GRE Quantitative Reasoning Practice Exam

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• Evaluate (x/y)^3.
• Compute 4 + 6 ÷ 3 × 2 using the standard order of operations.
• How many feet are in a mile?
• If n = 5, what is (xy)^n?
• Distance between two points (x1, y1) and (x2, y2) is given by which formula?
• What is x^0 equal to, for any nonzero x?
• (a+b)(a-b) equals which expression?
• If the coefficient a equals 0 in ax^2 + bx + c = 0, the equation reduces to what?
• A solution has concentration 0.15 and volume 120 liters. How many liters are the active ingredient?
• The domain of a relation is the set of the first components of the ordered pairs. If R contains (1,2) and (3,4), what is the domain?
• What is the sum of the measures of the interior angles of a triangle?
• Which expression correctly represents the number of permutations of n distinct objects taken k at a time?
• If A = {1, 2, 3} and B = {3, 4, 5}, what is A ∩ B?
• Which condition demonstrates the SAS (side-angle-side) criterion for triangle congruence?
• Where is the vertex of a central angle located?
• For independent events A and B, which expression gives P(A and B)?
• Volume of a right circular cylinder with radius r and height h is given by which formula?
• Is the relation R = {(1,2), (1,3), (2,4)} a function?
• How many inches are in one yard?
• For a central angle of 90 degrees, what percent of the circumference does the corresponding arc represent?
• What is the central angle for a full circle?
• If a and b are even integers, which statement about their sum a + b must be true?
• Area of a triangle with sides a and b and included angle C is (1/2) ab sin C; When C = 90°, this area equals which expression?
• A cube with edge e = 3 has volume V = e^3. What is V?
• A sector of a circle with central angle 90 degrees has area equal to which expression in terms of r?
• If xy and xz share a common factor x, which expression equals xy + xz?
• Which of the following is equal to x^-3?
• An arc with central angle 60 degrees in a circle of radius 7 has arc length which of the following?
• A solution has a concentration of 0.25 and a total volume of 80 liters. How many liters are the active ingredient?
• In a right triangle, which statement is true about the hypotenuse?
• What is 20 percent greater than 50?
• What is the range of the numbers 4, 9, 15, and 6?
• Which statement best describes sets and lists?
• If two points share the same coordinates, distance between them is which value?
• For an equilateral triangle, area is a = (1/4) s^2 √3. If the side length is 6 units, what is the area?
• With annual compounding, what is V for P = 1000, r = 5%, t = 2?
• Which statement best describes a linear equation?
• Solve the inequality: -2x < -6. Which statement about x is true?
• Two groups with different averages: Group A has 8 items with average 5; Group B has 12 items with average 7. What is the combined average?
• Given x > y > 0 and w > z > 0, which inequality must hold?
• Which expression is equal to x^-3?
• Three pounds contain how many ounces?
• If the diagonal of a square is 8, what is the area of the square?
• Which unit equals 12 inches?
• How many ways are there to choose 3 objects from 7 without regard to order (7C3)?
• The ratio 1:1:√2 corresponds to which type of triangle?
• An inscribed angle intercepts an arc of 80 degrees. What is the measure of the inscribed angle?
• What is the sign of a negative number raised to an even power?
• The range of a relation is the set of the second components. If R contains (1,2) and (3,4), what is the range?
• Is {2, 3} a subset of {1, 2, 3, 4, 5}?
• FOIL is a method used to multiply which type of expressions?
• Compute (3/10) ÷ (7/13).
• Expand (a + b)^2 using the standard binomial expansion.
• Which equation expresses the Pythagorean theorem?
• An equilateral triangle with side length 6 has area equal to which of the following?
• In a square with side length s, the length of the diagonal is:
• In an equilateral triangle, how many degrees is each interior angle?
• A quadratic equation can have how many real solutions at most?
• What is the standard area formula for a circle?
• Compute (x/y)^2.
• Two distinct points on a circle determine how many arcs?
• Using the permutation formula P = n(n−1)(n−2)…(n−r+1), what is P when n = 5 and r = 3?
• Which of the following describes the sign of a negative number raised to an odd power?
• If price is $7 per item and there are 9 items, what is the total value?
• Multiply decimals by treating them as whole numbers and then placing the decimal point. What is 12.34 × 0.56?
• Which expression is equivalent to a^2 b^2?
• Given a^3 / a^2 with a ≠ 0, what is the value?
• How many inches are in 3 feet?
• How many permutations are there when selecting and ordering k objects from n distinct objects (order matters)?
• A cube has edge length e = 4. What is the volume V = e^3?
• In an equilateral triangle, each interior angle measures how many degrees?
• If a vehicle travels the same distance at speeds a and b, the average speed is?
• The radius of a circle is the distance between which two points?
• If x > y and w > z, which inequality is true?
• Harmonic mean of the numbers 2, 6, and 3 is what?
• If two integers a and b are coprime, then LCM(a,b) equals
• Which of the following is a correct prime factorization of 18?
• Which of the following is equal to xy + xz?
• Which expression is a correct factorization of x^2 - 2xy + y^2?
• A sphere with radius r = 5 has surface area S = 4πr^2. What is S?
• If a quantity is multiplied by 2 and then by 0.5, what is the net percent change?
• What is the greatest common divisor of 8 and 12?
• In an isosceles triangle, which statement is true?
• Diameter is defined as which of the following?
• Factor x^30 - x^29.
• Dividing both sides of an inequality by a negative number reverses the inequality's direction.
• What is x^1 equal to?
• If (ab)^3 equals a^3 b^3 when a and b commute, which expression equals (ab)^3?
• If you multiply x^3 by x^5, what is the result?
• What is the median of the numbers 2, 3, 5, and 9?
• For the quadratic y = ax^2 + bx + c with a ≠ 0, the vertex lies on which vertical line?
• A set of ordered pairs is used to represent a relation where the order of the elements in a pair matters. Which description matches this concept?
• If w < 0 and x > y, which statement holds?
• What is the median of the numbers 1, 3, and 5?
• Expand (a - b)^3.
• If events E and F are independent with P(E) = 0.60 and P(F) = 0.50, what is P(E) and F?
• What does the inequality 5 < x < 8 say about x?
• How many permutations are there when 7 distinct objects are arranged in order taking 3 at a time (7P3)?
• What is the quadratic formula used to solve ax^2 + bx + c = 0?
• Using the group equation T = G1 + G2 - B + N, if G1 = 12, G2 = 9, B = 4, and N = 3, what is T?
• Which of the following is a valid Pythagorean triple?
• Area of an equilateral triangle with side length s equals which expression?
• If D = {0,1} and R = {a,b}, how many ordered pairs are in the Cartesian product D × R?
• If xy > 0, which of the following must be true?
• The measure of an inscribed angle that intercepts an arc equals which of the following?
• When multiplying by 10^x with x positive, the decimal point moves how many places?
• An initial quantity increases by 20% and then by 10%. What is the overall percent change?
• Which statement best defines a function in one variable?
• Which expression is equal to 1/x - 1/y for nonzero x and y?
• Which expression is equal to xy - xz?
• Which of the following is the ratio for a 30-60-90 triangle (short leg: long leg: hypotenuse)?
• Compute the area a of a trapezoid with height h = 4 and bases B = 7 and b = 2 using a = 1/2 h (B + b).
• Which ratio corresponds to the well-known Pythagorean triple listed in the material?
• If x > y, which inequality between x+z and y+z is always true?
• The angle bisectors of a triangle intersect at which point?
• In a right triangle, which side is opposite the right angle?
• A rectangular solid has how many faces?
• If the circle has radius 5, which expression equals its circumference?
• In the circle equation (x - 0)^2 + (y - 5)^2 = 9, the center is:
• Which expression is equivalent to (x + y)/xy when x and y are nonzero?
• The product of an even integer and an odd integer is:
• Which expression represents the number of ways to arrange n distinct objects in order, using all objects?
• A parabola is symmetric about which line?
• Which of the following is one of the first ten prime numbers?
• If xy < 0, which of the following is true?
• Which expression represents the number of combinations of choosing r items from n without regard to order?
• Is the empty set a subset of every set?
• The difference of two odd integers is:
• A value decreases from 200 to 150. What is the percent change?
• Compute (2 + 3)^2 − 4.
• Compute (10/7) × (-1/3).
• Which distribution is most commonly associated with a bell-shaped curve?
• Adding or subtracting the same nonzero constant to both sides of an inequality
• Which statement describes a function in set theory?
• Which is the expansion of (a+b)(c+d)?
• Which statement correctly describes an arc?
• The x-intercepts of the parabola y = x^2 - 5x + 6 are the solutions to which equation?
• If there are 4 apples and 6 oranges, what is the ratio of apples to oranges in simplest terms?
• For an equilateral triangle with side length 4 units, what is the area?
• If a line has slope m = 2 and y-intercept b = -5, which equation represents it?
• Which statement expresses the triangle inequality?
• For a cylinder with bases included, S = 2πrh(h + r). If r = 2 and h = 3, what is S (approximately)?
• The slope of the line through the points (2, 3) and (5, 11) is:
• The sum of two odd integers is:
• Area of a regular hexagon with side length t is equal to which expression?
• Which expression correctly represents the area of an equilateral triangle with side length s?
• If the side length is 4, what is the area of an equilateral triangle?
• Given the same relation R, what is the range of R?
• If A = {1, 2, 3} and B = {3, 4, 5}, which set equals A ∪ B?
• Which formula gives the circumference of a circle with radius r?
• The bases of a right circular cylinder are which shapes?
• What is the sum of the interior angles of a pentagon?
• If a and b are even integers, which statement about their difference a - b must be true?
• A hemisphere with radius r = 4 has surface area with the base included S = 3π r^2. What is S?
• Which of the following is a valid algebraic identity?
• The discriminant b^2 - 4ac determines the number of real solutions. If the discriminant is negative, the equation has
• If p = 7 and q = 2, simplify x^p / x^q.
• The standard deviation (population) of the numbers 2, 4, 6 is approximately 1.63. Which of the following is the correct value?
• Which of the following numbers is a prime number?
• If an arc measure is 260 degrees, what is the measure of the inscribed angle that subtends it?
• If you divide x^7 by x^4, what is the result?
• Which expression is a correct factorization of x^2 - 2xy + y^2?
• In a circle of radius r, the area of a sector with central angle c degrees is A. Which expression gives A?
• If m = 4 and n = 6, simplify x^m * x^n.
• If the side length s of an equilateral triangle is 5, the area equals which expression?
• -(a - b) equals which expression?
• If events E and F are independent with P(E)=0.40 and P(F)=0.30, what is P(E ∧ F)?
• A sphere has radius r = 3. The volume is V = 4/3πr^2 per the given formula. What is V?
• Compute x^2 - y^2 for x=9 and y=4.
• In the circle equation (x - 4)^2 + (y - (-2))^2 = 25, what is the center of the circle?
• Which inequality must hold when x > y > 0 and w > z > 0?
• The units digit of 3^8 is which digit?
• Using the arc length formula, what is L when n = 360?
• How many subsets does a set with 4 elements have?
• In the circle equation (x - a)^2 + (y - b)^2 = r^2, the radius is:
• Which expression is equivalent to x^0?
• Which statement about a scalene triangle is true?
• If xy and xz share a common factor x, which expression equals xy - xz?
• If an even number is subtracted by an odd number, the result is:
• Perimeter of a regular hexagon with side length r is given by which expression?
• Which expression gives the area of a rectangle with length L and width W?
• In a parallelogram, which of the following statements is always true?
• Compute x^4/x^2.
• Factor a^2 - b^2.
• What is the sum of the interior angles of an n-sided polygon?
• Simplify the expression (x^3)^4.
• Given P(E)=0.30, P(F)=0.50, and P(E ∧ F)=0.10, what is P(E ∪ F)?
• If three independent events A, B, and C have probabilities P(A) = 0.2, P(B) = 0.3, and P(C) = 0.4, what is the probability that none occur?
• An isosceles triangle has at least how many congruent sides?
• Which of the following is the measure of an inscribed angle that subtends a diameter?
• How many ounces are in one pound?
• If a data set consists of 4 three times and 7 twice, the weighted mean is 5.2. Which option is the weighted mean?
• Which statement correctly describes prime factorization?
• What is 10 percent greater than 200?
• The parabola y = ax^2 + bx + c opens upward if and only if:
• Which statement describes a finite set?
• A semicircle with diameter d = 6 has perimeter P = d(1/2π + 1). What is P (approximately to two decimals)?
• Which expression gives the diagonal d of a square with side length s?
• A hemisphere with radius r = 4 has surface area without the base S = 2π r^2. What is S?
• Subtracting the same value from both sides of an inequality affects the inequality sign how?
• The probability of an event E is defined as the ratio of the number of outcomes that satisfy E to what quantity?
• Compute (3/4) ÷ (2/3).
• The midpoint of (0, 0) and (6, 8) is which ordered pair?
• What is the least common multiple of 30 and 75?
• Which expression gives the area of a triangle with base b and height h?
• The least common multiple of 18 and 12 is
• Which expression correctly simplifies sqrt(a) / sqrt(b) (assuming a > 0, b > 0)?
• Which statement about compound interest is true?
• If a = 3 and b = 2, what is (a - b)^3?
• A hemisphere with radius r = 3 has volume V = 2/3 π r^2. What is V?
• If two lines intersect, the vertical (opposite) angles are:
• The solution to a system of two linear equations, when it has a unique solution, is:
• Assuming a ≥ 0 and b ≥ 0, which expression is equal to sqrt(a) multiplied by sqrt(b)?
• For any real number a, sqrt(a^2) equals which expression?
• Solve for y: 9/y = 3/6. What is y?
• The sum of the interior angles of a triangle is equal to 180 degrees. Which statement best reflects this fact?
• The sample standard deviation of the numbers 2, 4, 6 is 2. Which of the following is the correct value?
• The product of two even integers is:
• Compute (xy)^2.
• If w > 0 and x > y, which statement is true?
• Compute (x^2)^3.
• Compute x^2 - y^2 for x = 8 and y = 3.
• Which of the following numbers is prime?
• Area of a parallelogram with base 7 units and height 3 units is what?
• What is the shape called when a rectangle has four congruent sides?
• A rectangle with length 3 and width 4 has area?
• Which is the expansion of (2x + 5)(3x + 4)?
• Area of an equilateral triangle with side length s is equal to which expression?
• What expression represents the total number of outcomes according to the multiplication principle when a first stage has k options and a second stage has m options (independent)?
• If an inscribed angle intercepts a 60-degree arc, what is its measure?
• A rectangular solid has how many vertices?
• If the dimensions are length l, width w, and height h, the volume V equals which expression?
• Which of the following is the ratio for a 45-45-90 triangle?
• Which expression gives the area of a triangle with base b and height h?
• A car travels at 60 miles per hour for 2.5 hours. What distance does it cover?
• Compute (x+y)^2 for x=4 and y=5.
• Given R = {(4,9), (7,9), (4,2)}, what is the domain of R?
• Which expression correctly represents the area of a trapezoid with bases b1 and b2 and height h?
• If a machine completes 6 units per hour and runs for 5 hours, how many units are produced?
• What is 1/3 + (-2/5)?
• A quantity increases from 600 to 750. What is the percent increase?
• Which of the following is a composite number?
• Which expression equals x^2 - 2xy + y^2?
• What is the absolute value of −11?
• The surface area of a rectangular solid with dimensions l, w, h is given by which expression?
• If the diameter of a circle is d and the radius is r, which relation is correct?
• What is x^-1 equal to?
• How many pints are in one quart?
• If a function f has f(3) = -2, the point (3, -2) lies on the graph of f. Which option lists that point correctly?
• With more than one compounding per year, compute V for P = 1000, r = 6%, n = 4, t = 2.
• The solution set to the equation x^2 = 4 is which of the following?
• For a rectangular prism with side lengths l, w, h, the space diagonal D satisfies which equation?
• Two events E and F are mutually exclusive with P(E) = 0.25 and P(F) = 0.40. What is P(E ∪ F)?
• Using the curved surface area of a cylinder, S = 2πrh, with r = 3 and h = 5, what is S?
• What is the solution set to the equation x = 0?
• A cube has edge length e = 5. What is its surface area S = 6e^2?
• Expand (3x + 2)(x + 4).
• Relative frequency of a category is defined as which quantity?
• Which sequence represents the units digit of 3^n for n = 1, 2, 3, 4?
• In a data set, the frequency (count) of a category refers to which definition?
• The least common multiple of 6 and 21 is
• Which of the following represents a quadratic equation in standard form?
• Using the inclusion-exclusion principle for two events, P(A or B) equals what value if P(A) = 0.5, P(B) = 0.3 and P(AB) = 0.1?
• In a list, order matters and elements can repeat. Which statement is true about lists?
• Which statement is true about an equilateral triangle?
• The value of (-3)^5 is:
• In a regular hexagon with side length s, the longest diagonal equals which value?
• If an amount increases by 25% and then decreases by 10%, what is the overall percent change?
• Which set defines a sector?
• The sum of the measures of the four angles formed by two intersecting lines is:
• In a weighted average with weights 2 and 1, the combined value a = (2x + y)/3. If x = 4 and y = 7, what is a?
• A rectangular solid has how many edges?
• Which expression is equal to sqrt(a)/sqrt(b)?
• Which term describes a set that contains the product of any two of its elements under multiplication?
• With simple interest, the future value V is given by V = P(1 + rt/100). If P = 2000, r = 5, t = 3, what is V?
• According to the multiplication principle, if there are k options for the first choice and m options for an independent second choice, how many total ordered outcomes exist?
• Compute (-8/11) + (5/11).
• What is the name of the smooth curve used to approximate the tops of the bars in a histogram that represents a continuous probability distribution?
• Compute 5 × 2^3.
• Which term refers to the set of real numbers between two numbers?
• Area of a parallelogram is a = b h. If the base length is 8 units and the height is 5 units, what is the area?
• If P(A) = 0.2 and P(B) = 0.4 are independent, what is the probability that neither A nor B occurs?
• If 3/4 = x/8, what is x?
• Area of a square from its diagonal is given by a = 1/2 d^2. If the diagonal is 12 units, what is the area?
• Area of a triangle in terms of two sides a and b and the included angle C is which expression?
• What is the greatest common divisor of 30 and 75?
• When solving a system of linear equations by graphing, the solution is found where the graphs:
• The product of two odd integers is:
• If S is the sum of n numbers, the average is S/n. Which of the following expresses this relation?
• If 10/x = 5/6, what is x?
• If -(-y < -x) holds, which relationship between y and x must be true?
• In a right circular cylinder, which statement is true?
• The weighted mean of a dataset in which 2 appears twice, 3 appears three times, and 5 appears once is 3. Which of the following is the correct weighted mean?
• Which expression gives the number of combinations of n distinct objects taken k at a time (order does not matter)?
• A vehicle travels 75 miles per hour for 3 hours. What distance is covered?
• Which expression is equivalent to x^1?
• A sector subtending 60 degrees has area equal to which expression in terms of r?
• A sector is defined as the region bounded by which of the following?
• The total surface area of a right circular cylinder equals which expression?
• For the data set 1, 2, 3, 4, 5, 6, 7, 8, what is the interquartile range (IQR)?
• A sphere with radius r = 2 has volume V = 4/3πr^2. What is V?
• What is the value of 8C2?
• Adding the same value to both sides of an inequality affects the inequality sign how?
• Which statement is true about a parallelogram?
• A group has 5 items with average 10 and another group has 15 items with average 8. What is the overall average?
• In a parallelogram with side lengths a = 3 and b = 4, the value of p^2 + q^2, where p and q are diagonals, equals which number?
• The medians of a triangle intersect at a point called the centroid. How is each median divided by the centroid?
• In the data set {3, 3, 3, 2, 4}, what is the mode?
• (√a)^2 equals which of the following?
• A semicircle has diameter d = 10. The perimeter is P = d(1/2π + 1). What is P (approximately to two decimals)?
• The average (arithmetic mean) of the numbers 3, 7, 7, and 11 is 7. Which of the following is the correct value for the average?
• The least common multiple of 8 and 12 is
• If an arc measure is 140 degrees, what is the measure of the inscribed angle that subtends it?
• An angle inscribed in a semicircle must be which type of angle?
• In the standard form ax^2 + bx + c = 0, what condition must the coefficient a satisfy for the equation to be quadratic?
• Compute the area of a trapezoid with height h = 6 and bases B = 8 and b = 3, using a = 1/2 h (B + b).
• The least common multiple is the smallest positive integer that is a multiple of both numbers.
• In a triangle, a median is best described as which of the following?
• How many feet are in one yard?
• If one integer is even and the other is odd, the sum is:
• Coordinates for the midpoint of the line segment joining (x1, y1) and (x2, y2) are which expression?
• The units digit of 3^x for x ≥ 1 cycles through which sequence?
• In an isosceles triangle, which statement is true?
• Which of the following is among the first ten composite numbers?
• Which description correctly defines the standard deviation?
• Compute the sum: 2/5 + 3/4.
• Arc length formula: For central angle n degrees and radius r, which expression gives the arc length?
• For nonnegative a and b, which expression equals sqrt(a) * sqrt(b)?
• In solving inequalities, what happens to the inequality sign when you multiply both sides by a negative number?