GRE Quantitative Flashcards: Ratios Rates Proportions

What this deck covers

This deck focuses on Ratios Rates Proportions, giving you a quick way to review the definitions, rules, and examples that matter most for GRE Quantitative.

How to use these flashcards

Work through these flashcards in short sessions. Try to answer each prompt before flipping the card, then revisit any cards you miss until the explanation feels automatic.

Flashcard 1: What is the ratio of areas of similar figures if the side-length ratio is $3:5$?

Answer: $9:25$. Areas of similar figures scale with the square of the linear dimensions ratio.

Flashcard 2: What is the definition of a rate?

Answer: A ratio comparing quantities with different units. A rate is a special ratio that compares two quantities measured in different units, such as speed or density.

Flashcard 3: What is the definition of the ratio $a:b$ in fraction form?

Answer: $\frac{a}{b}$. The ratio $a:b$ expresses the relative magnitude of $a$ to $b$ as the fraction $\frac{a}{b}$.

Flashcard 4: What is the value of $x$ if $\frac{x}{15}=\frac{2}{5}$?

Answer: $6$. Solve the proportion by cross-multiplying: $x \cdot 5 = 15 \cdot 2$, so $x=30/5=6$.

Flashcard 5: What is the part-to-whole fraction for $b$ if $a:b=2:5$?

Answer: $\frac{5}{7}$. The whole is $2+5=7$ parts, so $b$ represents $5$ out of $7$.

Flashcard 6: What is the ratio of volumes of similar solids if the side-length ratio is $2:7$?

Answer: $8:343$. Volumes of similar solids scale with the cube of the linear dimensions ratio.

Flashcard 7: State the cross-multiplication rule for $\frac{a}{b}=\frac{c}{d}$.

Answer: $ad=bc$. Cross-multiplying the proportion $\frac{a}{b}=\frac{c}{d}$ yields $ad=bc$ to verify equality or solve for unknowns.

Flashcard 8: What is the larger part if two parts are in ratio $3:5$ and the total is $64$?

Answer: $40$. Total parts are 8; each part is $64/8=8$, so larger is $5 \times 8$.

Flashcard 9: State the general equation for inverse variation between $x$ and $y$ with constant $k$.

Answer: $y=\frac{k}{x}$. Inverse variation means $y$ decreases as $x$ increases, with product $xy$ constant.

Flashcard 10: What is the total if two parts are in ratio $3:5$ and the smaller part is $21$?

Answer: $56$. The smaller part (3 units) is 21, so each unit is 7; total is $8 \times 7$.

Flashcard 11: What is the mixture ratio of water to concentrate if $2$ liters of concentrate are added to $8$ liters of water?

Answer: $4:1$. The ratio water:concentrate is 8:2, simplified by dividing by 2.

Flashcard 12: What is the ratio of $12$ to $18$ in simplest form?

Answer: $2:3$. Simplify by dividing both 12 and 18 by their greatest common divisor of 6.

Flashcard 13: What is the part-to-whole fraction for $a$ if $a:b=2:5$?

Answer: $\frac{2}{7}$. The whole is $2+5=7$ parts, so $a$ represents $2$ out of $7$.

Flashcard 14: Identify the constant of proportionality $k$ if $y$ is proportional to $x$ and $y=18$ when $x=6$.

Answer: $k=3$. In direct proportion $y=kx$, substitute values to solve for $k=18/6$.

Flashcard 15: What is the percent of the whole represented by $3$ parts out of $8$ parts?

Answer: $37.5\%$. Convert the fraction $3/8$ to a percentage: $(3/8) \times 100$.

Flashcard 16: What is $y$ if $y$ is directly proportional to $x$, $y=10$ when $x=4$, and $x=12$?

Answer: $30$. Find $k=10/4=2.5$, then $y=2.5 \times 12$ for the new $x$.

Flashcard 17: What is the unit rate if $180$ miles are traveled in $3$ hours?

Answer: $60$ miles per hour. Divide total distance by total time to find the rate per unit time.

Flashcard 18: What is $a:c$ in simplest integer form if $a:b=3:7$ and $b:c=14:5$?

Answer: $6:5$. Simplify the ratio $a:c=6:5$ after combining and reducing to integers.

Flashcard 19: What is the ratio after scaling both terms of $4:7$ by $3$?

Answer: $12:21$. Scaling a ratio by a constant multiplies each term by that factor, preserving the ratio.

Flashcard 20: What is the combined ratio of $a:b=2:3$ and $b:c=4:5$ as $a:b:c$?

Answer: $8:12:15$. Align the common term $b$ by scaling to make it equal (12), then combine into a single ratio.

Flashcard 21: What is the value of $x$ if $x:8=3:4$?

Answer: $6$. Convert the ratio to a proportion $x/8=3/4$ and solve by cross-multiplying.

Flashcard 22: What is the definition of a proportion?

Answer: An equation stating that two ratios are equal. A proportion sets two ratios equal, indicating that the relationships between the pairs are equivalent.

Flashcard 23: What is the speed in miles per hour for $150$ miles in $2.5$ hours?

Answer: $60$ miles per hour. Compute the rate by dividing distance by time: $150 / 2.5$.