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Quantitative Reasoning - Algebra
Cards
x²-9x+18 = 0 Find x. A. x = 3, 9 B. x = 3, 6 C. x = -3, 6 D. x = 3, - E. x = -3,-6 - B A jet goes from City 1 to City 2 at an average speed of 600 miles per hour, and returns along the same path at an average speed of 300 miles per hour. What is the average speed, in miles per hour, for the trip? A. 350 miles/hour B. 300 miles/hour C. 500 miles/hour D. 400 miles/hour E. 450 miles/hour - D For all values of x, f(x) = 7x² - 3, and for all values of y, g(y) = 2y + 9. What is g(f(x))? A. 7y² - 3 B. 14y² + 3 C. 2x + 9 D. 14x² + 3 E. 14x² - 3 - D Quantitative Comparison
Quantity A: x Quantity B: 2x A. the relationship cannot be determined B. the two quantities are equal C. quantity A is greater D. quantity B is greater - A Let n be a positive integer such that one less than three-eighths of n is the third prime integer. What is the value of n? A. 24 B. 8 C. 16 D. 32 - C If (x - 5)² = 900, what is one possible value for x? A. - B. 10 C. - D. - E. 30 - A If 3x + y = 13 and x - 2y = -12, what is the value of x? A. 3 B. 2 C. 1 D. 2/ E. 1/3 - B
Quantity A: Sally's age Quantity B: Daisy's age A. quantity B is greater B. the two quantities are equal C. quantity A is greater D. the relationship cannot be determined - A Quantity A: 4³ Quantity B: 3⁴ A. quantity A is greater B. the two quantities are equal C. quantity B is greater D. answer cannot be determined - C If a = 1/3b and b = 4c, then in terms of c, a - b + c =? A. c B. -11/3c C. 5/3c D. -5/3c - D If x = 4 and y = 3x + 5, then 2y - 1 equals A. 15 B. 47 C. 22 D. 33 - D 25x²-36y² can be factored into:
A. (5x-6y)(5x+6y) B. (5x-6y)(5x-6y) C. (5x+6y)(5x+6y) D. 5 * ^ * (x² - y²) E. cannot be factored - A Financial Industry 18 Construction Industry 25 The degree measure of the sector representing the number of workers spending 5 to 9 years in the same role is how much greater in the construction industry chart than in the financial industry chart? A. 35° B. 25° C. 70° D. 7° E. 18° - B If [(7/8)]∧n = √([(7/8)]⁵), then what is the value of n? A. 1/ B. 2/ C. √ D. 25 E. 5/2 - E Column A: |x| Column B: x³ A. values are equal
The sum of two consecutive odd integers is 32. What is the value of the next consecutive odd integer? A. 33 B. 19 C. cannot be determined D. 17 E. 21 - B Quantitative Comparison Quantity A: x² Quantity B: x³ A. quantity A is greater B. relationship cannot be determined C. quantity B is greater D. two quantities are equal - B One of the roots of the equation x²+ kx - 12 = 0 is 3, and k is a constant. Quantity A: the value of k Quantity B: - A. quantity A is greater B. two quantities are equal C. quantity B is greater D. relationship cannot be determined - A What digit appears in the units place when 2^102 is multiplied out? A. 4 B. 8 C. 0
D. 2
E. 6 -
A
Which best describes the relationship between (x+y)³ and x³+y³ if x, y ≠ 0? A. (x+y)³ = x³+y³ B. relationship cannot be determined C. (x+y)³ > x³+y³ D. (x+y)³ < x³+y³ - B A given university has an average professor pay of $40,000 a year and an average administrator pay of $45,000 per year. If the ratio of professors to administrators is 4 to 3, and the total pay for professors and administrators in a year is $40,415,000, how many professors does the college have? A. 500 B. 411 C. 475 D. 548 E. 375 - D A farmer has 34 ft of fence, and wants to fence in his sheep. He wants to build a rectangular pen with one side formed by the side of his barn. He wants the area of the pen to be 120 ft². Which of the following is a possible dimension for the side opposite the barn? A. 12 ft B. 20 ft C. 7 ft D. 10 ft E. 5 ft - D If the average of two numbers if 3y and one of the numbers is y + z, what is the other number, in terms of y and z?
Quantity B: y A. two quantities are equal B. relationship cannot be determined C. quantity A is greater D. quantity B is greater - D The numerator of a fraction is the sum of 4 and 5 times the denominator. If you divide the fraction by 2, the numerator is 3 times the denominator. Find the simplified version of the fraction. A. 18 B. 6 C. 1/ D. 12 D. 1/2 - B Solve for z: 3(z + 4)³ - 7 = 17 A. 8 B. 2 C. - D. - E. 4 - D If a + b = 5, b + c = 10 and a + c = 8, what is the value of a + b + c? A. 10 B. 11. C. 23 D. 7.
E. 5 -
B
x + y = 12 and 2x - y = 6 Quantity A: x Quantity B: y A. quantity B is greater B. relationship cannot be determined C. quantity A is greater D. two quantities are equal - D Quantitative Comparison Quantity A: 2²+3² Quantity B: (2 + 3)² A. relationship cannot be determined B. quantity B is greater C. quantity A is greater D. two quantities are equal - B A theme park charges $10 for adults and $5 for kids. How many kids tickets were sold if a total of 548 tickets were sold for a total of $3750? A. 431 B. 248 C. 346 D. 269 E. 157 - C
C. 20
D. 5
D. 10 -
A
6 contestants have an equal chance of winning a game. One contestant is disqualified, so now the 5 remaining contestants again have an equal chance of winning. How much more likely is a contestant to win after the disqualification? A. 1/ B. 1/ C. 2/ D. 1/ E. 1/2 - B 7¹² - 7¹⁰ / 7¹¹ - 7⁹ = A. 1 B. 7 C. 49 D. 0 E. 343 - B If 10 pizzas cost x dollars and 6 sodas cost y dollars, what is the cost of 2 pizzas and 2 sodas in terms of x and y? A. 3x + 5y B. 15xy C. 3x+5y/ D. 5x + 3y/ E. 15x + 5y - C
If the average (arithmetic mean) of x, y, and 9 is 12, what is the average of x + 2, y - 6, and 10? A. 11 B. not enough information C. 10 D. 12 E. 9 - A 4/x = 2/ Find x. A. 8/ B. none C. 25/ D.. E. 50 - E An outpost has the supplies to last 2 people for 14 days. How many days will the supplies last for 7 people? A. 7 B. 4 C. 9 D. 5 E. 10 - B A function f(x) = -1 for all values of x. Another function g(x) = 3x for all values of x. What is g(f(x)) when x = 4? A. - B. 12
f(x) = |x² + 4x - 127| A. 67 B. - C. 36 D. - E. -36 - A Given the functions f(x) = 2x + 4 and g(x) = 3x - 6, what is f(g(x)) when x = 6? A. 192 B. 12 C. 28 D. 144 E. 16 - C What is the value of the function f(x) = 6x² + 16x - 6 when x = -3? A. 96 B. - C. 0 D. -108 - C a Ω b = a (b + 1) - 3 Quantity A: 1 Ω 1 Quantity B: 2 Ω 0 A. relationship cannot be determined B. quantity B is greater C. two quantities are equal D. quantity A is greater -
C
f(x) = 3x² - 5 g(x) = 9 - 2x Find f(g(5)). A. 131 B. - C. 4 D. - E. 70 - D Alice is twice as old as Tom, but four years ago, she was three years older than Tom is now. How old is Tom now? A. 3 B. 13 C. 21 D. 9 E. 7 - E For how many positive integers, x, is it true that x⁴ < 27x? A. more than 3 B. 3 C. none D. 2 E. 1 - D Solve for x: (x² - x) / (x - 1) = 1
C. 3
D. 6
E. -3 -
D
Simplify z³ - z² - 9z + 9. A. (z - 3)(z + 3)(z - 1) B. (z + 3)(z + 3)(z + 1) C. (z - 3)(z + 3) D. (z - 3)(z - 3)(z - 1) E. (z - 3)(z + 1)(z - 1) - E Jen and Karen are traveling for the weekend. They both leave from Jen's house and meet at their destination. Jen drives 45 mph the whole way. Karen drives 60 mph but leaves a half hour after Jen. How long after Jen leaves does Karen catch up with her? A. 2 hours B. she can't catch up C. 1.5 hours D. 3 hours E. 1 hour - A What is the value of (5 + x)(10 - y) when x = 3 and y = -3? A. 104 B. 108 C. 56 D. 38 - A x > 0
Quantity A: -5x + 4 Quantity B: 8 - 2x A. quantity B is greater B. relationship cannot be determined C. two quantities are equal D. quantity A is greater - A If 1/4x - 1/6y = 1/6 and y/z = 1/2, then what is the value of 3x - z? A. 6 B. 2 C. 4 D. 3 E. 1 - B John has $50 for soda and he must buy both diet and regular sodas. His total order must have at exactly two times as many cans of diet soda as cans of regular soda. What is the greatest number of cans of diet soda John can buy if regular soda is $.50 per can and diet soda is $.75 per can? A. 51 B. 25 C. none of the other answers D. 50 E. 75 - D y = 32 y = x² - 4 Quantity A: y/ Quantity B: x A. quantity A is greater B. relationship cannot be determined
