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Created by Master Student

Quantitative Reasoning Practice Test #3

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If 7a + 2b = 11 and a - 2b = 5, then what is the value of a ?

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If vector and vector = (3,-2), find the value of

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All of the elements of list M and list N are arranged in exactly 20 pairs, such that every element from list M is paired with a distinct element from list N. If in each such pair, the element from list M is larger than the element from list N, then which of the following statements must be true?

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A boat sights the top of a 40-foot lighthouse at an angle of elevation of 25degrees. How far away is the boat from the lighthouse ( the horizontal distance), to the nearest tenth of a foot?

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If the vertices of a triangle are (u,0), (v,8), and (0,0), then the area of the triangle is

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Write the product of (2 + 3i )(4 - 5i ) in standard form.

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A rectangular solid has three faces with areas of 28, 20, and 35 square centimeters. What is the volume of this solid?

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f(x) = 4x2 + 4x + 4, which of the following is equal to f(-3.5) ?

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z = logx (yx), then xz =

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The point (5, -10) is at a distance of 26 from point Q, and the point (2, -10) is at a distance of 25 from Q. Which of the following could be the coordinates of Q ?

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The set of points (x, y, z) such that x = 5 is

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If i = , then (5 - 3i)(4 + 2i) =

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At a certain software company, the cost, C, of developing and producing a computer software program is related to the number of copies produced, x, by the equation C = 30,000 + 2x. the company's total revenues, R, are related to the number of copies produced, x, by the equation R = 6x - 10,000. How many copies must the company produce so that the total revenue is equal to the cost?

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Rodney is starting a small business selling pumpkins. If he spends \$200 on supplies and sells his pumpkins for \$4 each, which of the following functions correctly shows the amount of money Rodney has gained or lost when he has sold x pumpkins?

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Which of the following ordered pairs is the solution to the equations 2y +x = 5 and -2y + x = 9?

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M & M plain candies come in six colors: brown, green, orange, red, tan, and yellow. Assume there are at least 3 of each color. If you pick three candies from a bag, how many color possibilities are there?

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What is the solution set for the equation |2x - 3| = 13?

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If for all real numbers x, a function f(x) is defined by f(x) = , then f(15) - f(14) =

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If fn+1 = fn-1 + 2 fn for n = 2, 3, 4, . . . , and f1 = 1 and f2 = 1, then f5 =

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Two identical rectangular solids, each of dimensions 3 Ã— 4 Ã— 5, are joined face to face to form a single rectangular solid with a length of 8. What is the length of the longest line segment that can be drawn within this new solid?

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What is the equation of a line with a y-intercept of 3 and an x-intercept of -5 ?

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a dance competition, each of six couples must compete against the other five couples in a dance-off three times before the winning couple can be declared. How many such dance-offs will occur?

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If a+ b = 10 and both a and b are positive integers,what is the largest possible value for a?

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The solution set of 3x + 4y < 0 lies in which quadrants?

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A sphere of radius 5 has the same volume as a cube with an edge of approximately what length?

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xand Y are independent events. If the probability event xwill occur is 0.2 and the probability event Y will occur is 0.9,what is the probability both x and Y will occur?

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At the end of a meeting all participants shook hands with each other. Twenty-eight handshakes were exchanged. How many people were at the meeting?

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If f(x) = 4x - 5 and g(x) = 3x, then f(g(2)) =

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If the cube root of the square root of a number is 2, what is the number?

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A wire is stretched from the top of a two-foot-tall anchor to the top of a 50-foot-tall antenna. If the wire is straight and has a slope of , then what is the length of the wire in feet?

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Jean canpaint a house in 10 hours, and Dan can paint the same house in 12 hours.If Jean begins the job and doesof it and the n Dan takes over and finishes the job, what is the total time it takes the m to paint the house?

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If 3(x + 5) - (x + 2) = 2x- 3x + 4, the n x =

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If there are known to be 4 broken transistors in a box of 12, and 3 transistors are drawn at random, what is the probability that none of the 3 is broken?

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Sarah is scheduling the first four periods of her school day. She needs to fill those periods with calculus, art, literature, and physics, and each of the se courses is offered during each of the first four periods. How many dIf ferent schedules can Sarah choose from?

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If and g(x) = x2 + 1, then f(g(2)) =

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||-5|- 16 + |-1|| =

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If = 0.625, then is equal to which of the following?

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If f(x) = 2 ln x + 3 and g(x) = ex, then f(g(3)) =

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If x2 - 4x -12 = 0, what is the sum of the two possible values of x?

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At what points does the circle given by the equation (y - 3)2 + (x - 2)2 = 16 intersect the y-axis?