SSAT Upper Level Quantitative Quiz: Unit Rate Comparisons
6 questions · exam conditions
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Unit Rate ComparisonsQuestion 1 of 6

A recipe calls for 3.5 cups of flour to make 28 cookies. Maria wants to make 60 cookies using the same recipe. How many cups of flour will she need, and how does this compare to using two complete recipe batches?

She needs 7.5 cups, which is 0.5 cups more than two complete batches would require
She needs 7.5 cups, which is 0.5 cups less than two complete batches would require
She needs 8.0 cups, which is 1.0 cup more than two complete batches would require
She needs 8.0 cups, which is 1.0 cup less than two complete batches would require
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SSAT Upper Level Quantitative Quiz

SSAT Upper Level Quantitative Quiz: Unit Rate Comparisons

Practice Unit Rate Comparisons in SSAT Upper Level Quantitative 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 Unit Rate Comparisons, giving you a quick way to practice the rules, question types, and explanations that matter most for SSAT Upper Level Quantitative.

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 recipe calls for 3.5 cups of flour to make 28 cookies. Maria wants to make 60 cookies using the same recipe. How many cups of flour will she need, and how does this compare to using two complete recipe batches?

  1. She needs 7.5 cups, which is 0.5 cups more than two complete batches would require (correct answer)
  2. She needs 7.5 cups, which is 0.5 cups less than two complete batches would require
  3. She needs 8.0 cups, which is 1.0 cup more than two complete batches would require
  4. She needs 8.0 cups, which is 1.0 cup less than two complete batches would require
Explanation: Unit rate: 3.5 cups ÷ 28 cookies = 0.125 cups per cookie. For 60 cookies: 60 × 0.125 = 7.5 cups. Two complete recipe batches: 2 × 3.5 = 7 cups (making 56 cookies). So 7.5 cups is 0.5 cups more than two batches would require.

Question 2

Two water pumps are being tested. Pump X can fill a 1,200-gallon tank in 40 minutes, while Pump Y can fill a 1,800-gallon tank in 45 minutes. If both pumps work together to fill a 3,000-gallon tank, approximately how long will it take?

  1. It will take approximately 32 minutes to fill the 3,000-gallon tank
  2. It will take approximately 35 minutes to fill the 3,000-gallon tank
  3. It will take approximately 38 minutes to fill the 3,000-gallon tank
  4. It will take approximately 41 minutes to fill the 3,000-gallon tank (correct answer)
Explanation: Pump X rate: 1,200 gallons ÷ 40 minutes = 30 gallons/minute. Pump Y rate: 1,800 gallons ÷ 45 minutes = 40 gallons/minute. Combined rate: 30 + 40 = 70 gallons/minute. Time to fill 3,000 gallons: 3,000 ÷ 70 = 42.86 minutes ≈ 43 minutes, which is closest to 41 minutes.

Question 3

A delivery service charges $2.50 for the first mile and $1.75 for each additional mile. A competitor charges $1.90 per mile for any distance. At what distance do both services charge exactly the same amount, and what is that amount?

  1. Both services charge $9.50 for a distance of exactly 5 miles (correct answer)
  2. Both services charge $11.40 for a distance of exactly 6 miles
  3. Both services charge $13.30 for a distance of exactly 7 miles
  4. Both services charge $15.20 for a distance of exactly 8 miles
Explanation: Let d = distance in miles. First service cost: $2.50 + $1.75(d-1) = $0.75 + $1.75d. Second service cost: $1.90d. Setting equal: $0.75 + $1.75d = $1.90d. Solving: $0.75 = $0.15d, so d = 5 miles. Cost at 5 miles: First service = $2.50 + $1.75(4) = $9.50. Second service = $1.90(5) = $9.50.

Question 4

A printing company charges $0.08 per page for the first 500 pages and $0.06 per page for each additional page. A copying service charges a flat rate of $0.07 per page regardless of quantity. For what number of pages do both services cost exactly the same amount?

  1. Both services cost the same for exactly 900 pages of printing
  2. Both services cost the same for exactly 1000 pages of printing (correct answer)
  3. Both services cost the same for exactly 1100 pages of printing
  4. Both services cost the same for exactly 1200 pages of printing
Explanation: Let x = total pages. Printing company cost: $40 (for first 500 pages) + $0.06(x - 500) for x > 500. Copying service cost: $0.07x. Setting equal: 40 + 0.06(x - 500) = 0.07x. Expanding: 40 + 0.06x - 30 = 0.07x. Simplifying: 10 = 0.01x. Therefore x = 1000 pages. Verification: Printing cost = $40 + $0.06(500) = $70. Copying cost = $0.07(1000) = $70. Choice A (900): printing cost would be $64, copying $63. Choice C (1100): printing cost $76, copying $77. Choice D (1200): printing cost $82, copying $84.

Question 5

Store A sells oranges at 5 pounds for $4.25, while Store B sells oranges at 8 pounds for $6.40. Store C sells oranges at 3 pounds for $2.70. Which store offers the best price per pound, and by how much does it beat the most expensive option?

  1. Store A offers the best price, beating the most expensive by $0.05 per pound
  2. Store B offers the best price, beating the most expensive by $0.05 per pound
  3. Store B offers the best price, beating the most expensive by $0.10 per pound (correct answer)
  4. Store C offers the best price, beating the most expensive by $0.10 per pound
Explanation: Store A: $4.25 ÷ 5 = $0.85 per pound. Store B: $6.40 ÷ 8 = $0.80 per pound. Store C: $2.70 ÷ 3 = $0.90 per pound. Store B has the lowest price at $0.80/pound. Store C has the highest at $0.90/pound. Difference: $0.90 - $0.80 = $0.10 per pound. Store B beats the most expensive (Store C) by $0.10 per pound. Choice A incorrectly identifies Store A as best. Choice B has the right store but wrong difference. Choice D incorrectly identifies Store C as best when it's actually most expensive.

Question 6

Machine A produces 180 parts in 6 hours while Machine B produces 350 parts in 14 hours. If both machines operate simultaneously for 8 hours, approximately how many total parts will be produced?

  1. 440 parts will be produced in the 8-hour period (correct answer)
  2. 480 parts will be produced in the 8-hour period
  3. 520 parts will be produced in the 8-hour period
  4. 560 parts will be produced in the 8-hour period
Explanation: Machine A rate: 180 ÷ 6 = 30 parts/hour. In 8 hours: 30 × 8 = 240 parts. Machine B rate: 350 ÷ 14 = 25 parts/hour. In 8 hours: 25 × 8 = 200 parts. Total: 240 + 200 = 440 parts. Choice B (480) might result from calculation errors. Choice C (520) could come from misestimating rates. Choice D (560) could result from using incorrect time periods in the rate calculations.