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

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Practice 109 Ratios, proportions; distance-rate-time questions in the app

What this topic is

On the ISEE Upper Quantitative Reasoning test, Ratios, proportions; distance-rate-time covers constant relationships among quantities, scaling those relationships, and linking distance, rate, and time.

A student must rewrite a given fraction as equivalent parts, find an unknown after amounts are added or subtracted from a three-part ratio, and use a unit price to find the cost of a longer length. Stems are brief word problems or given equations.

Answer choices are typically numbers or dollar amounts, and some items are quantitative comparisons. Common traps include treating ratio parts as finished values, mixing which quantity is smaller, and solving the proportion for the wrong unknown.

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 $\dfrac{x}{y}=\dfrac{2}{3}$ .

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 $x=2k$ and $y=3k$ . Then the columns are $2k+6$ and $3k+4$ . 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 $2k$ , $3k$ , and $5k$ . The changed smallest and largest numbers are equal, so $2k+12=5k-6$ . This gives $18=3k$ , so $k=6$ . The middle number is $3k=18$ .

Question 3Easier

A florist pays 4.50 for 3 meters of ribbon. Every meter has the same price. How much 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 $8\times1.50=12.00$ dollars.

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

Practice 109 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