Free Quantitative Reasoning MCQs with Answers

171. The numbers a , b , and c are positive and a equals 3.2bc . If b is increased by 150% and c is decreased by 60%, then a is

• A. increased by 90%
• B. increased by 10%
• C. unchanged
• D. decreased by 10%

Explanation: The given equation is a = 3.2bc. We are told that b is increased by 150%, making the new value of b = 2.5b (since 150% of b is 1.5b, adding this to the original b gives 2.5b). Similarly, c is decreased by 60%, making the new value of c = 0.4c (since 60% of c is 0.6c, subtracting this from the original c gives 0.4c).Substituting these new values into the equation for a gives: New a = 3.2 * 2.5b * 0.4c = 3.2bc. This is exactly the same as the original value of a, showing that a is unchanged despite changes in b and c.Therefore, the correct answer is Option C: unchanged. The other options are incorrect as they suggest changes in the value of a that do not occur based on the given percentage adjustments.

172. Number n is 25 less than 120 percent of itself. What is the value of n ?

• A. 125
• B. 120
• C. 105
• D. 90

Explanation: Start by translating the sentence into an equation: n = 120% * n - 25 We can simplify 120% as 1.2: n = 1.2n - 25 Now we can solve for n: n - 1.2n = -25 -0.2n = -25 n = (-25) / (-0.2) n = 125 Therefore, the value of n is 125.

173. Of the 500 cars displayed in a certain car dealer, 7 percent are blue and 4 percent are red. The number of blue cars in the car dealer are what percent greater than the number of red cars?

• A. 30%
• B. 50%
• C. 75%
• D. 125%

Explanation: The question asks us to determine how much greater the number of blue cars is compared to the number of red cars in percentage terms. First, calculate the number of blue and red cars: 7% of 500 is 35 blue cars, and 4% of 500 is 20 red cars.The difference between the number of blue and red cars is 35 - 20 = 15. To find how much greater the number of blue cars is than the number of red cars, use the formula: (difference / number of red cars) x 100% = (15 / 20) x 100% = 75%. Therefore, the number of blue cars is 75% greater than the number of red cars. Option C is correct because it reflects this calculation accurately, while the other options do not match the computed percentage difference.

174. If 2x/2y = 23 , then x must be equal to?

• A. y+3
• B. y-3
• C. 3-y
• D. 3y

Explanation: The original equation is 2x/2y = 23. Using the quotient rule for exponents, we have 2x-y = 23. This means that x - y = 3. Solving for x gives us x = y + 3. Therefore, the correct answer is x = y + 3. The other options are incorrect because they do not properly apply the properties of exponents to solve for x given the equation.

175. The smallest integer that, when squared, is less than 5 is

• A. 0
• B. 1
• C. 2
• D. -2

Explanation: The smallest integer that, when squared, is less than 5 is -2. This is because (-2)2 = 4, which is less than 5. The other options either result in higher squares or do not represent the smallest integer. Specifically, 0 squared is 0, 1 squared is 1, and 2 squared is 4, none of which are smaller than -2 when considering absolute value.

176. If y3=2y2 and y≠0, then y must be equal to

• A. 1
• B. ½
• C. 2
• D. 3

Explanation: As given,y3= 2y2Rearranging,y3/y2= 2y 3-2= 2y1 = 21y = 2Hence, the value of y must be 2.

177. Which expression has an answer of 18?

• A. 2 x 5 + 4
• B. 2 x (4+5)
• C. 5 x (2+4)
• D. 4 x (2+5)

Explanation: The correct option is B: 2 x (4+5). According to the BODMAS rule, solve the expression inside the brackets first, which is 4 + 5, giving 9. Then multiply by 2 to get 18. Other options fail to give 18 because they either multiply or add in a wrong sequence, resulting in different values: Option A gives 14, Option C gives 30, and Option D gives 28.

178. If n books cost r rupees. Then how much will m books cost?

• A. mr
• B. nr
• C. nr/m
• D. mr/n

Explanation: If n books cost r rupees, you can find the cost of m books using the concept of proportionality. The cost of books is directly proportional to the number of books. The proportionality constant is the cost per book. Let c be the cost of one book. So, n books cost r rupees can be written as: n.c=r Now, to find the cost of m books, set up the proportion: n/m=r/x Where x is the cost of m books. Cross-multiply to solve for x: n . x= m. r Now, divide both sides by n to find the cost of one book (c): x=mr/n

179. Arrange from smallest to largest

• A. 2, 2.6, 2 ¾ , 8/3
• B. 2, 2 ¾ , 2.6, 8/3
• C. 2, 2.6, 8/3, 2 ¾
• D. 2, 8/3, 2.6, 2 ¾

Explanation: 2 is the smallest 2 ¾ is larger than 2, 2.6 and 8/3 2.6 is smaller than 2 ¾ 8/3 is smaller than 2 ¾ but larger than 2.6 and 2 So, the correct arrangement from smallest to largest is: 2, 2.6, 8/3, 2 ¾

180. 288 minutes = _ % of 1 day

• A. 10
• B. 15
• C. 20
• D. 40

Explanation: To solve the problem, first calculate the total number of minutes in a day by multiplying 24 hours by 60 minutes, which equals 1440 minutes. The formula for percentage is (part/whole) x 100. Here, the 'part' is 288 minutes, and the 'whole' is 1440 minutes. Substituting these values into the formula gives:Percentage = (288/1440) x 100 = 20%Therefore, 288 minutes is 20% of one day.Option A (10%) and Option B (15%) are incorrect because they result in fewer minutes than 288 when calculated as percentages of 1440. Option D (40%) is incorrect because it results in more minutes than 288, specifically 576 minutes.