GED Math Quiz: Ratios And Percent

What this quiz covers

This quiz focuses on Ratios And Percent, giving you a quick way to practice the rules, question types, and explanations that matter most for GED Math.

How to use this quiz

Try each quiz question before looking at the correct answer. Use the explanations to review missed ideas, then come back to similar questions until the pattern feels familiar.

Question 1

1. $26,840 was the original value
2. $30,200 was the original value
3. $32,680 was the original value (correct answer)
4. $35,500 was the original value

Explanation: If the car depreciates 18% annually, it retains 82% of its value each year. After 2 years, it retains $(0.82)^2 = 0.6724$ of its original value. If original value = $x$, then $0.6724x = 22000$, so $x = \frac{22000}{0.6724} \approx 32,680$. Choice A assumes only 1 year of depreciation. Choice B uses simple rather than compound depreciation (22000 ÷ 0.64). Choice D uses 20% depreciation rate instead of 18%.

Question 2

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 3

1. $70.00
2. $80.00 (correct answer)
3. $96.60
4. $112.00

Explanation: Let the wholesale cost be $x$. After a 40% markup, the marked price is $1.40x$. After a 25% discount, the sale price is $0.75 \times 1.40x = 1.05x = 84$. Solving: $x = \frac{84}{1.05} = 80$. Choice A assumes the $84 is after only the discount. Choice C incorrectly adds the percentages (40% - 25% = 15%). Choice D assumes the $84 is the wholesale cost before any markup.

Question 4

1. 30 feet was the original length
2. 40 feet was the original length
3. 45 feet was the original length
4. 50 feet was the original length (correct answer)

Explanation: Let original width = $3x$ and original length = $5x$. New width = $3x \times 1.20 = 3.6x$ and new length = $5x \times 0.90 = 4.5x$. New area = $3.6x \times 4.5x = 16.2x^2 = 1584$. Solving: $x^2 = \frac{1584}{16.2} = 97.78$, so $x \approx 9.89 \approx 10$. Original length = $5x = 50$ feet. Choice A uses $x = 6$ (calculation error). Choice B uses $x = 8$ (incorrect area calculation). Choice C uses $x = 9$ (rounding error in solving for $x$).

Question 5

1. 38 points will be her new balance (correct answer)
2. 42 points will be her new balance
3. 46 points will be her new balance
4. 50 points will be her new balance

Explanation: Sarah starts with 1,840 points. She uses all 1,840 points (worth $1,840) plus pays $60 cash, for a total purchase of $1,900. She earns 2% of $1,900 = $38 worth of points = 38 new points. Since she used all her original points, her new balance is 38 points. Choice B adds the cash amount incorrectly (38 + 4). Choice C calculates 2% of $2,300 instead of $1,900. Choice D assumes she earns points on a $2,500 purchase.

Question 6

1. 24 lb (correct answer)
2. 32 lb
3. 40 lb
4. 48 lb

Explanation: When you encounter ratio problems, you're dealing with proportional relationships where quantities are divided according to a specific pattern. The key is understanding that ratios tell you the relative sizes of parts, not the actual amounts. The ratio $5:3$ means for every 5 pounds of rye seed, there are 3 pounds of fescue seed. Think of this as 5 parts rye to 3 parts fescue, giving you a total of $5 + 3 = 8$ parts altogether. Since you need 64 pounds total, each "part" equals $64 ÷ 8 = 8$ pounds. Therefore, fescue seed requires $3 × 8 = 24$ pounds, making A correct. Let's examine why the other answers miss the mark. Answer B (32 lb) represents exactly half the total mixture, which would only be correct if the ratio were $1:1$, not $5:3$. Answer C (40 lb) is what you'd get if you calculated the rye seed amount instead of fescue ($5 × 8 = 40$) — a common mix-up when students lose track of which component the question asks for. Answer D (48 lb) doesn't correspond to any logical calculation from this ratio and would leave only 16 pounds for the other component, which doesn't fit the $5:3$ pattern. For ratio problems, always identify the total number of parts first, then find the value of one part by dividing the total quantity by the number of parts. Finally, multiply by the specific number of parts for the component you're solving for.

Question 7

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 8

1. 6 film cameras
2. 9 film cameras
3. 12 film cameras (correct answer)
4. 15 film cameras

Explanation: Let film cameras = $3x$ and digital cameras = $7x$. After adding 8 digital cameras: $\frac{3x}{7x + 8} = \frac{1}{3}$. Cross-multiplying: $9x = 7x + 8$, so $2x = 8$ and $x = 4$. Therefore, film cameras = $3(4) = 12$. Choice A uses $x = 2$ (calculation error). Choice B uses $x = 3$ (misreading the final ratio). Choice D uses $x = 5$ (incorrect cross-multiplication).

Question 9

1. 1,800 people were surveyed
2. 2,000 people were surveyed
3. 2,400 people were surveyed (correct answer)
4. 2,800 people were surveyed

Explanation: Let the total number of people surveyed = $n$. Coffee preference = $0.40n$ and tea preference = $0.35n$. The difference is $0.40n - 0.35n = 0.05n = 120$. Solving: $n = \frac{120}{0.05} = 2400$. Choice A uses the wrong percentage difference (40% - 35% = 5%, but calculates as if it were 120/60). Choice B assumes 6% difference instead of 5%. Choice D uses 120/(40-35) incorrectly treating the percentages as absolute numbers.

Question 10

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% tax on the original $480 price, then subtracted the full 25$378.00) is simply the discounted price plus 5% instead of 7.5% tax. Choice D ($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.