Ratios, proportions, and rates — SSAT Upper practice questions

143 practice questions in the app
Free

Practice 143 Ratios, proportions, and rates questions in the app

What this topic is

A ratio compares two amounts, but it does not tell you the actual amounts until you scale it, and that idea drives ratios, proportions, and rates questions on the SSAT Upper.

When a ratio changes because some members join or leave, the reliable method is to write each group as a multiple of one unknown, such as two k and three k, and let the change fix k. Rate problems use distance equals rate times time, and when two travelers move toward each other, their speeds add.

Wrong choices usually come from treating the ratio numbers as the real totals, or from answering with one group instead of both.

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?

Show answer

Answer: E — 72

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

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?

Show answer

Answer: E — 48

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

Show answer

Answer: A — 6

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

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

Practice 143 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)