Free Quantitative Reasoning MCQs with Answers

161. The quantities x and y are positive. If x is decreased by 20 percent and y is increased by 20 percent, then the product of x and y is

• A. unchanged
• B. decreased by 4%
• C. increased by 5%
• D. decreased by 6%

Explanation: Let's assume that the original values of x and y are X and Y, respectively.If x is decreased by 20%, then its new value is:x = X - 0.2X = 0.8XIf y is increased by 20%, then its new value is:y = Y + 0.2Y = 1.2YThe product of x and y is:xy = (0.8X)(1.2Y) = 0.96XYSo the new product is 0.96 times the original product.This means that the product of x and y is decreased by 4%.Therefore, the answer is (B) decreased by 4%

162. By what percent is 4.5 x 10^5 greater than 9 x 10^4?

• A. 200%
• B. 400%
• C. 500%
• D. 600%

Explanation: To determine by what percent 4.5 x 105 is greater than 9 x 104, first calculate the difference between the two numbers:Difference = 4.5 x 105 - 9 x 104 = 3.6 x 105.Next, express this difference as a percentage of the original value (9 x 104):Percent increase = (Difference / Original value) x 100%= (3.6 x 105 / 9 x 104) x 100%= 4 x 100%= 400%Thus, the correct answer is Option B: 400%. Other options are incorrect because they either underestimate or overestimate the percentage increase.

163. If 125% of x is 80 and x is n % of 400, what is the value of n?

• A. 12
• B. 14
• C. 16
• D. 18

Explanation: To solve this problem, we start by calculating the value of x from the equation 125% of x = 80. Converting 125% to a decimal gives 1.25, so the equation becomes 1.25x = 80. Solving for x, we divide both sides by 1.25 to get x = 64.Next, we use the information that x is n% of 400. This can be expressed as x = (n/100) * 400. Substituting the value of x (64) into the equation, we have 64 = (n/100) * 400. Solving for n, we divide both sides by 400 to get 0.16 = n/100. Finally, multiplying both sides by 100 gives n = 16.Therefore, the correct answer is Option C (16), as this is the percentage that x (64) represents of 400. The other options are incorrect because they result from miscalculations of the percentage relationship.

164. 54 is 120% of k . Which of the following proportions could be used to solve the above expression?

• A. 100/120 = 54/k
• B. 54/100 = 120/k
• C. 100/54 = 120/k
• D. 120/100 = 54/k

Explanation: To solve the problem of finding what number (k) 54 is 120% of, we first convert 120% into a fraction: 120% = 120/100.We set up the proportion: 120/100 = 54/k, which states that 54 is 120% of k.By cross-multiplying and solving this equation, we can find the value of k.The other options are incorrect because they either swap the roles of values or incorrectly set up the percentage to base relationship.

165. If Kevin's monthly salary of $4,500 is 72 percent of Paul's monthly salary, what is Paul's monthly salary?

• A. $3240
• B. $5150
• C. $5870
• D. $6250

Explanation: To solve this problem, we need to determine what Paul's monthly salary is if Kevin's salary is 72% of it. We can express this relationship mathematically as:Kevin's salary = 72% of Paul's salary, or $4,500 = 0.72 × Paul's salary.To find Paul's salary (let's call it x), we divide Kevin's salary by the percentage in decimal form:x = $4,500 ÷ 0.72.This calculation gives us x = $6,250. Thus, Paul's monthly salary is $6,250.Option A ($3,240), Option B ($5,150), and Option C ($5,870) do not match this division result and are therefore incorrect.

166. The price of a cellphone was discounted by 25% and then discounted an additional 20%, to become $348. What was the original price of the cellphone before it was discounted twice?

• A. $580.00
• B. $620.00
• C. $650.00
• D. $680.00

Explanation: To solve this problem, we need to determine the original price of the cellphone before any discounts were applied. Let's use the variable x to represent the original price.The first discount reduces the price by 25%, meaning the new price is 75% of the original price. This can be expressed as 0.75x.The second discount reduces the price by an additional 20%. Now, the price becomes 80% of the already discounted price, which can be expressed as 0.8 * 0.75x = 0.6x.We know the final price after both discounts is $348, so we set up the equation: 0.6x = 348To find the original price, we solve for x:x = 348 / 0.6 = $580Thus, the original price of the cellphone was $580. Option A is correct because it matches this solution. The other options are incorrect because they do not lead to $348 after applying the sequential discounts.

167. A chemist mixes a 40% acid solution and a 30% acid solution. How many liters of the 40% solution must be added to produce 50 liters of a solution that is 36% acid?

• A. 24
• B. 26
• C. 30
• D. 32

Explanation: To solve this problem, we need to determine the amount of the 40% acid solution (x) to mix with the 30% acid solution to achieve a 36% concentration in 50 liters. Let x be the liters of the 40% solution, implying 50 - x liters of the 30% solution.The equation for acid content is: 0.4x + 0.3(50 - x) = 18, where 18 represents 36% of 50 liters.Solving, we get: 0.4x + 15 - 0.3x = 18, which simplifies to 0.1x = 3, leading to x = 30.Therefore, combining 30 liters of the 40% solution with 20 liters of the 30% solution yields the desired 36% concentration in 50 liters. Options A, B, and D do not meet the acid concentration requirement, making Option C the correct choice.

168. A sporting goods store added 50% profit cost and 8% tax to the price of a backpack, which then became $129.60. What was the price of the backpack before adding profit and tax?

• A. 70
• B. 80
• C. 90
• D. 100

Explanation: To find the original price of the backpack, let's denote it as $x.First, a 50% profit is added, making the price 1.5x. Next, an 8% tax is applied to this new price, resulting in 1.08(1.5x) = 1.62x.We are given that the final price is $129.60, so we can set up the equation:1.62x = 129.60Solving for x, we divide both sides by 1.62: x = 129.60 / 1.62 = 80.Therefore, the original price of the backpack before adding profit and tax was $80. Options A, C, and D are incorrect because they do not satisfy this calculation when the tax and profit percentages are removed.

169. There are 800 students in a school and 45% of the students are male. If 30% of the male students and 25% of the female students play varsity sports, how many students play varsity sports?

• A. 200
• B. 218
• C. 400
• D. 435

Explanation: The problem requires calculating the number of students who play varsity sports using given percentages. First, determine the number of male and female students:Number of male students = 45% of 800 = 360Number of female students = 55% of 800 = 440Next, calculate how many of these students play varsity sports:Male students playing varsity sports = 30% of 360 = 108Female students playing varsity sports = 25% of 440 = 110The total number of students playing varsity sports is the sum of the two groups:Total = 108 + 110 = 218Therefore, the correct answer is B) 218. The other options either underestimate or overestimate the total due to incorrect calculations or assumptions.

170. The price of a package of 4 pens is $8.00. The same pens are sold at $2.50 each. If Alex bought three packages of pens rather than buying 12 pens individually, the amount he saved on 12 pens is what percent of the amount he paid?

• A. 12%
• B. 20%
• C. 25%
• D. 30%

Explanation: To solve this problem, you need to understand the concept of percentage savings. First, calculate the cost of buying 12 pens individually: 12 pens at $2.50 each totals $30. Next, calculate the cost of buying 3 packages of 4 pens (12 pens total) at $8.00 per package: 3 packages cost $24. The savings from buying in packages is $30 - $24 = $6. The percentage saved is computed by dividing the savings by the package cost: ($6/$24) x 100% = 25%. Therefore, the correct answer is 25%. The other options represent incorrect calculations of the percentage saved based on the cost difference and the amount paid.