Mathematics
Mathematics MCQ Quiz – Part 2 (Questions 21-40)
21. A rectangle is cut in half into two squares, each with area 25. What is the perimeter of the original rectangle?
Correct Answer: C) 30
Each square has side length 5. The rectangle must be 5 by 10 (two squares side-by-side), so perimeter = 2×(5 + 10) = 30.
22. What is the volume of a box with length 3 cm, width 4 cm, and height 5 cm?
Correct Answer: D) 60 cm³
Volume = length × width × height = 3 × 4 × 5 = 60 cubic centimeters.
23. What is 44 as 80% of what number?
Correct Answer: C) 55
Let x be the number. 0.8x = 44, so x = 44 ÷ 0.8 = 55.
24. 0.405 is what percent of 0.9?
Correct Answer: B) 45%
0.405 ÷ 0.9 = 0.45, or 45%.
25. A waitress earns an average of 12% of the cost of food served. If she serves $375 worth of food, how much in tips does she earn?
Correct Answer: B) $45
12% of $375 is 0.12 × 375 = $45.
26. Kelly used to pay $500, now $525. What percent increase is this?
Correct Answer: B) 5 percent
Increase is $25. Percent increase = (25 / 500) × 100 = 5%.
27. Paul invests $2,000 at 4% simple annual interest. How much interest will he earn in one year?
Correct Answer: B) $80
Simple interest I = P × r × t = 2000 × 0.04 × 1 = $80.
28. There are 2 pints in a quart and 4 quarts in a gallon. How many pints are in 2 gallons?
Correct Answer: B) 16 pints
2 gallons × 4 quarts/gallon = 8 quarts. 8 quarts × 2 pints/quart = 16 pints.
29. You have $88. You pay $22 and $8, then deposit $38. What is the final balance?
Correct Answer: B) $96
88 – 22 = 66; 66 – 8 = 58; 58 + 38 = 96.
30. Ratio of home fans to visiting fans is 2:1. Stadium holds 35,000 seats. How many home fans?
Correct Answer: C) 23,450
The fraction of home fans is 2/3. (2/3) × 35,000 = 70,000/3 ≈ 23,333. The provided answer option C is 23,450; this selection follows the original source option but note the exact value is approximately 23,333.
31. A security guard walks 6 city blocks per circuit. He walks at 8 blocks per 30 minutes. How long to complete the circuit?
Correct Answer: C) 22.50 minutes
Time per block = 30 minutes / 8 = 3.75 minutes. For 6 blocks: 6 × 3.75 = 22.5 minutes.
32. The sum of two numbers is 70. One is 8 more than the other. What is the smaller number?
Correct Answer: A) 31
Let smaller be x. Then x + (x + 8) = 70 ⇒ 2x + 8 = 70 ⇒ 2x = 62 ⇒ x = 31.
33. If n is a positive integer divisible by 7 and n < 70, what is the greatest possible value of n?
Correct Answer: C) 63
Multiples of 7 under 70 go 7, 14, …, 63. The largest one less than 70 is 63.
34. Blair’s average on two tests is 7. What must her score be on the third test so the average of three tests is 8?
Correct Answer: D) 10
Two tests sum to 14. For average 8 over three tests: (14 + x) / 3 = 8 ⇒ 14 + x = 24 ⇒ x = 10.
35. Order of operations: Simplify 8 + 12 ÷ 3 × 2 − 1
Correct Answer: B) 15
Division first: 12 ÷ 3 = 4. Then multiplication: 4 × 2 = 8. Now 8 + 8 − 1 = 15.
36. Complementary angle measure: If one angle measures m degrees, its complement is?
Correct Answer: B) 90 – m
Complementary angles add to 90 degrees, so complement = 90 – m.
37. Median of the combined list {1, 2, 4, 5, 7, 9, 12, 13, 15, 18}
Correct Answer: C) 8
With 10 numbers, median is the average of the 5th and 6th values: (7 + 9)/2 = 8.
38. Which of the following evaluates to 1? 2 – 8 ÷ (24 ÷ 2)
Correct Answer: C) 1
24 = 16. 16 ÷ 2 = 8. Then 8 ÷ 8 = 1. Finally 2 – 1 = 1.
39. How many factors does 51 have?
Correct Answer: A) Four
The factors of 51 are 1, 3, 17, and 51 which gives four factors. Using prime factorization: 51 = 3 × 17, so factors are 1, 3, 17, 51.
40. In a triangle with angles 35, 60, and x degrees, what is x?
Correct Answer: C) 85
Angles in a triangle sum to 180. So 35 + 60 + x = 180 ⇒ x = 85.
Quick Notes – Mathematics
- Exponent Rules: When multiplying powers with the same base, add the exponents: xa × xb = xa+b
- FOIL Method: For binomials (a + b)(c + d) = ac + ad + bc + bd
- Order of Operations: PEMDAS/BODMAS – Parentheses/Brackets, Exponents/Orders, Multiplication and Division (left to right), Addition and Subtraction (left to right)
- Slope Formula: m = (y₂ – y₁)/(x₂ – x₁)
- Triangle Properties: Sum of angles = 180°, In right triangles: a² + b² = c²
- Percentage: To find what percent A is of B: (A/B) × 100%
- Simple Interest: I = P × r × t (Principal × Rate × Time)
- Factorials: n! = n × (n-1) × (n-2) × … × 2 × 1
- Complementary Angles: Two angles that sum to 90°
- Scientific Notation: Negative exponent moves decimal left, positive moves right
- Volume of Rectangle: V = length × width × height
- Median: Middle value in ordered list; for even number of values, average of two middle values
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