GED Math Practice Test
- Mathematical Reasoning
- 12 questions
- 18 minutes
These 12 questions cover the main skills on the GED Mathematical Reasoning test: number sense, percents, algebra, linear functions, geometry and basic statistics. On the real test a formula sheet is provided and a calculator is allowed for most questions, so focus on setting up each problem correctly.
Tap an option to mark your answer. You can change your mind, or tap the same option again to leave the question blank. The correct answers and explanations appear when you finish the test.Tap an option to answer; tap it again to leave the question blank.
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Question 1
What is the value of 18 − 3(4 − 2)2 ÷ 6?
Correct answer: C
Work inside the parentheses first: 4 − 2 = 2, and 22 = 4. Then multiply and divide from left to right (3 × 4 ÷ 6 = 2) and subtract: 18 − 2 = 16. The answer 10 comes from subtracting 18 − 3 first, which breaks the order of operations.
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Question 2
A jacket regularly priced at $80 is on sale for 25% off. A sales tax of 6% is added to the sale price. What is the total cost of the jacket?
Correct answer: B
The sale price is 80 × 0.75 = $60.00, and the tax is 6% of that amount: 60 × 0.06 = $3.60. The total is $63.60. The answer $64.80 comes from figuring the tax on the original $80 instead of on the sale price.
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Question 3
Over five years, the population of a town grew from 12,500 to 14,000. By what percent did the population increase?
Correct answer: C
Percent change = change ÷ original value = 1,500 ÷ 12,500 = 0.12, or 12%. Dividing by the new value instead (1,500 ÷ 14,000 ≈ 10.7%) is a common mistake.
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Question 4
What value of x makes the equation 3(x − 4) = 2x + 5 true?
Correct answer: D
Distribute to get 3x − 12 = 2x + 5. Subtract 2x from both sides and add 12 to both sides: x = 17. The answer 9 comes from multiplying only the x by 3 and forgetting to multiply the 4.
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Question 5
A plumber charges a $65 service fee plus $48 for each hour of work. A customer's bill was $257. Which equation can be used to find h, the number of hours the plumber worked?
Correct answer: A
The $65 fee is charged once, and the $48 rate is multiplied by the number of hours, so the bill is 65 + 48h. Solving gives h = 4 hours. Option C wrongly multiplies the one-time fee by the hours as well.
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Question 6
What is the slope of the line that passes through the points (−2, 5) and (4, −7)?
Correct answer: B
Slope = change in y ÷ change in x = (−7 − 5) ÷ (4 − (−2)) = −12 ÷ 6 = −2. Getting −6 means computing the change in x as 4 − 2 instead of 4 − (−2).
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Question 7
x 0 2 4 6 y 7 11 15 19 The table shows values of a linear function. Which equation represents the function?
Correct answer: A
When x = 0, y = 7, so the y-intercept is 7. Each time x increases by 2, y increases by 4, so the rate of change is 4 ÷ 2 = 2. Option B uses the change in y without dividing by the change in x.
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Question 8
If f(x) = 2x2 − 3x + 1, what is f(−2)?
Correct answer: C
Substitute −2 for x: 2(−2)2 − 3(−2) + 1 = 2(4) + 6 + 1 = 15. Remember that (−2)2 is positive 4 and that −3 times −2 is positive 6.
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Question 9
A 13-foot ladder leans against a wall. The bottom of the ladder is 5 feet from the base of the wall. How high up the wall does the ladder reach?
Correct answer: B
The ladder is the hypotenuse of a right triangle, so 52 + h2 = 132. Then h2 = 169 − 25 = 144, and h = 12 feet. The answer 13.9 comes from adding the squares instead of subtracting.
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Question 10
A rectangular room measures 14 feet by 11 feet. Carpet costs $3.50 per square foot. How much will it cost to carpet the entire floor?
Correct answer: D
The floor area is 14 × 11 = 154 square feet, and 154 × $3.50 = $539.00. The answer $175.00 comes from using the perimeter (50 feet) instead of the area.
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Question 11
Over five weeks, a store sold these numbers of bicycles: 30, 42, 25, 38, 45. What is the median number of bicycles sold?
Correct answer: D
Put the numbers in order first: 25, 30, 38, 42, 45. The middle value is 38. The value 36 is the mean, and 25 is simply the middle number of the unsorted list.
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Question 12
A bag contains 4 red, 6 blue and 5 green marbles. One marble is chosen at random. What is the probability that the marble is not blue?
Correct answer: A
There are 4 + 6 + 5 = 15 marbles, and 9 of them are not blue. The probability is 9/15, which simplifies to 3/5. The fraction 2/5 is the probability of drawing a blue marble.
Questions you leave blank are not counted as wrong.
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