A store sells T-shirts at a price of 3 for 65. If a team needs to buy 30 T-shirts, how much money would be saved by using the store with the better price?
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ISEE Middle Level Quantitative Reasoning Quiz
Practice Proportional Relationships in ISEE Middle Level Quantitative Reasoning with focused quiz questions that help you check what you know, review explanations, and build confidence with test-style prompts.
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A store sells T-shirts at a price of 3 for 40.AnotherstoresellsthesameT−shirtsat5for65. If a team needs to buy 30 T-shirts, how much money would be saved by using the store with the better price?
This quiz focuses on Proportional Relationships, giving you a quick way to practice the rules, question types, and explanations that matter most for ISEE Middle Level Quantitative Reasoning.
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.
A store sells T-shirts at a price of 3 for 40.AnotherstoresellsthesameT−shirtsat5for65. If a team needs to buy 30 T-shirts, how much money would be saved by using the store with the better price?
Explanation: First, find the price per shirt at each store. Store 1: 40/3shirts≈13.33/shirt. Store 2: 65/5shirts=13.00/shirt. Store 2 has the better price. Now, calculate the total cost for 30 shirts from each store. Store 1: Buying 30 shirts is like buying 10 sets of 3 shirts. Cost = 10 * 40=400. Store 2: Buying 30 shirts is like buying 6 sets of 5 shirts. Cost = 6 * 65=390. The savings is the difference between the two total costs: 400−390 = $20.
In a collection of marbles, the ratio of red to blue is 3:4, and the ratio of blue to green is 5:2. What is the ratio of red marbles to green marbles?
Explanation: We are given Red:Blue = 3:4 and Blue:Green = 5:2. To find the ratio of Red:Green, we need to make the 'Blue' term the same in both ratios. The least common multiple of 4 and 5 is 20. Convert the first ratio by multiplying by 5: Red:Blue = (35):(45) = 15:20. Convert the second ratio by multiplying by 4: Blue:Green = (54):(24) = 20:8. Now that the Blue term is 20 in both, we can combine them: Red:Blue:Green = 15:20:8. The ratio of red to green is 15:8.
A 6-foot tall person casts a 9-foot long shadow. At the same time of day, a telephone pole casts a 42-foot long shadow. How tall is the telephone pole?
Explanation: The ratio of an object's height to its shadow's length is constant at the same time of day. Let H be the height of the pole. Set up the proportion: (person's height / person's shadow) = (pole's height / pole's shadow). So, 6/9 = H/42. Simplify the ratio 6/9 to 2/3. Now, 2/3 = H/42. Cross-multiply: 3H = 2 * 42 = 84. Divide by 3: H = 28 feet.
A plant grows at a constant rate of 5 centimeters every 8 days. If the plant is currently 12 centimeters tall, how many full days from now will it take for the plant to be at least 30 centimeters tall?
Explanation: First, determine how much more the plant needs to grow: 30 cm - 12 cm = 18 cm. Next, set up a proportion to find the number of days, d, required for this growth: (5 cm / 8 days) = (18 cm / d days). Cross-multiply: 5d = 8 * 18 = 144. Solve for d: d = 144 / 5 = 28.8 days. Since the question asks for the number of full days it will take to be at least 30 cm tall, we must round up to the next whole day. After 28 days, it will not have reached the required height. Therefore, it will take 29 full days.
Compare the quantity in Column A to the quantity in Column B.
Column A: The time it takes a train to travel 250 miles at an average speed of 60 miles per hour. Column B: The time it takes a car to travel 220 miles at an average speed of 50 miles per hour.
Explanation: Calculate the time for Column A: Time = Distance / Speed = 250 miles / 60 mph = 25/6 hours. 25/6 = 4 and 1/6 hours. 1/6 of an hour is (1/6)*60 = 10 minutes. So, Column A is 4 hours and 10 minutes. Calculate the time for Column B: Time = Distance / Speed = 220 miles / 50 mph = 22/5 hours. 22/5 = 4 and 2/5 hours. 2/5 of an hour is (2/5)*60 = 24 minutes. So, Column B is 4 hours and 24 minutes. Since 4 hours and 24 minutes is longer than 4 hours and 10 minutes, the quantity in Column B is greater.
A car travels 165 miles using 5 gallons of gasoline. At this rate, how many gallons of gasoline would be needed to travel 396 miles?
Explanation: First, find the car's fuel efficiency in miles per gallon: 165 miles / 5 gallons = 33 miles per gallon. Then, divide the new distance by the fuel efficiency to find the gallons needed: 396 miles / 33 miles per gallon = 12 gallons. Alternatively, set up a proportion: (165 miles / 5 gallons) = (396 miles / x gallons). Cross-multiply: 165x = 396 * 5, which is 165x = 1980. Divide by 165: x = 12.
A model uses scale 1:10. If the real width is 7 feet, what is the model width?
Explanation: This question tests middle school quantitative reasoning skills related to solving proportional relationships. Proportional relationships involve comparing two ratios or rates and finding a missing value, often using cross-multiplication or setting up equivalent fractions. In this scenario, you are asked to solve a problem involving a scale model width from real width, requiring identification of the correct proportional relationship. Choice A is correct because it accurately applies the proportional relationship by dividing 7 / 10 = 0.7 feet for the model. Choice C is incorrect because it results from multiplying instead, like 7 × 10 = 70 feet. To help students, teach them to set up ratios correctly and cross-multiply to find the unknown. Practice identifying key words that signal a proportional relationship, and watch for common errors like flipping ratios or miscalculating units.
A recipe serves eight and needs 20 strawberries. How many strawberries are needed for 12 servings?
Explanation: This question tests middle school quantitative reasoning skills related to solving proportional relationships. Proportional relationships involve comparing two ratios or rates and finding a missing value, often using cross-multiplication or setting up equivalent fractions. In this scenario, you are asked to solve a problem involving scaling strawberries in a recipe for more servings, requiring identification of the correct proportional relationship. Choice A is correct because it accurately applies the proportional relationship by finding 20 / 8 = 2.5 per serving, then 2.5 × 12 = 30 strawberries. Choice B is incorrect because it results from adding instead of proportioning, like 20 + 5 or similar, yielding 25. To help students, teach them to set up ratios correctly and cross-multiply to find the unknown. Practice identifying key words that signal a proportional relationship, and watch for common errors like flipping ratios or miscalculating units.
A train goes 90 miles in two hours. At the same rate, how long for 225 miles?
Explanation: This question tests middle school quantitative reasoning skills related to solving proportional relationships. Proportional relationships involve comparing two ratios or rates and finding a missing value, often using cross-multiplication or setting up equivalent fractions. In this scenario, you are asked to solve a problem involving time for a train to travel a certain distance, requiring identification of the correct proportional relationship. Choice B is correct because it accurately applies the proportional relationship by finding the rate 90 / 2 = 45 mph, then 225 / 45 = 5 hours. Choice C is incorrect because it results from misapplying the proportion, like 90 / 225 × 2, yielding about 0.8 but rounded wrong to 6. To help students, teach them to set up ratios correctly and cross-multiply to find the unknown. Practice identifying key words that signal a proportional relationship, and watch for common errors like flipping ratios or miscalculating units.
The exchange rate is 1=0.80 euros. How many euros do you get for $50?
Explanation: This question tests middle school quantitative reasoning skills related to solving proportional relationships. Proportional relationships involve comparing two ratios or rates and finding a missing value, often using cross-multiplication or setting up equivalent fractions. In this scenario, you are asked to solve a problem involving currency exchange from dollars to euros, requiring identification of the correct proportional relationship. Choice A is correct because it accurately applies the proportional relationship by multiplying 50 × 0.80 = 40 euros. Choice B is incorrect because it results from inverting the rate, like 50 / 0.80 = 62.5 euros. To help students, teach them to set up ratios correctly and cross-multiply to find the unknown. Practice identifying key words that signal a proportional relationship, and watch for common errors like flipping ratios or miscalculating units.
The exchange rate is 1=120 yen. How many yen do you get for $35?
Explanation: This question tests middle school quantitative reasoning skills related to solving proportional relationships. Proportional relationships involve comparing two ratios or rates and finding a missing value, often using cross-multiplication or setting up equivalent fractions. In this scenario, you are asked to solve a problem involving currency exchange from dollars to yen, requiring identification of the correct proportional relationship. Choice A is correct because it accurately applies the proportional relationship by multiplying 35 × 120 = 4,200 yen. Choice B is incorrect because it results from miscalculating, like 30 × 120 = 3,600, forgetting the full amount. To help students, teach them to set up ratios correctly and cross-multiply to find the unknown. Practice identifying key words that signal a proportional relationship, and watch for common errors like flipping ratios or miscalculating units.
A recipe serves four and uses 10 ounces of cheese. How many ounces are needed for 14 servings?
Explanation: This question tests middle school quantitative reasoning skills related to solving proportional relationships. Proportional relationships involve comparing two ratios or rates and finding a missing value, often using cross-multiplication or setting up equivalent fractions. In this scenario, you are asked to solve a problem involving scaling cheese in a recipe for more servings, requiring identification of the correct proportional relationship. Choice C is correct because it accurately applies the proportional relationship by finding 10 / 4 = 2.5 per serving, then 2.5 × 14 = 35 ounces. Choice D is incorrect because it results from multiplying by 4, like 10 × 4 = 40 ounces. To help students, teach them to set up ratios correctly and cross-multiply to find the unknown. Practice identifying key words that signal a proportional relationship, and watch for common errors like flipping ratios or miscalculating units.
A recipe serves 10 and needs 3 cups of flour. How many cups of flour for 25 servings?
Explanation: This question tests middle school quantitative reasoning skills related to solving proportional relationships. Proportional relationships involve comparing two ratios or rates and finding a missing value, often using cross-multiplication or setting up equivalent fractions. In this scenario, you are asked to solve a problem involving scaling flour in a recipe for more servings, requiring identification of the correct proportional relationship. Choice A is correct because it accurately applies the proportional relationship by finding 3 / 10 = 0.3 per serving, then 0.3 × 25 = 7.5 cups. Choice B is incorrect because it results from misproportioning, like 3 × 2 = 6 cups. To help students, teach them to set up ratios correctly and cross-multiply to find the unknown. Practice identifying key words that signal a proportional relationship, and watch for common errors like flipping ratios or miscalculating units.
A runner goes nine miles in 72 minutes. At this pace, how many minutes for 15 miles?
Explanation: This question tests middle school quantitative reasoning skills related to solving proportional relationships. Proportional relationships involve comparing two ratios or rates and finding a missing value, often using cross-multiplication or setting up equivalent fractions. In this scenario, you are asked to solve a problem involving time for a runner to cover a distance, requiring identification of the correct proportional relationship. Choice C is correct because it accurately applies the proportional relationship by finding the rate 9 / 72 = 0.125 miles per minute, then 15 / 0.125 = 120 minutes. Choice D is incorrect because it results from misproportioning, like 72 × 2 = 144 minutes. To help students, teach them to set up ratios correctly and cross-multiply to find the unknown. Practice identifying key words that signal a proportional relationship, and watch for common errors like flipping ratios or miscalculating units.
A recipe serves five and uses 2 cups of rice. How much rice for 20 servings?
Explanation: This question tests middle school quantitative reasoning skills related to solving proportional relationships. Proportional relationships involve comparing two ratios or rates and finding a missing value, often using cross-multiplication or setting up equivalent fractions. In this scenario, you are asked to solve a problem involving scaling rice in a recipe for more servings, requiring identification of the correct proportional relationship. Choice C is correct because it accurately applies the proportional relationship by finding 2 / 5 = 0.4 per serving, then 0.4 × 20 = 8 cups. Choice D is incorrect because it results from doubling incorrectly, like 5 × 2 = 10 cups. To help students, teach them to set up ratios correctly and cross-multiply to find the unknown. Practice identifying key words that signal a proportional relationship, and watch for common errors like flipping ratios or miscalculating units.
If 8 oranges cost $3.60, what is the cost of 1.5 dozen oranges?
Explanation: First, find the cost of one orange: 3.60/8oranges=0.45 per orange. Next, determine how many oranges are in 1.5 dozen: 1.5 * 12 = 18 oranges. Finally, calculate the total cost for 18 oranges: 18 oranges * 0.45/orange=8.10.
Compare the quantity in Column A to the quantity in Column B. x and y are positive numbers, and 3x = 7y.
Column A: x Column B: y
Explanation: From the equation 3x = 7y, we can find the ratio of x to y. Divide both sides by 3y: x/y = 7/3. This means that x is 7/3 times as large as y. Since 7/3 is greater than 1, x must be greater than y. For example, if y=3, then 3x = 7(3), so 3x = 21 and x=7. In this case, 7 > 3. Since x and y must be positive, x will always be greater than y. Therefore, the quantity in Column A is greater.
Compare the quantity in Column A to the quantity in Column B.
Column A: The price per ounce of a 20-ounce box of cereal that costs 4.50.ColumnB:Thepriceperounceofa32−ounceboxofcerealthatcosts7.04.
Explanation: Calculate the unit price for Column A: 4.50/20ounces.Thisis45 / 200 = 9/40.Asadecimal,9/40=0.225.So,thepriceis22.5centsperounce.CalculatetheunitpriceforColumnB:7.04 / 32 ounces. This is $704 / 3200 cents. We can simplify by dividing by 32: 704 / 32 = 22. So, the price is 22 cents per ounce. Since 22.5 cents is greater than 22 cents, the quantity in Column A is greater.
A recipe for 12 muffins requires 1.5 cups of flour. A baker has a 10-cup bag of flour and needs to make 60 muffins for a school event. After making the 60 muffins, how many cups of flour will be left in the bag?
Explanation: First, find the amount of flour needed per muffin: 1.5 cups / 12 muffins = 0.125 cups/muffin. Then, calculate the total flour needed for 60 muffins: 60 muffins * 0.125 cups/muffin = 7.5 cups. Finally, subtract the amount used from the initial amount: 10 cups - 7.5 cups = 2.5 cups remaining. Alternatively, set up a proportion: (1.5 cups / 12 muffins) = (x cups / 60 muffins). Solving for x gives x = (1.5 * 60) / 12 = 7.5 cups. Then, 10 - 7.5 = 2.5 cups.
The property tax on a home is proportional to its assessed value. A home with an assessed value of 200,000hasapropertytaxof3,500. What is the property tax on a home with an assessed value of $280,000?
Explanation: Set up a proportion relating the tax to the value. Let T be the unknown tax. (3,500/200,000) = (T / 280,000).Tosimplify,wecandividethedollaramountsinthefirstratio:3,500/200,000=35/2000=7/400.So,7/400=T/280,000.SolveforT:T=(7/400)∗280,000.T=7∗(280,000/400)=7∗700=4,900.