Free Quantitative Reasoning MCQs with Answers

21. 1/400 in percentage =

• A. 0.25%
• B. 0.025%
• C. 0.0025%
• D. 0.00025%

Explanation: First convert the fraction into decimals.1/400 = 0.0025To convert this decimal to a percentage, we can multiply it by 100:0.0025 x 100% = 0.25%Therefore, the answer is (A) 0.25%

22. A chemist mixes x mL of a 34% acid solution with a 10% acid solution. If the resulting solution is 40 mL with 25% acidity, what is the value of x?

• A. 18.5
• B. 20
• C. 22.5
• D. 25

Explanation: To solve the question, we apply the concept of mixtures and percentages. We define x as the volume of the 34% acid solution in mL. The amount of acid in the 34% solution is given by 0.34x mL, while the amount of acid in the 10% solution is 0.1(40 - x) mL, since the total volume of the solution is 40 mL.The total amount of acid in the resulting solution is 25% of 40 mL, which is 10 mL. To find x, we set up the equation:0.34x + 0.1(40 - x) = 10Solving this equation, we simplify:0.34x + 4 - 0.1x = 100.24x = 6x = 25This calculation shows that the correct amount of the 34% acid solution needed is 25 mL, making option D the correct answer. Other options fail to satisfy the equation and do not yield the correct final acidity percentage.

23. There are 10 history books in a bookcase. When the number of books increases by x percent, the new number of history books is 24. What is the value of x?

• A. 58
• B. 70
• C. 120
• D. 140

Explanation: To solve this problem, use the formula for percentage increase: new number = original number × (1 + x/100). Here, the original number of history books is 10, and the new number is 24. Set up the equation:24 = 10 × (1 + x/100)Divide both sides by 10 to isolate the percentage increase:2.4 = 1 + x/100Subtract 1 from both sides:1.4 = x/100Multiply both sides by 100 to solve for x:x = 140Therefore, the correct answer is Option D: 140. This means the number of books increased by 140%, making Option D correct. The other options (58, 70, and 120) do not satisfy the equation, as shown in their respective explanations.

24. If x2y3=10 and x3y2=8, what is the value of x5y5?

• A. 18
• B. 20
• C. 40
• D. 80

Explanation: To find x5y5, multiply the two given equations: (x2y3 = 10) and (x3y2 = 8). The left side becomes x2+3y3+2 = x5y5. The right side becomes 10 * 8 = 80. Therefore, x5y5 = 80, making option D correct. Options A, B, and C are incorrect as they do not match the result of this multiplication.

25. If a copier makes 7 copies every 5 seconds, then he continues at this rate, how many minutes will it take to make 4200 copies?

• A. 50
• B. 60
• C. 70
• D. 80

Explanation: Let x be the time in seconds.The copier makes 7 copies every 5 seconds, so the rate is 7/5 copies per second.Now, set up the proportion:7/5=4200/xTo solve for x, cross-multiply:7x= 5 × 42007x= 21000Now, divide by 7 to find x:X = 21000/7= 3000So, it takes 3000 seconds to make 4200 copies.Now, let's convert 3000 seconds to minutes. There are 60 seconds in a minute:minutes=3000/60=50Therefore, it will take 50 minutes to make 4200 copies if the copier continues at this rate.

26. Which of the following shows correct value of x, such that the two expressions given below are equal.I) a+b - c/x + 4c - 3a + 2b/bII) a+b + 4c + 2b/b - c/a - 3a

• A. b
• B. c
• C. a
• D. 2

Explanation: Equate both the expressions a+b - c/x + 4c - 3a + 2b/b = a+b + 4c + 2b/b - c/a - 3a Solve for the value of x. Combine like terms: a - 3a + b + 4c -c/x + 2b/b = a - 3a + b + 4c +2b/b - c/a Simplify further: -2a + b + 4c - c/x + 2 = -2a + b + 4c + 2 - c/a Now, subtract −2a+b+4c+2 from both sides to isolate the c/x term: c/x = -c/a Finally, divide both sides by −c to solve for x: x=a

27. If 75% ofo 68 is the same as 85% of n, what is the value of n?

• A. 60
• B. 65
• C. 70
• D. 30

Explanation: To solve the problem, first understand the statement '75% of 68 is the same as 85% of n'. This translates to the equation 0.75 × 68 = 0.85 × n. Converting percentages to decimals, the equation becomes:0.75 × 68 = 0.85 × nCalculate 0.75 × 68 which equals 51. Now the equation is 0.85 × n = 51. Divide both sides by 0.85 to isolate n:n = 51 / 0.85 = 60Thus, n = 60 is the correct answer. The other options (65, 70, and 30) do not satisfy the equation when substituted for n.

28. What is 2005 × 100 + 2005?

• A. 2005002005
• B. 20052005
• C. 2007005
• D. 202505

Explanation: 200500 + 2005 equals 202505 Hence according to place value this is the correct answer.

29. 2007 ➗ (2+0+0+7) − (2 × 0 ×0 × 7) = ?

• A. 9
• B. 214
• C. 223
• D. 2007

Explanation: To solve the expression, follow the BODMAS rule: 1. Calculate inside the parentheses first: (2+0+0+7) = 9. 2. Then divide 2007 by 9: 2007 ➗ 9 = 223. 3. The multiplication within the subtraction part is (2×0×0×7) = 0. Subtracting 0 does not change the result, so the final answer is 223. Options A, B, and D result from errors in applying the order of operations or arithmetic mistakes.

30. Which number when squared is increased by 500%?

• A. 5
• B. 6
• C. 7
• D. 10

Explanation: To solve this question, we need to find the number that, when squared, increases by 500% compared to its original value.First, understand that a 500% increase means the final value is 6 times the original (100% original + 500% increase = 600% total).Let's analyze the correct option:For 6: When squared, 6 becomes 36. The percentage increase is calculated as: (36 - 6) / 6 x 100 = 500%. This confirms that squaring 6 results in a 500% increase.Now, examine the incorrect options:Option 5: Squaring 5 gives 25, which increases by 400%.Option 7: Squaring 7 gives 49, which increases by 600%.Option 10: Squaring 10 gives 100, which increases by 900%.Thus, 6 is the only number that, when squared, increases by exactly 500%.