Free Quantitative Reasoning MCQs with Answers

451. Based on the graph below, in how many of the games played did the soccer team score goals equal to the median number of goals for the 29 games?

• A. 6
• B. 7
• C. 8
• D. 9

Explanation: The correct answer is 9. The median number of goals scored is found by ordering the number of goals scored from least to greatest and then determining the middle value in the list. If the number of goals scored in each of the 29 games were listed in order from least to greatest, the median would be the fifteenth number of goals. The graph shows there were 8 games with 1 goal scored and 9 games with 2 goals scored. Therefore, the fifteenth number, or the median number, of goals scored must be 2. According to the graph, the soccer team scored 2 goals in 9 of the games played.

452. A television with a price of $300 is to be purchased with an initial payment of $60 and weekly payments of $30. Which of the following equations can be used to find the number of weekly payments, w, required to complete the purchase, assuming there are no taxes or fees?

• A. 300 = 30w − 60
• B. 300 = 30w
• C. 300 = 30w + 60
• D. 300 = 60w − 30

Explanation: Choice C is correct. To complete the purchase, the initial payment of $60 plus the w weekly payments of $30 must be equivalent to the $300 price of the television. The total, in dollars, of w weekly payments of $30 can be expressed by 30w. It follows that 300 = 30w + 60 can be used to find the number of weekly payments, w, required to complete the purchase.

453. In the figure, point B lies on AD. What is the value of 3x?

• A. 18
• B. 36
• C. 54
• D. 72

Explanation: Choice C is correct. Since point B lies on AD, angles ABC and CBD are supplementary. It's given that angle ABC is a right angle; therefore, its measure is 90°. It follows that the measure of angle CBD is 180° − 90°, or 90°. By the angle addition postulate, the measure of angle CBD is equivalent to x ° + 2x ° + 2x °. Therefore, 90 = x + 2x + 2x. Combining like terms gives 90 = 5x. Dividing both sides of this equation by 5 yields x = 18. Therefore, the value of 3x is 3(18), or 54.

454. Juan purchased an antique that had a value of $200 at the time of purchase. Each year, the value of the antique is estimated to increase 10% over its value the previous year. The estimated value of the antique, in dollars, 2 years after purchase can be represented by the expression 200a, where a is a constant. What is the value of a?

• A. 0.5
• B. 1.21
• C. 2
• D. 2.5

Explanation: The correct answer is 1.21. It's given that each year, the value of the antique is estimated to increase by 10% over its value the previous year. Increasing a quantity by 10% is equivalent to the quantity increasing to 110% of its original value or multiplying the original quantity by 1.1. Therefore, 1 year after the purchase, the estimated value of the antique is 200(1.1) dollars. Then, 2 years after purchase, the estimated value of the antique is 200(1.1)(1.1), or 200(1.21) dollars. It's given that the estimated value of the antique after 2 years is 200a dollars. Therefore, 200(1.21) = 200a. It follows that a = 1.21.

455. A helicopter, initially hovering 40 feet above the ground, begins to gain altitude at a rate of 21 feet per second. Which of the following functions represents the helicopter's altitude above the ground y, in feet, t seconds after the helicopter begins to gain altitude?

• A. y = 40 + 21
• B. y = 40 + 21t
• C. y = 40 - 21t
• D. y = 40t + 21

Explanation: Choice B is correct. It's given that the helicopter's initial height is 40 feet above the ground and that when the helicopter's altitude begins to increase, it increases at a rate of 21 feet per second. Therefore, the altitude gain t seconds after the helicopter begins rising is represented by the expression 21t. Adding this expression to the helicopter's initial height gives the helicopter's altitude above the ground y, in feet, t seconds after the helicopter begins to gain altitude: y = 40 + 21t.

456. A text messaging plan charges a flat fee of $5 per month for up to 100 text messages sent plus $0.25 for each additional text message sent that month. Which of the following graphs represents the cost, y, of sending x texts in a month?

• A. A
• B. B
• C. C
• D. D

Explanation: Choice A is correct. The text messaging plan charges a flat fee of $5 per month for up to 100 text messages. This is represented graphically with a constant value of y = 5 for 0 ≤ x ≤ 100. After 100 messages, each additional message sent costs $0.25. This is represented graphically with an increase of 0.25 on the y-axis for every increase of 1 on the x-axis. Choice A matches these descriptions.

457. The two graphs show the total amounts of money that Ian and Jeremy each have deposited into their savings accounts for the first seven weeks after opening their accounts. After they made their initial deposits, how much more did Ian deposit each week than Jeremy?

• A. $200
• B. $100
• C. $50
• D. $25

Explanation: Choice C is correct. The graph for Ian shows that the initial deposit was $100 and that each week the total amount deposited increased by $100. Therefore, Ian deposited $100 each week. The graph for Jeremy shows that the initial deposit was $300 and that each week the total amount deposited increased by $50. Therefore, Jeremy deposited $50 each week. Thus, Ian deposited $50 more than Jeremy did each week.

458. A printer produces posters at a constant rate of 42 posters per minute. At what rate, in posters per hour, does the printer produce the posters?

• A. 1250
• B. 2520
• C. 3150
• D. 2450

Explanation: The correct answer is 2,520. There are 60 minutes in one hour. At a rate of 42 posters per minute, the number of posters produced in one hour can be determined by (42 posters / 1 minute) (60 minutes / 1 hour), which is 2,520 posters per hour.

459. A teacher is creating an assignment worth 70 points. The assignment will consist of questions worth 1 point and questions worth 3 points. Which equation represents this situation, where x represents the number of 1-point questions and y represents the number of 3-point questions?

• A. 4xy = 70
• B. 4(x + y) = 70
• C. 3x + y= 70
• D. x + 3y = 70

Explanation: Choice D is correct. Since x represents the number of 1-point questions and y represents the number of 3-point questions, the assignment is worth a total of 1.x + 3.y or x + 3y, points. Since the assignment is worth 70 points, the equation x + 3y = 70 represents this situation.

460. Vivian bought party hats and cupcakes for $71. Each package of party hats cost $3, and each cupcake cost $1. If Vivian bought 10 packages of party hats, how many cupcakes did she buy?

• A. 41
• B. 43
• C. 51
• D. 52

Explanation: The correct answer is 41. The number of cupcakes Vivian bought can be found by first finding the amount Vivian spent on cupcakes. The amount Vivian spent on cupcakes can be found by subtracting the amount Vivian spent on party hats from the total amount Vivian spent. The amount Vivian spent on party hats can be found by multiplying the cost per package of party hats by the number of packages of party hats, which yields $3 • 10, or $30. Subtracting the amount Vivian spent on party hats, $30, from the total amount Vivian spent, $71, yields $71 - $30 , or $41. Since the amount Vivian spent on cupcakes was $41 and each cupcake cost $1, it follows that Vivian bought 41 cupcakes.