$x$ and $y$ are positive numbers, and $\dfrac{x}{y}=\dfrac{2}{3}$. Column A: $x+6$ / Column B: $y+4$

The quantity in Column A is greater

The quantity in Column B is greater

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Quantitative ReasoningFree

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

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.

Section: Quantitative Reasoning 37 questions on the paper
109 practice questions in the app

Sample questions

Question 1

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

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

AThe quantity in Column A is greater
BThe quantity in Column B is greater
CThe two quantities are equal
DThe relationship cannot be determined from the information given

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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 2

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?

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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 3

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

A1.50
B9.50
C12.00
D36.00

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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.

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

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

Sample questions

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Quantitative Reasoning