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Quantitative (Math)Free

Ratios, proportions, and rates — SSAT Upper practice questions

Ratios, proportions, and rates on the SSAT Upper Quantitative (Math) section covers part-to-part comparisons, how those comparisons change when amounts are added or removed, and combined-speed travel. A student has to set up a proportion from a word problem, keep one part fixed while the other changes, and find an original total or the time until two travelers meet. Questions are multi-step multiple-choice items whose choices often show the separate parts, a new total, or one of the given speeds. A frequent trap is reading 5:7 as a share of seven rather than of twelve parts, or adding the two speeds instead of using them to find meeting time.

  • Section: Quantitative (Math) 50 questions on the paper
  • 120 practice questions in the app

Sample questions

Question 1

At a music camp, the ratio of singers to instrumentalists was 5:75:7. After 6 instrumentalists left, the ratio became 5:65:6. How many students were in those two groups before the 6 instrumentalists left?

  1. A48
  2. B54
  3. C60
  4. D66
  5. E72
Show answer

Answer: E — 72

Let the numbers of singers and instrumentalists be 5k5k and 7k7k. After 6 instrumentalists left, 5k7k−6=56\dfrac{5k}{7k-6}=\dfrac{5}{6}, so 30k=35k−3030k=35k-30 and k=6k=6. The original total was 5k+7k=12k=725k+7k=12k=72.

Question 2

A bin contains white rice and brown rice in the ratio 3:53{:}5. After 12 cups of white rice are added, the amounts of the two kinds are equal. How many cups of rice were in the bin originally?

  1. A24
  2. B30
  3. C36
  4. D42
  5. E48
Show answer

Answer: E — 48

Let the original amounts be 3k3k and 5k5k. Equality after the addition gives 3k+12=5k3k+12=5k, so k=6k=6. The original total was 8k=488k=48 cups.

Question 3

Two kayakers start 78 miles apart and paddle toward each other at the same time. One travels at 8 miles per hour and the other at 5 miles per hour. After how many hours do they meet?

  1. A6
  2. B9.75
  3. C13
  4. D15.6
  5. E26
Show answer

Answer: A — 6

Their separation closes at 8+5=138+5=13 miles per hour. The meeting time is 78÷13=678\div13=6 hours.

Practice 120 Ratios, proportions, and rates questions in the app

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Quantitative (Math)

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