Free Quantitative Reasoning MCQs with Answers

281. Gisela would owe $15,500 in taxes each year if she were not eligible for any tax deductions. This year, Gisela is eligible for tax deductions that reduce the amount of taxes she owes by $2,325.00. If these tax deductions reduce the taxes Gisela owes this year by d%, what is the value of d?

• A. 5
• B. 10
• C. 15
• D. 20

Explanation: The correct answer is 15. To determine the percentage decrease, you use the formula: (Reduction Amount / Original Amount) * 100. In this case, the reduction amount is $2,325.00, and the original amount is $15,500. Therefore, the calculation is (2,325 / 15,500) * 100 = 15%. This means the tax deductions reduce the amount of taxes Gisela owes by 15%.Option A (5%) and Option B (10%) are too low because they do not account for the actual percentage reduction calculated by the formula. Option D (20%) is too high for the same reason. Only Option C correctly calculates the percentage decrease.

282. x2 - 1/ x-1 = -2What are all values of x that satisfy the equation above?

• A. -3
• B. 0
• C. 1
• D. -3 and -1

Explanation: Choice A is correct. Factoring the numerator of the rational expression x2 − 1/ x − 1 yields (x + 1)(x − 1) / x − 1 . The expression (x + 1)(x − 1) / x − 1 can be rewritten as ( x + 1/ 1 )( x − 1/ x − 1. Since x−1 /x−1 = 1, when x is not equal to 1, it follows that (x+1/1)( x−1/x−1) = ( x + 1/1 )(1) or x + 1. Therefore, the given equation is equivalent to x + 1 = −2. Subtracting 1 from both sides of x + 1 = −2 yields x = −3.

283. In the figure, triangle ABC is similar to triangle DEF. What is the value of cos(E)?

• A. 12/5
• B. 12/13
• C. 5/12
• D. 5/13

Explanation: Choice B is correct. Since figures are drawn to scale unless otherwise stated and triangle ABC is similar to triangle DEF, it follows that the measure of angle B is equal to the measure of angle E. Furthermore, it follows that side AB corresponds to side DE and that side BC corresponds to side EF. For similar triangles, corresponding sides are proportional, so AB/BC = DE/EF. In right triangle DEF, the cosine of angle E, or cos(E ), is equal to the length of the side adjacent to angle E divided by the length of the hypotenuse in triangle DEF. Therefore, cos(E) = DE/EF, which is equivalent to AB/BC. Therefore, cos(E) = 12/13.

284. √4x = x - 3What are all values of x that satisfy the given equation?I. 1II. 9

• A. I only
• B. II only
• C. I and II
• D. Neither I nor II

Explanation: Choice B is correct. Squaring both sides of the equation √4x = x − 3 yields 4x = (x − 3)2 , or 4x = (x − 3)(x − 3). Applying the distributive property on the right-hand side of the equation 4x = (x − 3)(x − 3) yields 4x = x2 − 3x − 3x + 9. Subtracting 4x from both sides of 4x = x2 − 3x − 3x + 9 yields 0 = x2 − 3x − 3x − 4x + 9, which can be rewritten as 0 = x2 − 10x + 9. Factoring the right-hand side of 0 = x2 −10x + 9 gives 0 = (x − 1)(x − 9). By the zero product property, if 0 = (x − 1)(x − 9), then 0 = x − 1 or 0 = x − 9. Adding 1 to both sides of 0 = x − 1 gives x = 1. Adding 9 to both sides of 0 = x − 9 gives x = 9. Substituting these values for x into the given equation will determine whether they satisfy the equation. Substituting 1 for x in the given equation yields √4(1) = 1 − 3, or √4 = -2, which is false. Therefore, x = 1 doesn't satisfy the given equation. Substituting 9 for x in the given equation yields √4(9) = 9-3 or √36 = 6, which is true. Therefore, x = 9 satisfies the given equation.

285. 2x + 3y = 12003x + 2y = 1300Based on the system of equations above, what is the value of 5x + 5y?

• A. 2200
• B. 2300
• C. 2400
• D. 2500

Explanation: To find the value of 5x + 5y, add the two equations: (2x + 3y) + (3x + 2y) = 1200 + 1300. This simplifies to 5x + 5y = 2500. Therefore, the correct answer is 2500.The other options (2200, 2300, 2400) are incorrect due to potential errors in adding the coefficients or the constants from the equations.

286. If u+ t =5 and u - t =2, what is the value of (u-t)(u2 - t2)?

• A. 5
• B. 10
• C. 15
• D. 20

Explanation: The correct answer is 20. Begin by recognizing that u2 − t2 can be factored as (u − t)(u + t). Thus, the expression (u − t)(u2 − t2) simplifies to (u − t)(u − t)(u + t). Given u + t = 5 and u − t = 2, substituting these values results in (2)(2)(5) = 20. The other options are incorrect because they result from errors in substitution or calculation.

287. Jake buys a bag of popcorn at a movie theater. He eats half of the popcorn during the 15 minutes of previews. After eating half of the popcorn, he stops eating for the next 30 minutes. Then he gradually eats the popcorn until he accidentally spills all of the remaining popcorn. Which of the following graphs could represent the situation?

• A. A
• B. B
• C. C
• D. D

Explanation: Choice B is correct because it accurately follows the sequence of events described. Initially, Jake eats half of his popcorn, which is represented by a linear decrease from the starting point. Then, he stops eating for 30 minutes, depicted as a horizontal line where the amount of popcorn remains constant. Afterward, he continues to eat until he spills everything, shown by another linear decrease followed by a vertical drop to zero at the 90-minute mark. Options A, C, and D are incorrect as they imply an increase in popcorn, which does not occur according to the story.

288. 4x + 6 = 18Which equation has the same solution as the given equation?

• A. 4x = 108
• B. 4x = 24
• C. 4x = 12
• D. 4x = 3

Explanation: Choice C is correct. Subtracting 6 from both sides of the given equation yields 4x = 12 , which is the equation given in choice C. Since this equation is equivalent to the given equation, it has the same solution as the given equation.

289. The total cost, in dollars, to rent a surfboard consists of a $25 service fee and a $10 per hour rental fee. A person rents a surfboard for t hours and intends to spend a maximum of $75 to rent the surfboard. Which inequality represents this situation?

• A. 10t ≤ 75
• B. 10 + 25t ≤ 75
• C. 25t ≤ 75
• D. 25 + 10t ≤ 75

Explanation: Choice D is correct. The cost of the rental fee depends on the number of hours the surfboard is rented. Multiplying t hours by 10 dollars per hour yields a rental fee of 10t dollars. The total cost of the rental consists of the rental fee plus the 25 dollar service fee, which yields a total cost of 25 + 10t dollars. Since the person intends to spend a maximum of 75 dollars to rent the surfboard, the total cost must be at most 75 dollars. Therefore, the inequality 25 + 10t ≤ 75 £represents this situation.

290. Each face of a fair 14-sided die is labeled with a number from 1 through 14, with a different number appearing on each face. If the die is rolled one time, what is the probability of rolling a 2?

• A. 1/14
• B. 2/14
• C. 12/14
• D. 13/14

Explanation: Choice A is correct. The total number of possible outcomes for rolling a fair 14-sided die is 14. The number of possible outcomes for rolling a 2 is 1. The probability of rolling a 2 is the number of possible outcomes for rolling a 2divided by the total number of possible outcomes, or 1/14.