SAT Math Quiz: Ratios And Proportions

What this quiz covers

This quiz focuses on Ratios And Proportions, giving you a quick way to practice the rules, question types, and explanations that matter most for SAT 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. 7.15 kg (correct answer)
2. 6.50 kg
3. 5.76 kg
4. 9.10 kg

Explanation: The recipe uses flour and sugar in the ratio 11:4, and we need to find how much flour is needed for 2.6 kg of sugar. Setting up the proportion: 11/4 = x/2.6, where x is the kg of flour needed. Cross-multiplying: 4x = 11(2.6) = 28.6, so x = 28.6/4 = 7.15 kg of flour. A common mistake is reversing the ratio - remember that 11:4 means 11 parts flour to 4 parts sugar, not the other way around. When scaling recipes, the ratio between ingredients must remain constant to maintain the same taste or consistency.

Question 2

1. 18.0 (correct answer)
2. 13.5
3. 20.0
4. 19.5

Explanation: Similar triangles have corresponding sides in the same ratio, so we need to find the scale factor between triangles ABC and DEF. Since BC = 15 corresponds to EF = 22.5, the scale factor is 22.5/15 = 1.5. This means all sides of DEF are 1.5 times the corresponding sides of ABC. Since AC = 12 in triangle ABC, the corresponding side in DEF is 12 × 1.5 = 18.0. The key principle is that similarity preserves ratios between all corresponding parts. When working with similar triangles, find the scale factor using any pair of known corresponding sides.

Question 3

1. 18
2. 21 (correct answer)
3. 19.5
4. 24

Explanation: The photograph maintains its aspect ratio during enlargement, with width changing from 8 to 14 inches. To find the scale factor, we calculate 14 ÷ 8 = 1.75. Since the shapes remain similar, all dimensions scale by the same factor. The new height is therefore 12 × 1.75 = 21 inches. We can verify using the proportion: 8/12 = 14/h, which gives 8h = 168, so h = 21 inches. A common error is adding the difference to the original height instead of multiplying by the scale factor. For similar figures, all corresponding dimensions scale by the same ratio.

Question 4

1. 15 feet (correct answer)
2. 10 feet
3. 18 feet
4. 12 feet

Explanation: This question asks us to find the actual width of a room given a scale drawing where 1 inch represents 5 feet, and the room measures 3 inches wide in the drawing. We can set up the proportion: drawing inches/actual feet = 1/5, which gives us 3/x = 1/5. Cross-multiplying, we get x = 15, so the actual width is 15 feet. Alternatively, we can think of this as scaling up: since each inch represents 5 feet, 3 inches represents 3 × 5 = 15 feet. A common mistake is confusing the scale direction or mixing up which measurement goes where in the proportion. When working with scales, always identify what one unit in the drawing represents in reality first.

Question 5

1. 75 g (correct answer)
2. 60 g
3. 50 g
4. 90 g

Explanation: In a trail mix with almonds:raisins:chocolate ratio of 6:5:4 and 225g total, find the amount of raisins. The total ratio parts are 6 + 5 + 4 = 15, so raisins represent 5/15 = 1/3 of the total. Calculate: (1/3) × 225 = 75 grams of raisins. A common mistake is using the wrong fraction, such as 5/6 or 5/9, by not including all components in the total. Always sum all ratio parts when finding the fraction each component represents.

Question 6

1. 133.3 cm
2. 80 cm (correct answer)
3. 28.8 cm
4. 64 cm

Explanation: Two similar rectangles have corresponding sides in ratio 3:5, with the smaller perimeter being 48 cm. Since perimeters of similar figures are in the same ratio as corresponding sides, set up: 3/5 = 48/x, where x is the larger perimeter. Cross-multiplying: 3x = 5 × 48 = 240, so x = 240/3 = 80 cm. A common error is applying the ratio to area instead of perimeter, or squaring the ratio. Remember that perimeters scale linearly with the side length ratio.

Question 7

1. 30 oz (correct answer)
2. 42 oz
3. 60 oz
4. 72 oz

Explanation: The question asks for the amount of blue tint used in a 102-ounce mixture with a blue-to-white ratio of 5:12. Set up the proportion by recognizing that blue tint represents 5 parts out of the total 17 parts (5 + 12). To solve, divide the total mixture by the total parts: 102 ÷ 17 = 6 ounces per part, then multiply by the blue parts: 6 × 5 = 30 ounces. You can also use the proportion 5/17 = x/102 and cross-multiply to get 17x = 510, so x = 30 ounces. A key error might be misadding the ratio parts or calculating the white base instead. Pay careful attention to units and verify the total parts when dealing with ratios.

Question 8

1. $13:39$
2. $26:78$
3. $1:3$ (correct answer)
4. $39:13$

Explanation: The question asks for the model's height-to-length ratio in simplest form, given a scale where 4.5 cm on model represents 1.2 m real, and real car height 1.56 m, length 4.68 m. Set up the proportion for the real ratio: height/length = 1.56/4.68. Simplify by dividing both by 1.56: 1 / 3, so 1:3. Since it's a scale model, the ratio is preserved in the model. The scale factor doesn't affect the ratio, as it's uniform. A key error is calculating the scale factor unnecessarily instead of directly simplifying the real dimensions.

Question 9

1. 0.4 m (correct answer)
2. 2.5 m
3. 0.25 m
4. 4 m

Explanation: This scale problem asks us to find the model length when given the actual length and scale ratio. The scale 1:25 means 1 unit on the model represents 25 units in reality. We set up the proportion 1:25 = x:10, where x is the model length in meters. Cross-multiplying gives us 25x = 1 × 10 = 10, so x = 10 ÷ 25 = 0.4 meters. This means the 10-meter actual car becomes a 0.4-meter (or 40 cm) model. A common error is inverting the scale relationship or forgetting that the model should be smaller than the actual object.

Question 10

1. 250 grams
2. 150 grams
3. 200 grams (correct answer)
4. 180 grams

Explanation: This question asks us to find how much sugar is needed when the ratio of sugar to flour is 2:3 and we have 300 grams of flour. We can set up the proportion: sugar/flour = 2/3, which gives us x/300 = 2/3. Cross-multiplying, we get 3x = 600, so x = 200 grams of sugar. We can also think of this as finding how many times 3 goes into 300 (which is 100), then multiplying the sugar portion by that same factor: 2 × 100 = 200 grams. A common mistake is mixing up which ingredient corresponds to which part of the ratio or forgetting to maintain consistent units. When working with recipes, pay careful attention to which ingredient is which in the given ratio.

Question 11

1. 40
2. 32
3. 30
4. 36 (correct answer)

Explanation: This question asks us to find the number of students in class A when the ratio of class A to class B is 4:5 and class B has 45 students. We can set up the proportion: class A/class B = 4/5, which gives us x/45 = 4/5. Cross-multiplying, we get 5x = 180, so x = 36. This means class A has 36 students. We can verify this by checking that 36:45 simplifies to 4:5 (dividing both by 9 gives us 4:5). A common mistake would be confusing which class corresponds to which part of the ratio or making an arithmetic error during cross-multiplication. Always double-check your arithmetic and verify that your answer creates the correct ratio when paired with the given information.

Question 12

1. 15
2. 14 (correct answer)
3. 18
4. 10

Explanation: This question asks us to find the number of oranges when the ratio of apples to oranges is 3:2 and there are 21 apples. We can set up the proportion: apples/oranges = 3/2, which gives us 21/x = 3/2. Cross-multiplying, we get 3x = 42, so x = 14. This means there are 14 oranges in the basket. We can also solve this by recognizing that 21 ÷ 3 = 7, so we multiply the orange portion by 7: 2 × 7 = 14 oranges. A common error would be setting up the proportion incorrectly or confusing which fruit corresponds to which part of the ratio. When checking your work, verify that your final answer maintains the original ratio: 21:14 should simplify to 3:2.

Question 13

1. 16 cm
2. 18 cm
3. 20 cm (correct answer)
4. 24 cm

Explanation: This question asks for the length of the leg in triangle B that corresponds to the 12 cm leg in similar triangle A, where triangle A has legs 9 cm and 12 cm, and triangle B's corresponding leg to 9 cm is 15 cm. Since the triangles are similar, the ratio of corresponding sides is constant, so set up the proportion 9/15 = 12/x, or use the scale factor 15/9 = 5/3. Multiply the smaller leg by the scale factor: x = 12 * (5/3) = 20 cm. Alternatively, cross-multiply in the proportion: 9x = 180, so x = 20 cm, matching units in cm. A key error is mismatching corresponding sides, such as using 12/15 directly. Another mistake could be adding ratios instead of multiplying. In similar figures, identify correspondences carefully and verify units to avoid setup errors.

Question 14

1. 9.1 m
2. 12.3 m (correct answer)
3. 18.0 m
4. 24.6 m

Explanation: The blueprint scale is 3 cm : 4.5 m, and the hallway measures 8.2 cm on the blueprint. Setting up the proportion: 3 cm/4.5 m = 8.2 cm/x m. Cross-multiplying: 3x = 8.2 × 4.5 = 36.9, so x = 12.3 m. The actual hallway length is 12.3 meters. A common error is inverting the ratio or using the wrong units. When working with scales, always set up the proportion with consistent units and check that your answer is reasonable - a hallway of 12.3 m is plausible.

Question 15

1. 26
2. 33
3. 39 (correct answer)
4. 45

Explanation: In similar right triangles, the smaller has hypotenuse 13 and leg 5, while the larger has corresponding leg 15. The scale factor is 15/5 = 3, meaning the larger triangle is 3 times the size. Therefore, the larger triangle's hypotenuse = 13 × 3 = 39. We can verify using the Pythagorean theorem: in the smaller triangle, the other leg = √(13² - 5²) = √(169 - 25) = 12, so in the larger triangle it's 36, and the hypotenuse = √(15² + 36²) = √(225 + 1296) = √1521 = 39. Always use the ratio of corresponding parts consistently.

Question 16

1. 3.00 L
2. 3.75 L (correct answer)
3. 4.80 L
4. 9.60 L

Explanation: This question asks for the liters of red paint to mix with 6 liters of blue paint to maintain a 5:8 red-to-blue ratio. The ratio means red/blue = 5/8, so set up the proportion 5/8 = r/6, where r is red paint in liters. Solve by cross-multiplying: 8r = 30, so r = 3.75 liters. Alternatively, scale the ratio by multiplying 8 by the factor to reach 6 (which is 6/8 = 0.75), then apply to red: 5 * 0.75 = 3.75 liters, keeping units in liters. A common error is inverting the ratio, like using 8:5, leading to more red than intended. Another mistake might be adding instead of proportioning. For mixing ratios, write the proportion clearly and check units to ensure the mixture stays consistent.

Question 17

1. 3.04 km
2. 19.0 km (correct answer)
3. 25.0 km
4. 30.4 km

Explanation: This map scale problem requires finding the actual distance when the map distance is 7.6 cm and the scale is 1 cm : 2.5 km. Set up the proportion: 1 cm/2.5 km = 7.6 cm/x km. Cross-multiplying gives: 1 × x = 2.5 × 7.6, so x = 19.0 km. A common mistake is dividing instead of multiplying, which would give 3.04 km. Remember that map scales show how map measurements relate to real distances - multiply the map distance by the scale factor.

Question 18

1. 288 (correct answer)
2. 144
3. 156
4. 276

Explanation: Let boys = 5k and girls = 7k; solving $(5k - 4)/(7k + 6) = 2/3$ gives k = 24, so total originally = 12k = 288. The distractors result from misapplying the ratio or halving totals.

Question 19

1. 72
2. 96
3. 135
4. 108 (correct answer)

Explanation: Convert 9 miles ≈ 14.4 km; times are 7.2/6 + 7.2/12 = 1.8 hours = 108 minutes. 96 uses a simple average speed, 135 uses miles without converting, and 72 uses the faster speed for the whole trip.

Question 20

1. 8
2. 27
3. 18
4. 12 (correct answer)

Explanation: Time per lap is 18/12 = 1.5 minutes, so 8 laps take 1.5×8 = 12 minutes. 27 minutes comes from inverting the proportion, 18 keeps the original time, and 8 incorrectly equates laps with minutes.