Pre-Algebra Placement Test Practice

Multiple choice pre-algebra questions to assess your skills in order of operations, integers, decimals, fractions, divisibility, factors, GCF, LCM, scientific notation, exponents, square roots, ratios, proportions, percentages, statistics, and algebraic applications. Detailed solutions are included below.

Question 1

Evaluate: \( 72 - 9 \div 3 \cdot 2 + 2 = \)

  1. 21
  2. 23
  3. 44
  4. 68
  5. 74
Show Detailed Solution

Solution: Use order of operations to evaluate multiplication and division first from left to right: \( 9 \div 3 \cdot 2 = 3 \cdot 2 = 6 \). Insert the result: \( 72 - 6 + 2 \). Evaluate addition and subtraction from left to right: \( 72 - 6 + 2 = 68 \).

Question 2

In scientific notation: \( 3.0 \times 10^{-5} + 0.0000022 = \)

  1. \(3.5 \times 10^{-5}\)
  2. \(3.22 \times 10^{-5}\)
  3. \(5.2 \times 10^{-6}\)
  4. \(3.5 \times 10^{-6}\)
  5. \(5.2 \times 10^{-11}\)
Show Detailed Solution

Solution: Rewrite \( 0.0000022 \) as \( 0.22 \times 10^{-5} \). Add: \( 3.0 \times 10^{-5} + 0.22 \times 10^{-5} = 10^{-5}(3.0 + 0.22) = 3.22 \times 10^{-5} \).

Question 3

If \( \frac{2}{3} \div \frac{4}{5} \times \frac{6}{7} \) is calculated and reduced to simplest form, what is the numerator?

  1. 12
  2. 8
  3. 7
  4. 6
  5. 3
Show Detailed Solution

Solution: \(\frac{2}{3} \times \frac{5}{4} \times \frac{6}{7} = \frac{10}{12} \times \frac{6}{7} = \frac{60}{84}\). Divide numerator and denominator by 12: \(\frac{5}{7}\). Numerator is 5.

Question 4

Calculate: \( \frac{3}{4} + \frac{2}{5} - \frac{1}{8} \)

  1. \(\frac{59}{80}\)
  2. \(\frac{17}{20}\)
  3. \(\frac{41}{40}\)
  4. \(\frac{16}{15}\)
  5. \(\frac{17}{15}\)
Show Detailed Solution

Solution: Common denominator is 40. \( \frac{30}{40} + \frac{16}{40} - \frac{5}{40} = \frac{46-5}{40} = \frac{41}{40} \).

Question 5

A shop owner increased a shirt's price from \( \$20 \) to \( \$26 \). What percentage increase is this?

  1. 6
  2. 26
  3. 30
  4. 46
  5. 60
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Solution: Change = \(26-20 = 6\). Percentage Increase = \(\frac{6}{20} \times 100\% = 30\%\).

Question 6

Evaluate: \( \frac{3}{4} + 0.85 + 20\% = \)

  1. 27.85
  2. 1.8
  3. 23.85
  4. 2.85
  5. 21.6
Show Detailed Solution

Solution: \( \frac{3}{4} + 0.85 + 20\% = 0.75 + 0.85 + 0.20 = 1.8 \).

Question 7

Tom worked 6 hours at \( \$5.50\)/hr. He bought 2 magazines at \( \$9.50 \) each and a pen at \( \$8.25 \). Money left?

  1. $60.25
  2. $15.25
  3. $33
  4. $27.25
  5. $5.75
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Solution: Earnings: \(6 \times 5.5 = 33\). Expenses: \(2 \times 9.5 + 8.25 = 19 + 8.25 = 27.25\). Balance: \(33 - 27.25 = 5.75\).

Question 8

Bill bought \(1\frac{3}{4}\) lbs Cheddar, 3.75 lbs blue cheese, and \(4\frac{1}{2}\) lbs goat cheese. What is ths total weight of cheese bought?

  1. 8
  2. 7.75
  3. 9.25
  4. 10
  5. 7
Show Detailed Solution

Solution: \(1.75 + 3.75 + 4.5 = 10\).

Question 9

In a school, 40% are 8 or younger. Remaining = 120. How many are 8 or younger?

  1. 80
  2. 160
  3. 480
  4. 320
  5. 740
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Solution: If 40% are younger, 60% (120) are older. \(0.6x = 120 \implies x = 200\). Younger: \(40\% \text{ of } 200 = 80\).

Question 10

In a school one-fifth of the total numbers of students have no siblings. Of the rest, 40% have one sibling. What percentage of the total number of students have more than one sibling?

  1. 60
  2. 80
  3. 48
  4. 20
  5. 45
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Solution: Rest is \(4/5\) ( = 80%). Students with >1 sibling: \(60\% \text{ of } 80\% = 0.6 \times 0.8 = 0.48 = 48\%\).

Question 11

A car hire company offers Plan A: \( \$20/day \) plus 5¢/km, and Plan B: \( \$15/day \) plus 7¢/km. In one day, for how many kilometers do both plans cost the same?

  1. 1000
  2. 800
  3. 242
  4. 400
  5. 250
Show Detailed Solution

Solution: Let \( x \) be the number of kilometers. \(20 + 0.05x = 15 + 0.07x \implies 5 = 0.02x \implies x = 250\).

Question 12

Joe worked \(x\) hours, earned \(y\) dollars. What is his earnings for \(z\) hours?

  1. \(yz/x\)
  2. \(z/xy\)
  3. \(xyz\)
  4. \(zx/y\)
  5. \(xy/z\)
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Solution: Rate = \(y/x\). Earnings for \(z\) hours = \(\frac{y}{x} \cdot z = \frac{yz}{x}\).

Question 13

A class of 30, with 20 girls, averaged 80. The girls averaged 85. What is the average of the boys?

  1. 60
  2. 70
  3. 80
  4. 85
  5. 90
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Solution: Total class points = \(30 \times 80 = 2400\). Girls' points = \(20 \times 85 = 1700\). Boys' points = \(2400 - 1700 = 700\). Boys' average = \(700 / 10 = 70\).

Question 14

Find \(y\) if \(\frac{y}{5} = \frac{10}{25}\).

  1. 80
  2. 25
  3. 2
  4. 8
  5. 1
Show Detailed Solution

Solution: \(25y = 50 \implies y = 2\).

Question 15

Evaluate: \(\sqrt{3^2 + 4^2} =\)

  1. 7
  2. 25
  3. 50
  4. 12
  5. 5
Show Detailed Solution

Solution: \(\sqrt{9 + 16} = \sqrt{25} = 5\).

Question 16

Club has 24 members (15 females, rest males). Ratio of males to total?

  1. 15:24
  2. 24:9
  3. 9:24
  4. 9:39
  5. 9:15
Show Detailed Solution

Solution: Males = \(24 - 15 = 9\). Ratio = 9:24.

Question 17

Write 2.05 as a mixed number.

  1. \(20\frac{1}{2}\)
  2. \(2\frac{1}{2}\)
  3. \(2\frac{1}{5}\)
  4. \(2\frac{1}{20}\)
  5. \(2\frac{2}{5}\)
Show Detailed Solution

Solution: \(2.05 = 2 + 5/100 = 2 + 1/20 = 2\frac{1}{20}\).

Question 18

Which number is divisible by 3?

  1. 101267
  2. 22345
  3. 934567
  4. 934566
  5. 11177811
Show Detailed Solution

Solution: Divisibility by 3: sum of digits must be divisible by 3. \(9+3+4+5+6+6 = 33\), which is divisible by 3. The number 934566 is divisible by 3

Question 19

Which is NOT a prime number?

  1. 27
  2. 29
  3. 17
  4. 37
  5. 23
Show Detailed Solution

Solution: \(27 = 3 \times 9\), so it is not prime.

Question 20

What is the slope of a line parallel to line through (2,0) and (-1,3)?

  1. -3
  2. 1
  3. 0
  4. 3
  5. -1
Show Detailed Solution

Solution: Slope \(m = (3-0)/(-1-2) = -1\). Parallel lines have the same slope.

Question 21

GCF of 32 and 48?

  1. 32
  2. 16
  3. 8
  4. 4
  5. 2
Show Detailed Solution

Solution: Factors of 32: 1, 2, 4, 8, 16, 32. Factors of 48: 1, 2, 3, 4, 6, 8, 12, 16, 24, 48. GCF is 16.

Question 22

Which pair has an LCM of 24?

  1. 6 and 8
  2. 6 and 12
  3. 4 and 6
  4. 4 and 3
  5. 4 and 8
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Solution: The least common multiple (LCM) of 6 and 8 is 24.