

If R, S, and T are points on a line, and if R is 5 meters from T and 2 meters from S, how far is S from T ? (1) R is between S and T. (2) S is to the left of R, and T is to the right of R.

If, in the figure above, ABCD is a rectangular region, what is the value of the ratio a r e a o f E D A a r e a o f E B C a r e a o f E D A a r e a o f E B C ? (1) AD = 4 (2) AE = 2 and EB = 4

In the xy-coordinate plane above, what are the coordinates of point N ? (1) Triangle MNP is equilateral. (2) Point M has coordinates (−4,0).

If x and y are the lengths of the legs of a right triangle, what is the value of xy ? (1) The hypotenuse of the triangle is 10 2 √ 10 2 . (2) The area of the triangular region is 50.

A six-sided mosaic contains 24 triangular pieces of tile of the same size and shape, as shown in the figure above. If the sections of tile fit together perfectly, how many square centimeters of tile are in the mosaic? (1) Each side of each triangular piece of tile is 9 centimeters long. (2) The mosaic can be put inside a rectangular frame that is 40 centimeters wide.

A rectangular solid has length, width, and height of L cm, W cm, and H cm, respectively. If these dimensions are increased by x%, y%, and z%, respectively, what is the percentage increase in the total surface area of the solid? (1) L, W, and H are in the ratios of 5:3:4. (2) x = 5, y = 10, z = 20

The rectangular rug shown in the figure above has an accent border. What is the area of the portion of the rug that excludes the border? (1) The perimeter of the rug is 44 feet. (2) The width of the border on all sides is 1 foot.

The length, width, and height of a rectangular box, in centimeters, are L, W, and H. If the volume of this box is V cubic centimeters and the total area of the 6 sides of this box is A square centimeters, what is the value of V/A ? (1) At least 2 of L, W, and H are equal to 5. (2) L, W, and H all have the same value.

In the figure above, what is the area of region PQRST ? (1) PQ = RS (2) PT = QT

In the figure above, PQRT is a rectangle. What is the length of segment PQ ? (1) The area of region PQRS is 39 and TS = 6. (2) The area of region PQRT is 30 and QR = 10.

In the figure above, the vertices of ΔOPQ and ΔQRS have coordinates as indicated. Do ΔOPQ and ΔQRS have equal areas? (1) b = 2a (2) d = 2c

In the figure above, what is the value of z? (1) x = y = 1 (2) w = 2

A noncompressible ball in the shape of a sphere is to be passed through a square opening in a board. What is the perimeter of the opening? (1) The radius of the ball is equal to 2 inches. (2) The square opening is the smallest square opening through which the ball will fit.

In the figure shown, is ℓ 1 ∥ ℓ 2 ? (1) r = s (2) t = u

What is the volume of the right circular cylinder X ? (1) The height of X is 20. (2) The base of X has area 25π.

In the figure above, point D is on AC. What is the degree measure of ∠BAC? (1) The measure of ∠BDC is 60° (2) The degree measure of BAC is less than the degree measure of BCD.

What is the value of z in the figure above? (1) x = 50 (2) y = 35

If X and Y are points in a plane and X lies inside the circle C with center O and radius 2, does Y lie inside circle C? (1) The length of line segment XY is 3. (2) The length of line segment OY is 1.5.