Mathematics Knowledge Practice Test 2

Correct answer: A — 58

To find the average (mean), add all the numbers together $$(45 + 72 + 88 + 31 + 54 = 290)$$ and then divide the sum by the total count of numbers (5). $$290 \div 5 = 58$$

Correct answer: B — 14

The mode is the number that appears most frequently in a data set. In this list, the number 14 appears three times, which is more often than any other number.

Correct answer: B — $$12:1$$

A ratio compares two quantities. The ratio of nurses to doctors is 60 to $$5 (60:5)$$. To simplify, divide both numbers by their greatest common divisor, which is 5. $$60 \div 5 = 12$$ and $$5 \div 5 = 1$$. Therefore, the simplified ratio is $$12:1$$

Correct answer: B — 52.5 feet

Set up a proportion using the given scale: 1 inch / 15 feet = 3.5 inches / x feet. Cross-multiply to solve for x: $$1 \times x = 15 \times 3.5$$, which equals 52.5. The actual length is 52.5 feet.

Correct answer: A — 5

First, convert the hours to minutes so the units match the question. 1.5 hours is equal to 90 minutes $$(1.5 \times 60 = 90)$$. Next, divide the total number of items by the total minutes to find the rate per minute: 450 items ÷ 90 minutes = 5 items per minute.

Correct answer: A — 1, 2, 3, 6, 7, 14, 21, 42

The factors of a number are all the integers that divide evenly into it. 42 can be divided evenly by 1, 2, 3, 6, 7, 14, 21, and 42. Option C is missing 1 and 42. Options B and D contain numbers that do not divide evenly into 42 (such as 4 and 8).

Correct answer: B — $$2 \times 2 \times 3 \times 5$$

Prime factorization requires all factors in the expression to be prime numbers. While $$3 \times 4 \times 5$$ equals 60, the number 4 is a composite number, not prime. Breaking it down completely: $$60 = 2 \times 30 = 2 \times 2 \times 15 = 2 \times 2 \times 3 \times 5$$

Correct answer: B — $$3 \times 3 \times 5 \times 7$$

To find the prime factorization, divide the number by prime numbers. 315 ends in 5, so it is divisible by 5: $$315 = 5 \times 63$$. Then, 63 is divisible by 3: $$63 = 3 \times 21$$. Finally, 21 is $$3 \times 7$$. Grouping all the prime factors together gives $$3 \times 3 \times 5 \times 7$$. Options A, C, and D contain composite numbers (21, 9, and 35).

Correct answer: B — 1, 2, 3, 6, 19, 38, 57, 114

Factors of 114 are found in factor pairs: $$1 \times 114 = 114$$, $$2 \times 57 = 114$$, $$3 \times 38 = 114$$, and $$6 \times 19 = 114$$. Therefore, the complete and correct list of all factors is 1, 2, 3, 6, 19, 38, 57, and 114.

Correct answer: B — 97

The number 97 is a prime number, meaning its only positive integer divisors are 1 and itself. The prime factorization of a prime number is simply the number itself. Because the number 1 is technically not classified as a prime number, '$$1 \times 97$$' is not considered a proper prime factorization. Therefore, the answer is just 97.