GED Math Practice Test: Practice Test 4

Question 1

1. $\frac{3}{11}$ (correct answer)
2. $\frac{6}{11}$
3. $\frac{9}{11}$
4. $\frac{5}{12}$

Explanation: Total ways to choose 3 balls from 12: $C(12,3) = 220$. Ways to choose 1 red from 5: $C(5,1) = 5$. Ways to choose 1 blue from 4: $C(4,1) = 4$. Ways to choose 1 yellow from 3: $C(3,1) = 3$. Favorable outcomes = $5 \times 4 \times 3 = 60$. Probability = $\frac{60}{220} = \frac{3}{11}$. Choice B doubles the correct probability. Choice C assumes too many favorable outcomes. Choice D uses wrong total count.

Question 2

1. 200–249 kWh
2. 250–299 kWh
3. 300–349 kWh (correct answer)
4. 350–399 kWh

Explanation: The tallest bar corresponds to 300–349 kWh, indicating most households fall in that interval. The bars for the other intervals are shorter, so those choices are incorrect.

Question 3

1. $30n - 1200$ (correct answer)
2. $30n + 1200$
3. $130n - 1200$
4. $130n + 1200$

Explanation: The correct answer is A. Profit = Revenue - Cost = R(n) - C(n) = 80n - (50n + 1200) = 80n - 50n - 1200 = 30n - 1200. Choice B incorrectly adds the constant term instead of subtracting it. Choice C incorrectly adds the coefficients of n instead of subtracting. Choice D makes both errors: adding coefficients and adding the constant.

Question 4

1. 10 (correct answer)
2. 12
3. 15
4. 25

Explanation: Let 'c' be the number of cars and 'v' be the number of vans. We can create a system of two equations:

1. Total vehicles: c + v = 25
2. Total seating capacity: 5c + 8v = 155 From equation (1), express c in terms of v: c = 25 - v. Substitute this expression into equation (2): 5(25 - v) + 8v = 155 125 - 5v + 8v = 155 125 + 3v = 155 3v = 30 v = 10 There are 10 vans in the fleet.

Question 5

1. $\frac{11}{15}$ (correct answer)
2. $\frac{2}{5}$
3. $\frac{3}{5}$
4. $\frac{1}{3}$

Explanation: When you encounter probability questions asking for "either...or" scenarios, you're dealing with the addition principle. You need to find the probability of multiple favorable outcomes occurring. First, let's establish the total number of jelly beans: 6 red + 4 blue + 5 green = 15 total jelly beans. The probability of selecting either red or green means you want any jelly bean that isn't blue. There are 6 red + 5 green = 11 favorable outcomes. Using the basic probability formula: $P(\text{red or green}) = \frac{\text{favorable outcomes}}{\text{total outcomes}} = \frac{11}{15}$ Let's examine why the other answers are incorrect. Answer B ($\frac{2}{5}$) equals $\frac{6}{15}$, which represents only the probability of selecting red—this ignores the green jelly beans entirely. Answer C ($\frac{3}{5}$) equals $\frac{9}{15}$, suggesting there are only 9 favorable outcomes, which underestimates the actual count. Answer D ($\frac{1}{3}$) equals $\frac{5}{15}$, which represents only the probability of selecting green—this ignores the red jelly beans. The correct answer is A: $\frac{11}{15}$. Study tip: For "either...or" probability questions, always count all favorable outcomes carefully and remember that "or" typically means addition in probability. Double-check your work by ensuring your favorable outcomes plus unfavorable outcomes equal the total (here: 11 favorable + 4 blue = 15 total).

Question 6

1. A student who studies 0 hours per week is predicted to score approximately 45 points on the final exam.
2. For each additional hour of weekly study, the predicted final exam score increases by approximately 4 points. (correct answer)
3. A student who studies 10 hours per week will score exactly 85 points on the final exam.
4. The correlation between weekly study hours and final exam scores is negative.

Explanation: The line of best fit passes through approximately (2, 53) and (12, 93), giving a slope of (93-53)/(12-2) = 40/10 = 4 points per hour. This means for each additional hour of study, the predicted score increases by 4 points. Choice A correctly identifies the y-intercept but slope interpretation is more clearly supported by the data points shown. Choice C is wrong because a line of best fit predicts but does not determine exact scores. Choice D is wrong because the association is clearly positive.

Question 7

1. $725
2. $775 (correct answer)
3. $815
4. $850

Explanation: Midpoints: 550, 650, 750, 850, 950, 1050. Frequencies: 4, 6, 10, 8, 5, 2. Total salary = $(550)(4)+(650)(6)+(750)(10)+(850)(8)+(950)(5)+(1050)(2) = 2200+3900+7500+6800+4750+2100 = 27250$. Total employees = 35. Mean = $27250/35 ≈ 778.57 ≈ 775$. A: uses lower bounds. B: correct. C: uses upper bounds. D: averages midpoints unweighted.

Question 8

1. $12(s + 150) + 8s = 2880$ (correct answer)
2. $12s + 8(s + 150) = 2880$
3. $12(150) + 8s = 2880$
4. $12s + 8s + 150 = 2880$

Explanation: Let s = student tickets. Since they sold 150 more adult tickets than student tickets, adult tickets = s + 150. Revenue = (adult price × adult tickets) + (student price × student tickets) = 12(s + 150) + 8s = 2880. Choice B incorrectly assigns the higher price to student tickets and adds 150 to student tickets instead of adult. Choice C assumes exactly 150 adult tickets were sold. Choice D treats 150 as additional revenue instead of additional tickets.

Question 9

1. 18 miles
2. 19 miles
3. 21 miles (correct answer)
4. 24 miles

Explanation: Map scale problems test your ability to work with proportional relationships. When you see a scale like "1 inch represents 6 miles," you're dealing with a ratio that stays constant throughout the entire map. To solve this, set up a proportion using the given scale. Since 1 inch on the map equals 6 miles in reality, and the towns are 3.5 inches apart on the map, you can calculate: $3.5 \text{ inches} \times 6 \text{ miles per inch} = 21 \text{ miles}$ Alternatively, you can set up the proportion: $\frac{1 \text{ inch}}{6 \text{ miles}} = \frac{3.5 \text{ inches}}{x \text{ miles}}$. Cross-multiplying gives you $x = 3.5 \times 6 = 21$ miles. Looking at the wrong answers: Choice A (18 miles) likely comes from miscalculating $3.5 \times 6$ or possibly confusing the setup. Choice B (19 miles) doesn't follow from any logical calculation with these numbers. Choice D (24 miles) might result from rounding 3.5 up to 4 and then multiplying by 6, which is incorrect since you must use the exact map measurement given. When working with map scales, always identify what one unit represents, then multiply by the actual measurement you're given. Don't round intermediate steps—use the exact measurements provided. The key is recognizing that map scale creates a direct proportion: if the map distance increases, the real distance increases by the same factor.

Question 10

1. $9m < 60$ (correct answer)
2. $60 < 9m$
3. $9m + 60 < 0$
4. $\dfrac{9}{m} < 60$

Explanation: When comparing costs between different pricing structures, you need to set up an inequality that directly compares the total cost of each plan for the same time period. Plan A costs 9 per month, so for $$m$$ months, the total cost is $$9m$$ dollars. Plan B costs a flat 60 per year regardless of usage. To find when Plan A is cheaper than Plan B, you set up the inequality: Plan A cost < Plan B cost, which gives you $9m < 60$. Let's verify this makes sense: if you use the service for 6 months, Plan A costs $9 \times 6 = 54$ dollars, while Plan B costs $60. Since $54 < 60$, Plan A is indeed cheaper, confirming our inequality is correct. Looking at the wrong answers: Choice B ($60 < 9m$) represents when Plan B is cheaper than Plan A—the opposite of what we want. Choice C ($9m + 60 < 0$) incorrectly adds the costs together instead of comparing them, and since both plans cost money, this sum could never be negative. Choice D ($\dfrac{9}{m} < 60$) uses division instead of multiplication, which would give you a cost per month squared rather than a total monthly cost. Study tip: When comparing costs in word problems, always identify what each option costs for the same time period, then set up your inequality as "cheaper option < more expensive option." Watch out for answer choices that flip the inequality or use incorrect operations.

Question 11

1. 20 liters of pure water
2. 30 liters of pure water (correct answer)
3. 40 liters of pure water
4. 90 liters of pure water

Explanation: The original solution has $60 \times 0.15 = 9$ liters of salt. Let $x$ be the liters of water added. The new mixture has volume $(60 + x)$ and still contains 9 liters of salt. For 10% concentration: $\frac{9}{60 + x} = 0.10$. Solving: $9 = 0.10(60 + x) = 6 + 0.10x$, so $3 = 0.10x$ and $x = 30$. Choice A assumes 12% final concentration. Choice C uses incorrect proportion setup. Choice D assumes equal volumes of solution and water.

Question 12

1. 6
2. 10 (correct answer)
3. 19
4. 16

Explanation: To solve this system, first eliminate the fractions by multiplying each equation by the least common multiple of its denominators. For the first equation, multiply by 6: 6((\frac{1}{2}x) + (\frac{1}{3}y)) = 6(7) --> 3x + 2y = 42 For the second equation, multiply by 10: 10((\frac{1}{5}x) - (\frac{1}{2}y)) = 10(-1) --> 2x - 5y = -10 Now, solve the new system:

1. 3x + 2y = 42
2. 2x - 5y = -10 Multiply equation (1) by 5 and equation (2) by 2 to eliminate y: 5(3x + 2y = 42) --> 15x + 10y = 210 2(2x - 5y = -10) --> 4x - 10y = -20 Add the two resulting equations: (15x + 10y) + (4x - 10y) = 210 + (-20) 19x = 190 x = 10 The question asks for the x-coordinate, which is 10.

Question 13

1. $372.60
2. $378.00
3. $386.40 (correct answer)
4. $399.60

Explanation: When you encounter a problem involving both a discount and sales tax, remember that these calculations happen in sequence, not simultaneously. You must apply the discount first to get the sale price, then calculate tax on that reduced amount. Start by finding the sale price after the 25% discount. Since the phone is 25% off, you pay 75% of the original price: $\$480 \times 0.75 = \$360$. This is your discounted price before tax. Next, calculate the 7.5% sales tax on this discounted price, not the original price. The tax is: $\$360 \times 0.075 = \$27$. Add this tax to the discounted price: $\$360 + \$27 = \$386.40$. Looking at the wrong answers: Choice A ($372.60) represents what you'd get if you incorrectly calculated 7.5$480 price, then subtracted the full 25% discount afterward. Choice B ($378.00) is simply the discounted price plus 5$399.60) results from calculating the 7.5% tax on the original $480 price rather than the discounted price. The correct answer is C) $386.40. Study tip: Always remember the order matters in multi-step percentage problems. Discounts come first, then taxes are calculated on the discounted amount. Think of it this way: the store rings up your discounted price, then the register adds tax to that amount—never to the original price.

Question 14

1. $I = 1200(0.035)t$ (correct answer)
2. $I = 1200 + 0.035t$
3. $I = \dfrac{1200}{0.035t}$
4. $I = 1200t + 0.035$

Explanation: When you encounter simple interest problems, remember that simple interest is calculated using the formula: Interest = Principal × Rate × Time, or $I = Prt$. Let's identify each component from the problem: the principal (P) is $1,200, the annual interest rate (r) is 3.5% = 0.035, and the time (t) is the variable we're solving for. Substituting these values into the formula gives us $I = 1200 × 0.035 × t$, which can be written as $I = 1200(0.035)t$. Looking at the answer choices: Choice A correctly applies the simple interest formula with all components in the right places. Choice B adds 0.035t to the principal amount, which would represent a balance calculation rather than interest earned, and incorrectly treats the rate as a dollar amount rather than a percentage. Choice C divides the principal by the rate and time, which has no basis in interest calculations and would actually decrease as time increases. Choice D adds the principal times time to the rate, mixing up the variables completely and treating the percentage rate as a standalone dollar amount. The key trap here is confusing interest earned with account balance. Remember that simple interest problems ask for either the interest earned (using $I = Prt$) or the total balance (Principal + Interest). Always convert percentages to decimals, and make sure you're answering what the question actually asks for—in this case, just the interest portion, not the total account value.

Question 15

1. 68 sq ft
2. 72 sq ft
3. 84 sq ft (correct answer)
4. 96 sq ft

Explanation: Split the L-shape into two rectangles: top rectangle is 8 ft × 6 ft = 48 sq ft; bottom rectangle is 6 ft × 6 ft = 36 sq ft. Total area = 48 + 36 = 84 sq ft. A: 68 results from calculation errors. B: 72 omits part of one rectangle. D: 96 assumes the full outer bounding rectangle without subtracting the missing corner.

Question 16

1. After 2 hours, both will cost $\$5$
2. After 3 hours, both will cost $\$9$
3. After 4 hours, both will cost $\$9$
4. After 3 hours, both will cost $\$7$ (correct answer)

Explanation: This is a classic "when will two linear equations be equal" problem that you'll see often on the GED. When you encounter different pricing structures, set up equations for each option and find where they intersect. Let's define the total cost for each parking option after $h$ hours:

• Garage: $\$3$ for first hour + $\$2$ for each additional hour = $3 + 2(h-1)$
• Lot: $\$1$ for first hour + $\$3$ for each additional hour = $1 + 3(h-1)$

Question 17

1. $\frac{1}{2}$
2. $1$
3. $3$
4. $2$ (correct answer)

Explanation: When you encounter a quadratic function problem with given zeros and a minimum/maximum value, you're working with the vertex form and factored form together. The zeros tell you where the parabola crosses the x-axis, while the minimum value gives you information about the vertex. Since the zeros are at $x = -1$ and $x = 5$, you can write the function in factored form: $y = a(x + 1)(x - 5)$. The vertex occurs at the midpoint between the zeros, so $x = \frac{-1 + 5}{2} = 2$. Since $a$ will be positive (the function has a minimum, not maximum), the vertex is at $(2, -18)$. To find $a$, substitute the vertex coordinates into your factored form: $-18 = a(2 + 1)(2 - 5) = a(3)(-3) = -9a$. Solving for $a$: $a = \frac{-18}{-9} = 2$. Let's check why the other answers don't work. Choice A ($a = \frac{1}{2}$) would give a minimum value of $-9$, not $-18$. Choice B ($a = 1$) would produce a minimum of $-9$ as well. Choice C ($a = 3$) would create a minimum of $-27$, which is too low. Remember this key strategy: when you have zeros and a vertex value, use the factored form $y = a(x - r_1)(x - r_2)$ where $r_1$ and $r_2$ are the zeros. The vertex x-coordinate is always the average of the zeros, and you can substitute the vertex point to solve for $a$.

Question 18

1. The mean increases more than the median, creating greater separation between them (correct answer)
2. The median increases more than the mean, creating greater separation between them
3. Both the mean and median increase by the same amount, maintaining their relationship
4. The mean decreases while the median increases, reversing their relative positions

Explanation: Original 9 values in order: 28, 29, 30, 31, 32, 32, 33, 34, 35. Original median = 32 (5th value). Original mean = 284 ÷ 9 = 31.56. With 10th value (45): new ordered set is 28, 29, 30, 31, 32, 32, 33, 34, 35, 45. New median = (32 + 32) ÷ 2 = 32 (unchanged). New mean = 329 ÷ 10 = 32.9. The mean increased by 1.34 minutes while the median stayed the same, so the separation increased. Choice B incorrectly suggests median increases more. Choice C incorrectly suggests both change equally. Choice D incorrectly suggests mean decreases.

Question 19

1. 42
2. 44 (correct answer)
3. 46
4. 43

Explanation: In the original 15-value set, the median is the 8th value when arranged in order. We know the 8th value is 42 and 9th value is 46. When we add two values of 44, they will be inserted between positions 8 and 9 in the ordered list. The new arrangement around the middle will be: ...42, 44, 44, 46... In a 17-value set, the median is the 9th value (middle position). After insertion, the 9th position will be occupied by one of the 44 values. Choice A (42) represents the original 8th value. Choice C (46) represents the original 9th value. Choice D (43) might result from incorrectly averaging 42 and 44.

Question 20

1. $6$
2. $9$ (correct answer)
3. $12$
4. $18$

Explanation: Hemisphere volume: $\tfrac{1}{2}\cdot\tfrac{4}{3}\pi(6)^3=\tfrac{2}{3}\pi(216)=144\pi$. Set equal to cylinder volume: $\pi(4)^2 h=16\pi h=144\pi$, so $h=9$. A uses ratio $6/...$incorrectly. C uses full sphere formula. D forgets to square the cylinder radius.

Question 21

1. $t = 1$ second and $t = 4$ seconds only
2. $t = 2$ seconds and $t = 3$ seconds only
3. $t = 2$ seconds only, at the maximum height
4. $t = 1$ second and $t = 3$ seconds only (correct answer)

Explanation: This question tests your ability to solve quadratic equations in a real-world context. When you see a quadratic function modeling height over time, you're typically looking for specific values of time when the object reaches a particular height. To find when the object is at 128 feet, you need to set the height function equal to 128 and solve for $t$: $-16t^2 + 64t + 80 = 128$ Subtract 128 from both sides: $-16t^2 + 64t - 48 = 0$ Divide everything by -16 to simplify: $t^2 - 4t + 3 = 0$ This factors as $(t - 1)(t - 3) = 0$, giving you $t = 1$ and $t = 3$ seconds. Let's examine why the other answers are wrong. Choice A includes $t = 4$ seconds, but substituting this into the original equation gives $h(4) = -16(16) + 64(4) + 80 = 80$ feet, not 128. Choice B gives $t = 2$ and $t = 3$ seconds. While $t = 3$ is correct, $t = 2$ yields $h(2) = -16(4) + 64(2) + 80 = 144$ feet. Choice C suggests only $t = 2$ at maximum height, but as we calculated, the height at $t = 2$ is 144 feet, and the maximum occurs at the vertex, not necessarily when height equals 128. When solving quadratic equations in context, always check your solutions by substituting back into the original equation. This catches calculation errors and ensures your answers make sense within the problem's constraints.

Question 22

1. 6 meters (correct answer)
2. 8 meters
3. 10 meters
4. 12 meters

Explanation: Let w = width. Then length = 2w + 2. Area = w(2w + 2) = 120. This gives us 2w² + 2w = 120, or w² + w - 60 = 0. Factoring: (w + 8)(w - 6) = 0. Since width must be positive, w = 6 meters. Choice B results from solving 2w² + 2w - 120 = 0 incorrectly. Choice C comes from setting up the equation as w(2w - 2) = 120. Choice D results from confusing width and length in the final answer.

Question 23

1. 15 units
2. 25 units
3. 20 units
4. 12.5 units (correct answer)

Explanation: When you see a revenue function like this, you're dealing with a quadratic optimization problem. Revenue functions often form parabolas that open downward, meaning there's a maximum point at the vertex. To find the maximum revenue, you need to find where the derivative equals zero. First, expand the revenue function: $R = x(50 - 2x) = 50x - 2x^2$. Taking the derivative: $R' = 50 - 4x$. Setting this equal to zero: $50 - 4x = 0$, which gives you $4x = 50$, so $x = 12.5$ units. You can verify this is a maximum because the second derivative $R'' = -4$ is negative, confirming the parabola opens downward. Looking at the wrong answers: Choice A (15 units) likely comes from missolving the equation or confusing the setup. Choice B (25 units) might result from incorrectly thinking the maximum occurs at $x = 50/2 = 25$ without accounting for the coefficient of the $x^2$ term. Choice C (20 units) could come from arithmetic errors or confusion about the vertex formula. The correct answer is D) 12.5 units because this is where the derivative equals zero, giving the maximum revenue. Study tip: For quadratic optimization problems on the GED, remember that maximums and minimums occur where the derivative equals zero. If you're uncomfortable with calculus, you can also use the vertex formula: for $ax^2 + bx + c$, the x-coordinate of the vertex is $x = -b/(2a)$.

Question 24

1. $3 + 1.50h$
2. $3 + 1.50(h - 1)$ (correct answer)
3. $4.50h$
4. $3h + 1.50$

Explanation: The correct answer is B. The cost is $3 for the first hour plus$1.50 for each additional hour. Since there are (h-1) additional hours beyond the first hour, the expression is 3 + 1.50(h-1). Choice A incorrectly charges $1.50 for all h hours including the first. Choice C treats it as a simple rate problem. Choice D incorrectly multiplies the flat rate by h and adds the hourly rate once.

Question 25

1. 15
2. 18.4 (correct answer)
3. 19.5
4. 21.2

Explanation: Total customers: 8+12+15+22+30+28+20+18+12 = 165. Hours open: 9. Mean = 165/9 ≈ 18.33 ≈ 18.3, which rounds to 18.4. Distractor A might come from finding the median. C could result from miscounting hours. D from calculation error.