Quantitative Reasoning - Algebra Cards

What is the value of (5 + x)(10 - y) when x = 3 and y = -3? A. 104 B. 108 C. 56 D. 38

A

Solve for x: (-3x + 3) / (x - 1) = x A. -3 and 1 B. -3 C. no solution possible D. 5

B

x²-9x+18 = 0 Find x. A. x = 3, 9 B. x = 3, 6 C. x = -3, 6 D. x = 3, -6 E. x = -3,-6

B

y = 32 y = x² - 4 Quantity A: y/7 Quantity B: x A. quantity A is greater B. relationship cannot be determined C. quantity B is greater D. two quantities are equal

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

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

A train travels at a constant rate of 20 meters per second. How many kilometers does it travel in 10 minutes? (1 km = 1000 m) A. 12 B. 2 C. 20 D. 5 D. 10

A

Audrey, Penelope, and Clementine are all sisters. Penelope is 8 years older than Clementine and 2 years younger than Audrey, if the sum of Penelope and Clementine's age is Audrey's age, how old is Clementine's age? A. 2 B. 8 C. 3 D. 4

A

Factor 3u⁴ - 24uv³ A. 3u(u-2v)(u² + 2uv + 4v²) B. 3u(u³-8v³) C. 3u(u-2v)(u + 2v) D. 3u[u³-(2v)³] E. 3u(u-2v)(u² - 2uv - 4v²)

A

Find f(6). f(x) = |x² + 4x - 127| A. 67 B. -67 C. 36 D. -136 E. -36

A

If (x - 5)² = 900, what is one possible value for x? A. -25 B. 10 C. -35 D. -10 E. 30

A

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

If x³ = 8, then x² (4/(3 - x))(2/(4 - x)) - (4/x²) = ? A. 15 B. 0 C. 35 D. 22 D. 16

A

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

Jon invested part of $16,000 at 3% and the rest at 5% for a total return of $680. Quantity A: the amount Jon invested at 5% interest Quantity B: the amount Jon invested at 3% interest A. quantity A is greater B. two quantities are equal C. relationship cannot be determined D. quantity B is greater

A

Kim is twice as old as Claire. Nick is 3 years older than Claire. Kim is 6 years older than Emily. Their ages combined equal 81. How old is Nick? A. 17 B. 27 C. 22 D. 13

A

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: -1 A. quantity A is greater B. two quantities are equal C. quantity B is greater D. relationship cannot be determined

A

Quantitative Comparison Quantity A: 3x + 4y Quantity B: 4x + 3y A. relationship cannot be determined B. quantity A is greater C. quantity B is greater D. two quantities are equal

A

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

Sally is 2 years younger than Abby Daisy is 5 years older than Tracy Abby is 6 years older than Tracy 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

Simplify the result of the following steps, to be completed in order: 1. Add 7x to 3y 2. Multiply the sum by 4 3. Add x to the product 4. Subtract x - y from the sum A. 28x + 13y B. 28x + 12y C. 28x + 11y D. 29x + 13y E. 28x - 13y

A

Solve for x: x² + 4x = 5 A. -5 or 1 B. none of the other answers C. -1 or 5 D. -1 E. -5

A

Two cars start 25 miles apart and drive away from each other in opposite directions at speeds of 50 and 70 miles per hour. In approximately how many minutes will they be 400 miles apart? A. 187.5 B. none of the other answers C. 3.33 D. 3.125 E. 200

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

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

x/30y = 4 1797 + 3y = 15x Quantity A: y Quantity B: 1 A. quantities are equal B. quantity A is greater C. relationship cannot be determined D. quantity B is greater

A

x² - 3x - 18 = 0 Quantity A: x Quantity B: 6 A. relationship cannot be determined B. quantity A is greater C. two quantities are equal D. quantity B is greater

A

y = x² - 10 y = 15 Quantity A: y/3 Quantity B: x A. relationship cannot be determined B. two quantities are equal C. quantity A is greater D. quantity B is greater

A

y is a real number such that y ≥ 1 Quantity A: (y²)(y⁴) Quantity B: y⁸ A. relationship cannot be determined B. quantity B is greater C. two quantities are equal D. quantity A is greater

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. 1/6 B. 1/30 C. 2/5 D. 1/5 E. 1/2

B

7¹² - 7¹⁰ / 7¹¹ - 7⁹ = A. 1 B. 7 C. 49 D. 0 E. 343

B

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

Column A: |x| Column B: x³ A. values are equal B. relationship cannot be determined C. column B is greater D. column A is greater

B

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

Find the intersection of the following two equations: 3x + 4y = 6 15x - 4y = 3 A. (18,0) B. (0.5, 1.125) C. (3, 4) D. (1, 0.5) E. (0.2, 0)

B

Find the slope of the inequality equation y - 7 < x + 2y - 14 A. -7 B. -1 C. 1 D. 7 E. 0

B

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

If 3x + y = 13 and x - 2y = -12, what is the value of x? A. 3 B. 2 C. 1 D. 2/3 E. 1/3

B

If 6h - 2g = 4g + 3h In terms of g, h = ? A. 5g B. 2g C. 3g D. 4g E. g

B

If a + b = 5, b + c = 10 and a + c = 8, what is the value of a + b + c? A. 10 B. 11.5 C. 23 D. 7.5 E. 5

B

Jack has 14 coins consisting of nickels and dimes that total $.90. How many nickels does Jack have? A. 6 B. 10 C. 4 D. 8 E. 12

B

Let x be an integer such that |x| < 1 Quantity A: x² Quantity B: 0 A. quantity B is greater B. they are equal C. quantity A is greater D. relationship cannot be determined

B

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

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

The cost, in cents, off manufacturing x pencils is 1200 + 20x. The pencils sell for 50 cents each. What number of pencils would need to be sold so that the revenue received is at least equal to the manufacturing cost? A. 30 B. 40 C. 36 D. 33 E. 27

B

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. 1/3 D. 12 D. 1/2

B

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

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

(b * b⁴ * b⁷)½/(b³ * b∧x) = b⁵ If b is not negative then x = ? A. 1 B. 7 C. -2 D. -1

C

4x² + 5x = 3x² - x - 5 Quantity A: x Quantity B: 1 A. relationship cannot be determined B. two quantities are equal C. quantity B is larger D. quantity A is larger

C

A hybrid car gets 40 miles per gallon. Gasoline costs $3.52 per gallon. What is the cost of the gasoline needed for the car to travel 120 miles? A. $9.54 B. $14.08 C. $10.56 D. $12.53 E. $10.36

C

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

Bill and Bob are working to build toys. Bill can build k toys in 6 hours. Bob can build k toys in 3 hours. How long would it take Bob and Bill to build 4k toys working together? A. 2 hours B. 4 hours C. 8 hours D. 12 hours E. 9 hours

C

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

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/15 D. 5x + 3y/15 E. 15x + 5y

C

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

Quantitative Comparison 3x + 4y = 5 x - y = 6 Quantity A: x Quantity B: y A. two quantities are equal B. relationship cannot be determined C. quantity A is greater D. quantity B is greater

C

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

Sarah's current age is three times Ron's age two years ago. Sarah is currently 14 years older than Ron. What is the sum of Sarah and Ron's current age? A. 32 B. 24 C. 34 D. 36

C

Two palm trees grow next to each other in Luke's backyard. One of the trees gets sick, so Luke cuts off the top 3 feet. The other tree, however, is healthy and grows 2 feet. How tall are the two trees if the healthy tree is now 4 feet taller than the sick tree, and together they are 28 feet tall? A. 14 and 14 feet B. cannot be determined C. 12 and 16 feet D. 8 and 20 feet E. 11 and 17 feet

C

What is the value of the function f(x) = 6x² + 16x - 6 when x = -3? A. 96 B. -12 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

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

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 store sells potatoes for $0.24 and tomatoes for $0.76. Fred bought 12 individual vegetables. If he paid $6.52 total, how many potatoes did Fred buy? A. 7 B. 8 C. 2 D. 5

D

Find x 6/x = 9/19 A. 3/38 B. not possible C. 7/12 D. none of these E. 9/114

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

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

If 8s - 6k = 4s - 2k, then, in terms of s, k = ? A. 2s B. 5s C. 3s D. s E. cannot be determined

D

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 f(x) = -x² + 6x - 5, then which could be the value of a if f(a) = f(1.5)? A. 4 B. 1 C. 2.5 D. 4.5 E. 3.5

D

If x = 4 and y = 3x + 5, then 2y - 1 equals A. 15 B. 47 C. 22 D. 33

D

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

Quantitative Comparison x > 0 Column A: 5x Column B: 5/x A. quantity B is greater B. quantities are equal C. quantity A is greater D. relationship cannot be determined

D

Solve for the y-intercept: 3y + 11 ≥ 5y + 6x - 1 A. -6 B. -12 C. 3 D. 6 E. -3

D

Solve for x. 4x + 3y = 6 2x + 2y = 4 A. x = 3/4 B. x = -2 C. x > 0 D. x = 0 E. x = 2

D

Solve for x: 2(x + 1)² - 5 = 27 A. -2 or 5 B. 3 or 4 C. -3 or 2 D. 3 or -5 E. -2 or 4

D

Solve for z: 3(z + 4)³ - 7 = 17 A. 8 B. 2 C. -8 D. -2 E. 4

D

What is f(-3) if f(x) = x²+5? A. 4 B. -14 C. 15 D. 14 E. -4

D

Worker A can make a trinket in 4 hours. Worker B can make a trinket in 2 hours. When they work together, how long will it take them to make a trinket? A. 3 hours B. 1 1/2 hours C. 1/2 hour D. 1 1/3 hours E. 6 hours

D

f(x) = 3x² - 5 g(x) = 9 - 2x Find f(g(5)). A. 131 B. -1 C. 4 D. -2 E. 70

D

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

x² + 5x - 24 = 0 y² - 9y + 20 = 0 Quantity A: x Quantity B: y A. two quantities are equal B. relationship cannot be determined C. quantity A is greater D. quantity B is greater

D

11 / (x - 7) + 4 / (7 - x) = ? A. 15/(x-7) B. 15/(7-x) C. 15 D. 7/(7-x) E. (-7)/(7-x)

E

4/x = 2/25 Find x. A. 8/25 B. none C. 25/8 D. .25 E. 50

E

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. -1 B. 12 C. -12 D. 3 E. -3

E

Abby works at a car dealership and receives a commission "c" which is a percent of the profit the dealership makes from the sale, which is the difference between the price "p" of the car and the value "v" of the car. How much, in dollars, does the dealership earn per transaction? A. (p - v)(0.01c) B. pv(0.01c) C. (p - v)(1 - c) D. p(v - 0.01c) E. (p - v)(1 - 0.01c)

E

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

Factor y² - 4. A. y(y - 4) B. (y - 2)(y - 2) C. (y + 2)(y + 2) D. none of the other answers are correct E. (y + 2)(y - 2)

E

If 2x + y = 9 and y - z = 4 then 2x + z = ? A. 13 B. cannot be determined C. 21 D. 29 E. 5

E

If [(7/8)]∧n = √([(7/8)]⁵), then what is the value of n? A. 1/5 B. 2/5 C. √5 D. 25 E. 5/2

E

If f(x) = 3x + 7 and g(x) = x² - 12, what is f(g(x))? A. 9x³ + 29 B. 9x² - 29 C. 3x³ - 29 D. 3x² + 29 E. 3x² - 29

E

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? A. y + z B. 3y + z C. 4y - z D. 5y + z E. 5y - z

E

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

Solve for x: x² - 3x - 28 = 0 A. -28, -31 B. 28, 31 C. -7, 4 D. 14, -11 E. 7, -4

E

Solve for x: (x² - x) / (x - 1) = 1 A. x = -2 B. x = -1 C. x = 1 D. x = 2 E. no solution

E

x and y are both integers If x - 3x < 21, y > 1, and y < 4, which of the following is a possible value of x? A. 7 B. -5 C. 3 D. -6 E. -7

E