Download Arithmetic Practice Test Practice Exam and more Exams Technology in PDF only on Docsity!
Question 1. Which of the following numbers is a whole number but not a natural number? A) 0 B) 1 C) 5 D) 12 Answer: A Explanation: Whole numbers include 0 and all positive integers; natural numbers start at 1, so 0 is whole but not natural. Question 2. What is the value of the digit 7 in the number 5,437? A) 7 B) 70 C) 700 D) 7, Answer: C Explanation: In 5,437 the 7 is in the hundreds place, representing 7 × 100 = 700. Question 3. Round 3.6789 to the nearest hundredth. A) 3.6 B) 3.67 C) 3.68 D) 3. Answer: C Explanation: The third decimal is 8 (≥5), so round the second decimal up: 3.68. Question 4. Evaluate using PEMDAS: 8 + 2 × 5² − 4. A) 38 B) 48 C) 58 D) 68 Answer: B Explanation: Exponents first: 5² = 25. Then multiplication: 2 × 25 = 50. Then left‑to‑right: 8 + 50 − 4 = 54. Wait calculation error—actually 8 + 50 − 4 = 54, not listed. Re‑evaluate: order is correct; answer should be 54. Since not in options, correct option is none—adjust options. Corrected Options: A) 54 B) 48 C) 58 D) 68 Answer: A Explanation: As shown, 8 + (2 × 25) − 4 = 8 + 50 − 4 = 54. Question 5. Which property is illustrated by 9 + 4 = 4 + 9?
A) Associative B) Commutative C) Distributive D) Identity Answer: B Explanation: The commutative property states that order does not affect the sum. Question 6. Find the greatest common factor (GCF) of 24 and 36. A) 4 B) 6 C) 8 D) 12 Answer: D Explanation: Prime factors: 24 = 2³·3, 36 = 2²·3²; common factors 2²·3 = 12. Question 7. What is the least common multiple (LCM) of 5 and 7? A) 12 B) 35 C) 70 D) 5 Answer: B Explanation: Since 5 and 7 are relatively prime, LCM = 5 × 7 = 35. Question 8. Which of the following numbers is prime? A) 49 B) 51 C) 53 D) 55 Answer: C Explanation: 53 has no divisors other than 1 and itself. Question 9. The prime factorization of 84 is: A) 2·2·3·7 B) 2·2·2·3·7 C) 2·3·7 D) 2·2·3· Answer: A Explanation: 84 = 2²·3·7. Question 10. Simplify the fraction 45/60. A) 3/4 B) 2/3 C) 5/8 D) 7/
Explanation: Multiply by reciprocal: (5/8) × (3/2) = 15/16. Question 16. Convert the mixed number 3 ¾ to an improper fraction. A) 15/4 B) 13/4 C) 12/4 D) 11/ Answer: B Explanation: 3 ¾ = 3 + 3/4 = 12/4 + 3/4 = 15/4. Wait 3 ¾ = 3 + 3/4 = 15/4, not 13/4. Correct answer is A. Answer: A Explanation: 3 ¾ = (3×4 + 3)/4 = 15/4. Question 17. Write 0.625 as a fraction in simplest form. A) 5/8 B) 13/20 C) 25/40 D) 3/ Answer: A Explanation: 0.625 = 625/1000 = 5/8 after dividing by 125. Question 18. Which decimal is a terminating decimal? A) 1/3 B) 5/8 C) 2/7 D) 1/ Answer: B Explanation: 5/8 = 0.625, which terminates; the others produce repeating decimals. Question 19. Express 7/9 as a percent. A) 77.8% B) 78% C) 70% D) 79% Answer: A Explanation: 7 ÷ 9 ≈ 0.777…, multiply by 100 → 77.777…% ≈ 77.8%. Question 20. What percent of 250 is 40?
A) 12% B) 14% C) 16% D) 18%
Answer: C Explanation: (40 ÷ 250) × 100 = 16%. Question 21. Increase 85 by 12%. A) 93.2 B) 95.2 C) 97.2 D) 99. Answer: C Explanation: 12% of 85 = 10.2; add → 85 + 10.2 = 95.2. Wait answer mismatch. Actually 12% of 85 = 10.2, sum = 95.2 → option B. Answer: B Explanation: As shown, the increased amount is 95.2. Question 22. A jacket originally costs $120 and is sold for 25% off. What is the sale price? A) $85 B) $90 C) $95 D) $ Answer: B Explanation: 25% of 120 = 30; subtract → 120 − 30 = 90. Question 23. Write the ratio 45 : 60 in simplest form. A) 3 : 4 B) 5 : 6 C) 9 : 12 D) 15 : 20 Answer: A Explanation: Divide both terms by GCF = 15 → 3 : 4. Question 24. If a car travels 180 miles in 3 hours, what is its unit rate in miles per hour? A) 50 B) 55 C) 60 D) 65 Answer: C Explanation: Rate = distance ÷ time = 180 ÷ 3 = 60 mph.
Question 29. If y varies inversely with x and y = 8 when x = 4, what is y when x = 16? A) 1 B) 2 C) 4 D) 8 Answer: B Explanation: Inverse variation: y = k/x. k = 8·4 = 32; y = 32/16 = 2. Question 30. Evaluate 2³ × 2⁴. A) 2⁷ B) 2¹² C) 2⁰ D) 2⁵ Answer: A Explanation: Adding exponents: 3 + 4 = 7, so 2⁷. Question 31. What is 5⁰? A) 0 B) 1 C) 5 D) Undefined Answer: B Explanation: Any non‑zero number raised to the zero power equals 1. Question 32. Simplify (–3)⁴. A) – 81 B) 81 C) – 27 D) 27 Answer: B Explanation: Even exponent makes the result positive: (–3)⁴ = 81. Question 33. Find the square root of 144. A) 10 B) 11 C) 12 D) 13 Answer: C Explanation: 12 × 12 = 144.
Question 34. Which of the following is a perfect cube? A) 27 B) 40 C) 50 D) 65 Answer: A Explanation: 27 = 3³. Question 35. Estimate the cube root of 50 (to the nearest integer). A) 3 B) 4 C) 5 D) 6 Answer: B Explanation: 3³ = 27, 4³ = 64; 50 is closer to 64, so estimate ≈ 4. Question 36. Express 0.000345 in scientific notation. A) 3.45 × 10⁻⁴ B) 3.45 × 10⁻³ C) 3.45 × 10⁻⁵ D) 3.45 × 10⁻⁶ Answer: A Explanation: Move decimal 4 places right: 3.45 × 10⁻⁴. Question 37. Multiply (2 × 10³) × (5 × 10⁴). A) 1 × 10⁸ B) 7 × 10⁸ C) 1 × 10⁷ D) 1 × 10⁶ Answer: A Explanation: Multiply coefficients (2·5 = 10) and add exponents (3 + 4 = 7): 10 × 10⁷ = 1 × 10⁸. Question 38. Divide (9 × 10⁵) ÷ (3 × 10²). A) 3 × 10³ B) 3 × 10⁴ C) 3 × 10⁶ D) 3 × 10⁷ Answer: B Explanation: 9÷3 = 3; subtract exponents 5‑ 2 = 3 → 3 × 10 ³. Wait compute: 10⁵ ÷ 10 ² = 10³, so result 3 × 10 ³. Option A matches. Answer: A
Question 44. The data set is {4, 8, 15, 16, 23, 42}. What is the median? A) 15 B) 15.5 C) 16 D) 23 Answer: C Explanation: Ordered set has 6 numbers; median is average of 3rd and 4th: (15 + 16)/2 = 15.5. Wait option B is 15.5. So correct answer is B. Answer: B Explanation: As calculated, median = 15.5. Question 45. What is the mode of the set {7, 9, 7, 12, 9, 7}? A) 7 B) 9 C) 12 D) No mode Answer: A Explanation: 7 appears three times, more than any other number. Question 46. Find the range of the data set {3, 5, 9, 12, 15}. A) 12 B) 10 C) 9 D) 8 Answer: A Explanation: Range = max − min = 15 − 3 = 12. Question 47. Calculate the mean of {2, 4, 6, 8, 10}. A) 5 B) 6 C) 7 D) 8 Answer: B Explanation: Sum = 30; divide by 5 → mean = 6. Question 48. In a bar graph, the bar for “Apples” reaches 40 units while “Oranges” reaches 55 units. What is the percent increase from Apples to Oranges? A) 27.5% B) 30% C) 35% D) 45%
Answer: A Explanation: Increase = 55 − 40 = 15; percent = (15/40)·100 = 37.5%. None of the options match. Adjust options: A) 37.5% B) 30% C) 35% D) 45% Answer: A Explanation: Percent increase is 37.5%. Question 49. A store sells 3 shirts for $45. What is the unit price per shirt? A) $12 B) $13 C) $14 D) $ Answer: D Explanation: Unit price = 45 ÷ 3 = $15. Question 50. If a car travels at 55 mph for 2.5 hours, how far does it go? A) 110 mi B) 125 mi C) 137.5 mi D) 150 mi Answer: C Explanation: Distance = rate × time = 55 × 2.5 = 137.5 mi. Question 51. Simple interest on $800 at 5% per year for 3 years is: A) $100 B) $120 C) $130 D) $ Answer: B Explanation: I = P·r·t = 800·0.05·3 = 120. Question 52. A restaurant bill is $68. If you leave a 15% tip, what is the total amount paid? A) $75.20 B) $77.20 C) $78.20 D) $80. Answer: B Explanation: Tip = 0.15·68 = 10.20; total = 68 + 10.20 = 78.20. Wait option C is 78.20. So correct answer C. Answer: C
Explanation: Total time = 4.5 h; speed = 300 ÷ 4.5 = 66.666… ≈ 66.7 km/h. Question 57. What is the least common denominator of 1/6 and 1/8? A) 24 B) 48 C) 12 D) 14 Answer: A Explanation: LCM of 6 and 8 is 24. Question 58. Simplify: (3/5) ÷ (9/10). A) 2/3 B) 3/2 C) 5/6 D) 6/ Answer: B Explanation: Multiply by reciprocal: (3/5) × (10/9) = 30/45 = 2/3? Wait 30/45 simplifies to 2/3. So answer A. Answer: A Explanation: Result is 2/3. Question 59. Which of the following is an irrational number? A) √16 B) 0.75 C) √2 D) 5/ Answer: C Explanation: √2 cannot be expressed as a fraction; it is irrational. Question 60. Convert 3.2 × 10⁶ millimeters to meters. A) 3.2 × 10³ m B) 3.2 × 10⁴ m C) 3.2 × 10⁵ m D) 3.2 × 10⁶ m Answer: A Explanation: 1 m = 1,000 mm = 10³ mm; divide exponent by 3: 10⁶ mm = 10³ m, so 3.2 × 10³ m. Question 61. A circle has a radius of 7 cm. What is its circumference (use π ≈ 3.14)?
A) 21.98 cm B) 43.96 cm C) 49 cm D) 154 cm Answer: B Explanation: C = 2πr ≈ 2·3.14·7 ≈ 43.96 cm. Question 62. The same circle’s area is: A) 49π cm² B) 154 cm² C) 153.86 cm² D) 100 cm² Answer: C Explanation: A = πr² ≈ 3.14·49 ≈ 153.86 cm². Question 63. If a 12‑oz bottle of juice costs $1.44, what is the cost per ounce? A) $0.10 B) $0.12 C) $0.14 D) $0. Answer: B Explanation: Cost per ounce = 1.44 ÷ 12 = 0.12. Question 64. A discount of 18% is applied to a $250 item. What is the discounted price? A) $205 B) $210 C) $215 D) $ Answer: A Explanation: Discount = 0.18·250 = 45; price = 250 − 45 = 205. Question 65. The ratio of cats to dogs in a shelter is 7 : 5. If there are 84 cats, how many dogs are there? A) 50 B) 60 C) 70 D) 80 Answer: B Explanation: 7 parts = 84 → 1 part = 12; dogs = 5 × 12 = 60. Question 66. In a proportion, 12 : x = 3 : 5. Find x.
Question 71. If a fraction is equivalent to 0.777…, which fraction represents it? A) 7/9 B) 7/8 C) 3/4 D) 5/ Answer: A Explanation: 0.\overline{7} = 7/9. Question 72. A number increased by 25% becomes 125. What was the original number? A) 90 B) 95 C) 100 D) 105 Answer: C Explanation: Let original be x; x + 0.25x = 1.25x = 125 → x = 100. Question 73. The sum of the interior angles of a polygon with n sides is 1260°. Find n. A) 7 B) 8 C) 9 D) 10 Answer: C Explanation: Sum = 180(n − 2) → 180(n − 2) = 1260 → n − 2 = 7 → n = 9. Question 74. Evaluate (–2)³ + 4². A) – 8 B) 0 C) 8 D) 12 Answer: C Explanation: (–2)³ = – 8; 4² = 16; sum = 8. Question 75. Which of the following is the correct factorization of x² − 9? A) (x + 3)(x + 3) B) (x − 3)(x + 3) C) (x − 9)(x + 9) D) (x − 3)(x − 3) Answer: B Explanation: Difference of squares: a² − b² = (a − b)(a + b).
Question 76. If 5ⁿ = 125, what is n? A) 2 B) 3 C) 4 D) 5 Answer: B Explanation: 5³ = 125, so n = 3. Question 77. Convert 2500 milliliters to liters. A) 0.25 L B) 2.5 L C) 25 L D) 250 L Answer: B Explanation: 1 L = 1000 mL; 2500 mL = 2.5 L. Question 78. A right triangle has legs of length 6 cm and 8 cm. What is the length of the hypotenuse? A) 10 cm B) 12 cm C) 14 cm D) 16 cm Answer: A Explanation: By Pythagoras: √(6² + 8²) = √(36 + 64) = √100 = 10. Question 79. What is 15% of 600 expressed as a fraction in simplest form? A) 3/5 B) 9/20 C) 3/20 D) 9/ Answer: B Explanation: 0.15 × 600 = 90; 90/600 = 3/20 after simplification. Question 80. A bag contains 5 red, 7 blue, and 8 green marbles. What is the probability of randomly selecting a blue marble? A) 5/20 B) 7/20 C) 8/20 D) 12/ Answer: B Explanation: Total marbles = 20; blue = 7; probability = 7/20.
Explanation: 13 ÷ 40 = 0.325. Question 86. Which of the following is the correct decimal representation of the fraction 7/12? A) 0.5833… B) 0.5714… C) 0.6 D) 0. Answer: A Explanation: 7 ÷ 12 = 0.5833 repeating. Question 87. A number is increased by 40% and then decreased by 25% of the original number. The final result is 84. What was the original number? A) 100 B) 110 C) 120 D) 130 Answer: C Explanation: Let original = x. Increase: x + 0.40x = 1.4x. Decrease 25% of original: subtract 0.25x → final = 1.4x − 0.25x = 1.15x = 84 → x = 84 ÷ 1.15 ≈ 73.04. Not matching options. Let's adjust problem: Suppose decrease is 25% of the increased amount. Then final = 1.4x − 0.25·1.4x = 1.4x·0.75 = 1.05x =84 → x =80. Not in options. We'll create a simpler one. Revised Question 87. A number is increased by 20% to become 72. What was the original number? A) 55 B) 60 C) 65 D) 70 Answer: B Explanation: 1.20x = 72 → x = 72 ÷ 1.20 = 60. Question 88. If 0.\overline{36} is expressed as a fraction, what is it? A) 4/11 B) 9/25 C) 12/33 D) 33/ Answer: A Explanation: Let x = 0.3636…; 100x = 36.36…; subtract: 99x = 36 → x = 36/99 = 4/11.
Question 89. A store sells notebooks at $2.50 each. If a customer buys 7 notebooks and receives a 10% discount on the total, what is the amount paid? A) $15.75 B) $16.00 C) $16.25 D) $17. Answer: A Explanation: Total before discount = 7·2.50 = $17.50; discount = 0.10·17.50 = 1.75; paid = 17.50 − 1.75 = 15.75. Question 90. A rectangular garden is twice as long as it is wide. If its perimeter is 60 m, what is its area? A) 200 m² B) 225 m² C) 250 m² D) 300 m² Answer: C Explanation: Let width = w, length = 2w. Perimeter = 2(w + 2w) = 6w = 60 → w = 10 m, length = 20 m; area = 10·20 = 200 m². Wait area 200, option A. Answer: A Explanation: As computed, area = 200 m². Question 91. Convert 5/8 to a percent. A) 55% B) 60% C) 62.5% D) 65% Answer: C Explanation: 5 ÷ 8 = 0.625 × 100 = 62.5%. Question 92. A loan of $1,200 is repaid with simple interest at 6% per year for 4 years. What is the total amount repaid? A) $1,288 B) $1,320 C) $1,384 D) $1, Answer: D Explanation: Interest = 1200·0.06·4 = 288; total = 1200 + 288 = 1488. Not in options. Let's adjust interest rate: 5% for 4 years → interest = 1200·0.05·4 = 240; total = 1440. Not listed. Use 5% for 2 years → interest = 120. Total = 1320 (option B).
