Free Quantitative Reasoning MCQs with Answers

471. In the figure shown, line c intersects parallel lines s and t. What is the value of x ?

• A. 4 + 5
• B. 80
• C. 90
• D. 75

Explanation: The correct answer is 70. Based on the figure, the angle with measure 110o and the angle vertical to the angle with measure xo are same side interior angles. Since vertical angles are congruent, the angle vertical to the angle with measure xo also has measure xo . It's given that lines s and t are parallel. Therefore, same side interior angles between lines s and t are supplementary. It follows that x = 110 + 180. Subtracting 110 from both sides of this equation yields x = 70.

472. An event planner is planning a party. It costs the event planner a onetime fee of $35 to rent the venue and $10.25 per attendee. The event planner has a budget of $200. What is the greatest number of attendees possible without exceeding the budget?

• A. 0.07
• B. 15
• C. 13
• D. 27

Explanation: Choice C is correct. Let x be the 2015 population of Greenville. It's given that the population increased by 7% from 2015 to 2016. The increase in population can be written as 0.07 (x) . The 2016 population of Greenville is given as the sum of the 2015 population of Greenville and the increase in population from 2015 to 2016. This can be rewritten as x + 0.07(x), or 1.07(x). Therefore, the value of k is 1.07.

473. For a particular machine that produces beads, 29 out of every 100 beads it produces have a defect. A bead produced by the machine will be selected at random. What is the probability of selecting a bead that has adefect?

• A. 1/2,900
• B. 1/29
• C. 29/100
• D. 29/10

Explanation: Choice C is correct. It's given that 29 out of every 100 beads that the machine produces have a defect. It follows that if the machine produces k beads, then the number of beads that have a defect is 29/100k, for some constant k. If a bead produced by the machine will be selected at random, the probability of selecting a bead that has a defect is given by the number of beads with a defect, 29/100 k,divided by the number of beads produced by the machine, k. Therefore, the probability of selecting a bead that has a defect is , (29/100 k) / k or 29/100 .

474. Each side of a square has a length of 45. What is the perimeter of this square?

• A. 180
• B. 120
• C. 170

Explanation: The correct answer is 180. The perimeter of a polygon is equal to the sum of the lengths of the sides of the polygon. It's given that each side of the square has a length of 45. Since a square is a polygon with 4 sides, the perimeter of this square is 45+45+45+45, or 180.

475. The table gives the distribution of votes for a new school mascot and grade level for 80 students. If one of these students is selected at random, what is the probability of selecting a student whose vote for new mascot was for a lion?

• A. 1/9
• B. 1/5
• C. 1/4
• D. 2/3

Explanation: Choice C is correct. If one of these students is selected at random, the probability of selecting a student whose vote for the new mascot was for a lion is given by the number of votes for a lion divided by the total number of votes. The given table indicates that the number of votes for a lion is 20 votes, and the total number of votes is 80 votes. The table gives the distribution of votes for 80 students, and the table shows a total of 80 votes were counted. It follows that each of the 80 students voted exactly once. Thus, the probability of selecting a student whose vote for the new mascot was for a lion is 20/80, or 1/4.

476. An object is kicked from a platform. The equation h represents this situation, where h is the height of the object above the ground, in meters, t seconds after it is kicked. Which numberrepresents the height, in meters, from which the object was kicked?

• A. 0
• B. 4.9
• C. 7
• D. 9

Explanation: Choice D is correct. It's given that the equation h=_4.9 t represents this situation, where h is the height, in meters, of the object t seconds after it is kicked. It follows that the height, in meters, from which the object was kicked is the value of h when t = 0. Substituting 0 for t in the equation h = 4.9 t 2 + 7 t + 9 yields h = -4.9 (0)2 + 7 (0) + 9, or h =9. Therefore, the object was kicked from a height of 9 meters..

477. One gallon of paint will cover 220 square feet of a surface. A room has a total wall area of w square feet. Which equation represents the total amount of paint P, in gallons, needed to paint the walls of the room twice?

• A. P = w/110
• B. P = 440w
• C. P = w / 220
• D. P = 220 w

Explanation: Choice A is correct. It's given that w represents the total wall area, in square feet. Since the walls of the room will be painted twice, the amount of paint, in gallons, needs to cover 2w square feet. It's also given that one gallon of paint will cover 220 square feet. Dividing the total area, in square feet, of the surface to be painted by the number of square feet covered by one gallon of paint gives the number of gallons of paint that will be needed. Dividing 2w by 220 yields 2w/220, or w/110 . Therefore, the equation that represents the total amount of paint P, in gallons, needed to paint the walls of the room twice is P = w/110.

478. Which expression is equivalent to (m4 q4 z-1 )(mq5z3) ,where m, q, and z are positive?

• A. m4 q20 z−3
• B. m5q9z2
• C. m6q8z-1
• D. m20q12z-2

Explanation: Choice B is correct. Applying the commutative property of multiplication, the expression (m4q4z-1) (mq5 z3) can be rewritten as (m4m)(q4 q5 )(z-1z3) . For positive values of x , (xa)(xb)= x a+b. Therefore, the expression (m4m)(q4 q5 )(z-1 z3 ) can be rewritten as (m4+1)(q 4+5)(z-1+3 ), or m5q9z2.

479. 5x + 10x + 16 = 0How many distinct real solutions does the given equation have?

• A. Exactly One
• B. Exactly Two
• C. Infiniely many
• D. Zero

Explanation: Choice D is correct. The number of solutions of a quadratic equation of the for max 2 +bx + =c 0, where a, b, and c are constants, can be determined by the value of the discriminant, b2 -4ac If the value of the discriminant is positive, then the quadratic equation has exactly two distinct real solutions. If the value of the discriminant is equal to zero, then the quadratic equation has exactly one real solution. If the value of the discriminant is negative, then the quadratic equation

480. 3 more than 8 times a number x is equal to 83. Which equation represents this situation?

• A. (3)(8)x = 8
• B. 8x = 83 + 3
• C. 3x + 8 = 83
• D. 8x + 3 = 83

Explanation: Choice D is correct. The given phrase "8 times a number x" can be represented by the expression 8x. The given phrase "3 more than" indicates an increase of 3 to a quantity. Therefore "3 more than 8 times a number x" can be represented by the expression 8x + 3. Since it's given that 3 more than 8 times a number x is equal to 83, it follows that 8x + 3 is equal to 83, or 8x + 3 = 83. Therefore, the equation that represents this situation is 8x + 3 = 83.