Ratios, proportions; distance-rate-time — ISEE Upper practice questions

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Practice 111 Ratios, proportions; distance-rate-time questions in the app

What this topic is

A ratio compares parts, and most Ratios, proportions; distance-rate-time questions turn on keeping those parts in step.

If two quantities are in the ratio two to three, they can be written as two times some number and three times the same number, which turns a wordy setup into a simple equation. Unit-price problems use the same idea: find the cost of one unit, then scale up.

Distance-rate-time items rest on distance equals rate times time, and a well-known misconception is averaging two speeds directly when the times spent at each speed differ. Answer choices frequently include the result of setting a proportion upside down.

Sample questions

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

Question 1Mid

$x$ and $y$ are positive numbers, and $\frac{x}{y} = \frac{2}{3}$ .

Column A	Column B
$x + 6$	$y + 4$

The quantity in Column A is greater✗ Not this oneThe quantity in Column B is greater✗ Not this oneThe two quantities are equal✗ Not this oneThe relationship cannot be determined from the information given✓ Correct

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Answer: D — The relationship cannot be determined from the information given

Let $x = 2 k$ and $y = 3 k$ . Then the columns are $2 k + 6$ and $3 k + 4$ . Different positive values of $k$ make Column A greater, equal, or less, so the relationship cannot be determined.

Question 2Mid

Three positive numbers are in the ratio $2 : 3 : 5$ . If 12 is added to the smallest number and 6 is subtracted from the largest number, the two resulting numbers are equal. What is the middle number?

12✗ Not this one18✓ Correct24✗ Not this one30✗ Not this one

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Answer: B — 18

Let the three numbers be $2 k$ , $3 k$ , and $5 k$ . The changed smallest and largest numbers are equal, so $2 k + 12 = 5 k - 6$ . This gives $18 = 3 k$ , so $k = 6$ . The middle number is $3 k = 18$ .

Question 3Easier

A florist pays 4.50 dollars for 3 meters of ribbon. Every meter has the same price. How much, in dollars, will 8 meters of ribbon cost?

1.50✗ Not this one9.50✗ Not this one12.00✓ Correct36.00✗ Not this one

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Answer: C — 12.00

The unit price is $4.50 / 3 = 1.50$ dollars per meter. Therefore, 8 meters cost $8 \times 1.50 = 12.00$ dollars.

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

Practice 111 Ratios, proportions; distance-rate-time questions in the app

Ratios, proportions; distance-rate-time — ISEE Upper practice questions

What this topic is

Sample questions

More ISEE Upper topics

Quantitative Reasoning