Ratios, proportions, and rates — SSAT Upper practice questions

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135 practice questions in the app
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Practice 135 Ratios, proportions, and rates questions in the app

What this topic is

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.

Sample questions

Pick an answer to see whether it is right — nothing is saved, and nothing needs an account.

Question 1Mid

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

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Answer: E — 72

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

Question 2Mid

A bin contains white rice and brown rice in the ratio $3{:}5$ . 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?

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Answer: E — 48

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

Question 3Mid

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?

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Answer: A — 6

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

Every question is picked for where you are right now, wrong answers come back until they stick, and it all works offline.

Practice 135 Ratios, proportions, and rates questions in the app

Ratios, proportions, and rates — SSAT Upper practice questions

What this topic is

Sample questions

More SSAT Upper topics

Quantitative (Math)