GED Math Quiz: Ratios And Percent
10 questions · exam conditions
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Ratios And PercentQuestion 1 of 10

A map uses a scale of 1 inch representing 6 miles. Two towns are 3.5 inches apart on the map. How far apart are the towns in miles?

18 miles
19 miles
21 miles
24 miles
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GED Math Quiz

GED Math Quiz: Ratios And Percent

Practice Ratios And Percent in GED Math with focused quiz questions that help you check what you know, review explanations, and build confidence with test-style prompts.

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.

All questions

Question 1

A map uses a scale of 1 inch representing 6 miles. Two towns are 3.5 inches apart on the map. How far apart are the towns in miles?

  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 inches×6 miles per inch=21 miles3.5 \text{ inches} \times 6 \text{ miles per inch} = 21 \text{ miles} Alternatively, you can set up the proportion: 1 inch6 miles=3.5 inchesx miles\frac{1 \text{ inch}}{6 \text{ miles}} = \frac{3.5 \text{ inches}}{x \text{ miles}}. Cross-multiplying gives you x=3.5×6=21x = 3.5 \times 6 = 21 miles. Looking at the wrong answers: Choice A (18 miles) likely comes from miscalculating 3.5×63.5 \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 2

A landscaping company mixes grass seed so that the ratio of rye seed to fescue seed is 5:35:3. If the company needs a total of 6464 pounds of seed, how many pounds should be fescue?

  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 5:35:3 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=85 + 3 = 8 parts altogether. Since you need 64 pounds total, each "part" equals 64÷8=864 ÷ 8 = 8 pounds. Therefore, fescue seed requires 3×8=243 × 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 1:11:1, not 5:35:3. Answer C (40 lb) is what you'd get if you calculated the rye seed amount instead of fescue (5×8=405 × 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 5:35:3 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 3

A car's value depreciates by 18% each year. If the car is worth $22,000 after 2 years of depreciation, what was its original value when new?

  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(0.82)^2 = 0.6724 of its original value. If original value = xx, then 0.6724x=220000.6724x = 22000, so x=220000.6724≈32,680x = \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 4

A solution contains 15% salt by volume. How many liters of pure water must be added to 60 liters of this solution to create a mixture that is 10% salt by volume?

  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 60×0.15=960 \times 0.15 = 9 liters of salt. Let xx be the liters of water added. The new mixture has volume (60+x)(60 + x) and still contains 9 liters of salt. For 10% concentration: 960+x=0.10\frac{9}{60 + x} = 0.10. Solving: 9=0.10(60+x)=6+0.10x9 = 0.10(60 + x) = 6 + 0.10x, so 3=0.10x3 = 0.10x and x=30x = 30. Choice A assumes 12% final concentration. Choice C uses incorrect proportion setup. Choice D assumes equal volumes of solution and water.

Question 5

A store marks up all items by 40% above wholesale cost. During a sale, the store offers a 25% discount off the marked price. If a customer pays $84 for an item during the sale, what was the wholesale cost of the item?

  1. $70.00
  2. $80.00 (correct answer)
  3. $96.60
  4. $112.00
Explanation: Let the wholesale cost be xx. After a 40% markup, the marked price is 1.40x1.40x. After a 25% discount, the sale price is 0.75×1.40x=1.05x=840.75 \times 1.40x = 1.05x = 84. Solving: x=841.05=80x = \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 6

A rectangular garden has length and width in the ratio 5:3. If the width is increased by 20% and the length is decreased by 10%, the new area is 1,584 square feet. What was the original length of the garden?

  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 = 3x3x and original length = 5x5x. New width = 3x×1.20=3.6x3x \times 1.20 = 3.6x and new length = 5x×0.90=4.5x5x \times 0.90 = 4.5x. New area = 3.6x×4.5x=16.2x2=15843.6x \times 4.5x = 16.2x^2 = 1584. Solving: x2=158416.2=97.78x^2 = \frac{1584}{16.2} = 97.78, so x≈9.89≈10x \approx 9.89 \approx 10. Original length = 5x=505x = 50 feet. Choice A uses x=6x = 6 (calculation error). Choice B uses x=8x = 8 (incorrect area calculation). Choice C uses x=9x = 9 (rounding error in solving for xx).

Question 7

A store offers a loyalty program where customers earn points equal to 2% of their purchase amount. Sarah has 1,840 points and wants to use them for a purchase where she'll earn additional points equal to 2% of the amount spent. If she uses all her points (worth $1 each) and pays an additional $60 cash, what will her new point balance be after this purchase?

  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 8

In a photography class, the ratio of film cameras to digital cameras is 3:7. If 8 more digital cameras are added to the class, the new ratio becomes 1:3. How many film cameras are in the class?

  1. 6 film cameras
  2. 9 film cameras
  3. 12 film cameras (correct answer)
  4. 15 film cameras
Explanation: Let film cameras = 3x3x and digital cameras = 7x7x. After adding 8 digital cameras: 3x7x+8=13\frac{3x}{7x + 8} = \frac{1}{3}. Cross-multiplying: 9x=7x+89x = 7x + 8, so 2x=82x = 8 and x=4x = 4. Therefore, film cameras = 3(4)=123(4) = 12. Choice A uses x=2x = 2 (calculation error). Choice B uses x=3x = 3 (misreading the final ratio). Choice D uses x=5x = 5 (incorrect cross-multiplication).

Question 9

In a survey, 40% of respondents preferred coffee, 35% preferred tea, and the rest preferred neither. If 120 more people preferred coffee than tea, how many people were surveyed in total?

  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 = nn. Coffee preference = 0.40n0.40n and tea preference = 0.35n0.35n. The difference is 0.40n−0.35n=0.05n=1200.40n - 0.35n = 0.05n = 120. Solving: n=1200.05=2400n = \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

A phone originally priced at $480 is on sale for 25% off. After the discount, a 7.5% sales tax is added. What is the final price paid for the phone?

  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: $480×0.75=$360\$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: $360×0.075=$27\$360 \times 0.075 = \$27. Add this tax to the discounted price: $360+$27=$386.40\$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 480price,thensubtractedthefull25480 price, then subtracted the full 25% discount afterward. Choice B (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.