Free Quantitative Reasoning MCQs with Answers

11. The average height of 10 students is 155 cm. Later on it is discovered that while calculating the average, the reading of 157 cm was wrongly read as 147 cm. The correct average is

• A. 196
• B. 154
• C. 200
• D. 156

Explanation: A, B, C are incorrect, as 156cm is the correct average height. D is correct as the total height of 10 students = 10 x 155 = 1550 cm. Since 157cm was incorrectly read as 147 cm, 1550 - 147 + 157 = 15601560/10 = 156 cm

12. Mario received y text messages each minute for 10 minutes yesterday, and received t text messages each minute for 20 minutes today. What is the total number of text messages he received for two days in terms of y and t?

• A. 30yt
• B. 200yt
• C. 20y+10t
• D. 10y+20t

Explanation: To find the total number of text messages Mario received for two days, calculate the messages for each day separately:For yesterday, with y messages each minute for 10 minutes, Mario received a total of 10y messages.For today, with t messages each minute for 20 minutes, Mario received a total of 20t messages.Therefore, the total number of messages for two days is 10y + 20t.Options A and B are incorrect as they do not consider the given times for each day. Option C is incorrect due to the incorrect placement of coefficients for y and t. The correct answer is Option D because it correctly calculates the total messages received by considering the specific times for each day.

13. The sum of three-fourths of the number a and 24 is positive 9. What is the value of a ?

• A. -44
• B. -20
• C. 20
• D. 44

Explanation: The correct answer is Option B: -20.By solving the equation 3/4a + 24 = 9, we find that a = -20 after isolating the variable. Therefore, the value of a is -20.Options A, C, and D are incorrect because they do not yield the correct value of a when the equation is solved.

14. If 5(x-2)-3x=2(x-5), which of the following must be true?

• A. x is 3
• B. x is 4
• C. x is 5
• D. The equation is true for all values of x.

Explanation: The correct answer is Option D: The equation is true for all values of x.By simplifying both sides using the BODMAS rule, it can be seen that the equation holds true for all values of x, not just specific ones. Options A, B, and C are incorrect because they only consider specific values, while the correct answer encompasses all possible values of x.

15. g(x)=kx3+3For the function g defined above, k is a constant and g(-1)=5. What is the value of g(1) ?

• A. -3
• B. -1
• C. 1
• D. 3

Explanation: To find the value of k, you can use the given condition g(-1) = 5:5 = k(-13) + 3k = -2Substitute k = -2 back into the function to find g(1):g(1) = -2(13) + 3 = 1Therefore, the correct answer is Option C. Options A, B, and D are incorrect because they do not satisfy the initial condition g(-1) = 5 when substituted back into the function.

16. Which of the following is the equation of the line that passes through the point (4, -1) and has a slope −2?

• A. x + 2y = 2
• B. x - 2y = 6
• C. 2x - y = 9
• D. 2x+y=7

Explanation: The equation for the line is y=mx+cWe have the value of m = slope = -2 and it passes through point (4,-1) so, x = 4 and y = -1Substitute these values in the equation to find the value of c which is the y-intercept.-1 = (4)(-1) + C-1 = -8 + CC = -1 + 8 = 7So now we know that the value of m=-1 and C=7 so put these values in the equation, to find the equation of line. Also, make the value of c the subject as per the options.y = mx + cy = -2x + 72x + y = 7

17. Line L in the xy- plane contains points from each of the Quadrants I, III, and IV, but no points from Quadrant II. Which of the following must be true?

• A. The slope of line L is zero.
• B. The slope of line L is undefined.
• C. The slope of line L is positive.
• D. The slope of line L is negative.

Explanation: The correct answer is Option C. A positive slope enables the line to rise from left to right, intersecting Quadrants I, III, and IV while avoiding Quadrant II. This aligns with the given criteria. Option A is incorrect as a horizontal line (slope of zero) cannot pass through three quadrants. Option B is wrong because a vertical line (undefined slope) would intersect only two quadrants. Option D is incorrect because a negative slope would not satisfy the requirement of avoiding Quadrant II.

18. A rock climber is climbing up a 450-foot-high cliff. By 9:30 AM, the climber had reached 90 feet up the cliff, and by 11:00 AM, he had reached 210 feet up the cliff. If he climbs with a constant speed, by what time will he reach the top of the cliff?

• A. 1:45 PM
• B. 2:00 PM
• C. 2:15 PM
• D. 2:30 PM

Explanation: Constant speed is equal distance covered in equal time periods So he will cover the rest of the distance by the same time intervals as before Distance covered : 210 ft As we have the time interval from 9: 30 to 11:00 A.M we will use the distance covered in this interval only in the ratio method Distance covered in interval 9 : 30 to 11:AM 210 - 90= 120 ft Distance remaining : 450 - 210=240 So using ratio method Ft./hrs 120/1.5=240/ x Cross multiplying =120 * x=1.5 * 240 x = 3 hrs 3 hrs is the time interval between 11 and the reaching time of the climber. So, Reaching time - option =3 hrs (converting in 24 hour clock before subtraction by adding 12 to the options) Option A) =12:00+ 1 : 45 =13 45 =13 45 - 11 = 2 hrs 45 mim Option gives wrong outcomes Option B) 12 :00 + 2 14 00 hrs 14 - 11 = 3 hrs Option is giving correct outcome Option C) 12:00 + 2 :15 14 :15 - 11= 3 hrs 15 min Option gives wrong outcomes Option D) 12:00 +2:30 =14:30 14 : 30 - 11 = 3 hrs 30 mins Option gives wrong outcomes

19. Jason and Mary are running on a 200 meter track. The expressions in the table above show the distance to the finish line t seconds after they started the race. How many meters will Mary have left to finish the race when Jason is on the finish line?

• A. 10.5 meters
• B. 11.5 meters
• C. 12.5 meters
• D. 13.5 meters

Explanation: We are given two expressions that represent the distance to the finish line for Jason and Mary at time t seconds:Jason: -8t + 200Mary: -7.5t + 200This means both runners start 200 meters away from the finish line, and their speeds are 8 m/s for Jason and 7.5 m/s for Mary.Step 1: When does Jason reach the finish line?To find that, we set Jason's distance to 0:-8t + 200 = 0 Add 8t to both sides: 200 = 8t Now divide by 8: t = 25So Jason finishes the race in 25 seconds.Step 2: How far is Mary at t = 25?Now plug t = 25 into Mary's expression:-7.5(25) + 200 = -187.5 + 200 = 12.5

20. On a map, 1 inch represents 5 miles. If a certain state is represented on a map by a rectangle 10 inches by 7.2 inches, what is the area of the state in square miles?

• A. 360 mi2
• B. 720 mi2
• C. 1080 mi2
• D. 1800 mi2

Explanation: To find the area of the state in square miles, convert the dimensions from inches to miles using the given scale. The length of the rectangle on the map is 10 inches, which converts to 10 x 5 = 50 miles. The width is 7.2 inches, converting to 7.2 x 5 = 36 miles. The area of the state is determined by multiplying these two dimensions: Area = 50 miles x 36 miles = 1800 mi2.Options A, B, and C result from errors in conversion or calculation. Option A (360 mi2) has an incorrect conversion, Option B (720 mi2) likely involves partial conversion, and Option C (1080 mi2) reflects a miscalculation. Therefore, the correct area is Option D (1800 mi2).