Beat the GMAT Geometry Practice Questions

When a cylindrical tank is filled with water at a rate of 22 cubic meters per hour, the level of water in the tank rises at a rate of 0.7 meters per hour. Which of the following best approximates the radius of the tank in meters?

(A) (√10)/2 (B) √10 (C) 4 (D) 5 (E) 10

If the length of an edge of cube X is twice the length of an edge of cube Y, what is the ratio of the volume of cube Y to the volume of cube X?

(A) 1/2 (B) 1/4 (C) 1/6 (D) 1/8 (E) 1/27

The inside dimensions of a rectangular wooden box are 6 inches by 8 inches by 10 inches. A cylindrical canister is to be placed inside the box so that it stands upright when the closed box rests on one of its six faces. Of all such canisters that could be used, what is the radius, in inches, of the one that has the maximum volume?

(A) 3 (B) 4 (C) 5 (D) 6 (E) 8

What is the area of a triangle created by the intersections of the lines x=4, y=5 and y=-{3/4}x+20?

(A) 42 (B) 54 (C) 66 (D) 72 (E) 96

The figure shows a regular decagon (10-side polygon). Angle x is formed by extending two of the sides of the decagon. What is the degree measure of angle x?

(A) 96 (B) 108 (C) 120 (D) 144 (E) 150

A project requires a rectangular sheet of cardboard satisfying the following requirement: When the sheet is cut into identical rectangular halves, each of the resulting rectangles has the same ratio of length to width as the original sheet. Which of the following sheets comes closest to satisfying the requirement?

(A) A sheet measuring 7 inches by 10 inches (B) A sheet measuring 8 inches by 14 inches (C) A sheet measuring 10 inches by 13 inches (D) A sheet measuring 3 feet by 5 feet (E) A sheet measuring 5 feet by 8 feet

Right cylinder A has diameter 6 and height 5. Right cylinder B has diameter 10 and height 3. Which cylinder has the largest volume and what is the difference between the two volumes?

(A) A's volume is greater than B's volume, and the difference is 30 pi (B) A's volume is greater than B's volume, and the difference is 15 pi (C) A's volume is equal to B's volume (D) B's volume is greater than A's volume, and the difference is 15 pi (E) B's volume is greater than A's volume, and the difference is 30 pi

A square wooden plaque has a square brass inlay in the center, leaving a wooden strip of uniform width around the brass square. lf the ratio of the brass area to the wooden area is 25 to 39, which of the following could be the width, in inches, of the wooden strip? i. 1 ii. 3 iii. 4

(A) I onlY (B) ll onlY (C) I and ll only (D) I and lll only (E) l, ll, and lll

A circle is inscribed in triangle ABC. If point D lies on side AB, is angle ABC a right angle? (1) DE is parallel to BC (2) AB = BC

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A rectangle has a perimeter of 28 inches. What are the dimensions of the rectangle? (1) The area of the rectangle is 40 inches squared. (2) The length is 6 inches more than the width

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AB is the diameter of the circle. CD is parallel to AB. What is the length of minor arc CD? (1) The radius of the circle is 12. (2) The measure of ∠CAB is 30º

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For triangle ABC, angle ABC = 90 degrees, and side AC has a length of 15. if point D lies on side AC, and a line is drawn from point B to point D, what is the length of line segment BD? (1) Triangle ABC is isosceles. (2) Line segment BD is perpendicular to side AC.

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If ABCD is a trapezoid, where AB is parallel to CD, what is the area of ABCD? (1) 2(AB) + CD = 12 (2) The height of the trapezoid is 5 inches

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If L & W represent the length and width, respectively, of the rectangle above, what is the perimeter? 1). 2L+W=40 2). L+W=25

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In isosceles RST what is measure of < R 1) the measure of <T is 100 2) the measure of < S is 40

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In the diagram, the fourteen rectangular tiles are all identical. What percent of the area of rectangle ABCD is covered by the tiles? (1) ABCD is a square. (2) EFGH is a square.

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In the xy-plane , line l intersects a circle with center at origin. Is the slope of line l equal to zero? 1) line l passes through second quadrant. 2) line l is perpendicular to the tangent of the circle.

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Is the perimeter of triangle with the sides a, b and c greater than 30? (1) a-b=15 (2) The area of the triangle is 50

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Is triangle ABC an isosceles triangle? (1) AD = DC (2) The area of triangle ABD equals the area of triangle BDC

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What is the area of right triangle XYZ? (1) Side YZ is 9 inches long. (2) Side XZ is 15 inches long.

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What is the perimeter of rectangle R ? (1) R is a square. (2) The area of R is 36.

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What is the value of x + y in the figure above? (1) w = 95 (2) z = 125

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Which of the following lists number of points at which a circle can intersect a triangle?

1) 2,6 2) 2,4,6 3) 1,2,3,6 4) 1,2,3,4,6 5) 1,2,3,4,5,6

What is the approximate perimeter of a square that has a diagonal of length 6?

1. 4 2. 13 3. 17 4. 20 5. 24

O is the center of the circle above, OB=2, and angle AOB measures 120 degrees. What is the area of triangular region AOB?

A 1 B 2 C (√3)/2 D √ 3 E 2 √ 3

Which of the following inequalities indicates the set of all values of d for which the lengths of the three sides of a triangle can be 3,4, and d?

A) 0<d<1 B) 0<d<5 C) 0<d<7 D) 1<d<5 E) 1<d<7

A wagon wheel with a circumference of 14π has seven straight spokes that originate at the center of the wheel. If the distance between consecutive spokes on the wheel's circumference is equivalent, what is the perimeter of each sector of the circle bounded by consecutive spokes?

A) 14 + 2π B) 7π C) 14π D) 14 + 4π E) 7 + 7π

There are two concentric circles with radii 10 and 8. If the radius of the outer circle increased by 10% and the radius of the outer circle decreased by 50%, approximately by what percent did the area between the circles grow?

A) 140% B) 141% C) 190% D) 192% E) 292%

A small, rectangular park has a perimeter of 560 feet and a diagonal measurement of 200 feet. What is its area, in square feet?

A) 19200 B) 19600 C) 20000 D) 20400 E) 20800

A circle with a radius of 4 has an equilateral triangle inscribed in it. What is the perimeter of the inscribed equilateral triangle?

A) 6 root 2 B) 6 root 3 C) 12 root 3 D) 12 root2 E) 24

The perimeter of a rectangular yard is completely surrounded by a fence that measures 40 meters. What is the length of the yard if the area of the yard is 64 meters squared?

A)8 B)10 C)12 D)14 E)16

In the rectangular coordinate system below, the are of triangular region PQR is

A. 12.5 B.14 C. 10√2 D.16 E. 25

A large cube is formed from the material obtained by melting 3 cubes of sides 3 units, 4 units and 5 units. What is the ration of the sum of the total surface area of the small cubes to that of the large cubes?

A. 1:1 B. 12:7 C. 25:18 D. 12:13 E. 12:17

Find the maximum number of spheres with a radius of 1 that can be fit into a cuboid with dimesions 6 , 8, 10 respectively.

A. 4 B. 12 C. 60 D. 90 E. 120

A thin piece of wire 40 meters long is cut into two pieces. One piece is used to form a circle with radius r, and the other is used to form a square. No wire is left over. Which of the following represents the total area, in square meters, of the circular and square regions in terms of r?

A. πr^2 B. πr^2 + 10 C. πr^2 + (1/4)π^2r^2 D. πr^2 + (40-2πr)^2 E. πr^2 + [10-(1/2)πr]^2

The sides of a square region, measured to the nearest centimeter, are 6 centimeters long. The least possible value of the actual area of the square region is

A.36.00 sq cm B.35.00 sq cm C.33.75 sq cm D.30.25 sq cm E.25.00 sq cm

The perimeter of a certain isosceles right triangle is 16+16root2. What is the length of the hypotenuse of the triangle?

A.8 B.16 C.4root2 D.8root2 E.16root2

To save money, Arkadelphia Cream Cheese will reduce each dimension of its rectangular box container (which is entirely full of cream cheese) by 50%, and reduce the price it charges its consumers by 50% as well. By what percentage does this increase the price-per-cubic-inch that each consumer will pay for cream cheese?

A.No change B.50% C.100% D.300% E.400%

If the lengths of the sides of a triangle are a, b, and 7, which of the following could be the value of a - b? 1)4 11)7 111)12

I only II only I and II only II and III only I, II, and III

In the figure above, points P and Q lie on the circle with center O. What is the value of S?

a) 1/2 b) 1 c) √2 d) √3 e) (√2)/2