Ratios, Rates, and Proportions - GRE Quantitative Reasoning
Card 1 of 23
What is the part-to-whole fraction for $a$ if $a:b=2:5$?
What is the part-to-whole fraction for $a$ if $a:b=2:5$?
Tap to reveal answer
$\frac{2}{7}$. The whole is $2+5=7$ parts, so $a$ represents $2$ out of $7$.
$\frac{2}{7}$. The whole is $2+5=7$ parts, so $a$ represents $2$ out of $7$.
← Didn't Know|Knew It →
What is the larger part if two parts are in ratio $3:5$ and the total is $64$?
What is the larger part if two parts are in ratio $3:5$ and the total is $64$?
Tap to reveal answer
$40$. Total parts are 8; each part is $64/8=8$, so larger is $5 \times 8$.
$40$. Total parts are 8; each part is $64/8=8$, so larger is $5 \times 8$.
← Didn't Know|Knew It →
What is the ratio after scaling both terms of $4:7$ by $3$?
What is the ratio after scaling both terms of $4:7$ by $3$?
Tap to reveal answer
$12:21$. Scaling a ratio by a constant multiplies each term by that factor, preserving the ratio.
$12:21$. Scaling a ratio by a constant multiplies each term by that factor, preserving the ratio.
← Didn't Know|Knew It →
What is the value of $x$ if $x:8=3:4$?
What is the value of $x$ if $x:8=3:4$?
Tap to reveal answer
$6$. Convert the ratio to a proportion $x/8=3/4$ and solve by cross-multiplying.
$6$. Convert the ratio to a proportion $x/8=3/4$ and solve by cross-multiplying.
← Didn't Know|Knew It →
What is the unit rate if $180$ miles are traveled in $3$ hours?
What is the unit rate if $180$ miles are traveled in $3$ hours?
Tap to reveal answer
$60$ miles per hour. Divide total distance by total time to find the rate per unit time.
$60$ miles per hour. Divide total distance by total time to find the rate per unit time.
← Didn't Know|Knew It →
What is the speed in miles per hour for $150$ miles in $2.5$ hours?
What is the speed in miles per hour for $150$ miles in $2.5$ hours?
Tap to reveal answer
$60$ miles per hour. Compute the rate by dividing distance by time: $150 / 2.5$.
$60$ miles per hour. Compute the rate by dividing distance by time: $150 / 2.5$.
← Didn't Know|Knew It →
What is the combined ratio of $a:b=2:3$ and $b:c=4:5$ as $a:b:c$?
What is the combined ratio of $a:b=2:3$ and $b:c=4:5$ as $a:b:c$?
Tap to reveal answer
$8:12:15$. Align the common term $b$ by scaling to make it equal (12), then combine into a single ratio.
$8:12:15$. Align the common term $b$ by scaling to make it equal (12), then combine into a single ratio.
← Didn't Know|Knew It →
What is $a:c$ in simplest integer form if $a:b=3:7$ and $b:c=14:5$?
What is $a:c$ in simplest integer form if $a:b=3:7$ and $b:c=14:5$?
Tap to reveal answer
$6:5$. Simplify the ratio $a:c=6:5$ after combining and reducing to integers.
$6:5$. Simplify the ratio $a:c=6:5$ after combining and reducing to integers.
← Didn't Know|Knew It →
What is the part-to-whole fraction for $b$ if $a:b=2:5$?
What is the part-to-whole fraction for $b$ if $a:b=2:5$?
Tap to reveal answer
$\frac{5}{7}$. The whole is $2+5=7$ parts, so $b$ represents $5$ out of $7$.
$\frac{5}{7}$. The whole is $2+5=7$ parts, so $b$ represents $5$ out of $7$.
← Didn't Know|Knew It →
What is the total if two parts are in ratio $3:5$ and the smaller part is $21$?
What is the total if two parts are in ratio $3:5$ and the smaller part is $21$?
Tap to reveal answer
$56$. The smaller part (3 units) is 21, so each unit is 7; total is $8 \times 7$.
$56$. The smaller part (3 units) is 21, so each unit is 7; total is $8 \times 7$.
← Didn't Know|Knew It →
What is the percent of the whole represented by $3$ parts out of $8$ parts?
What is the percent of the whole represented by $3$ parts out of $8$ parts?
Tap to reveal answer
$37.5%$. Convert the fraction $3/8$ to a percentage: $(3/8) \times 100$.
$37.5%$. Convert the fraction $3/8$ to a percentage: $(3/8) \times 100$.
← Didn't Know|Knew It →
State the cross-multiplication rule for $\frac{a}{b}=\frac{c}{d}$.
State the cross-multiplication rule for $\frac{a}{b}=\frac{c}{d}$.
Tap to reveal answer
$ad=bc$. Cross-multiplying the proportion $\frac{a}{b}=\frac{c}{d}$ yields $ad=bc$ to verify equality or solve for unknowns.
$ad=bc$. Cross-multiplying the proportion $\frac{a}{b}=\frac{c}{d}$ yields $ad=bc$ to verify equality or solve for unknowns.
← Didn't Know|Knew It →
What is the ratio of $12$ to $18$ in simplest form?
What is the ratio of $12$ to $18$ in simplest form?
Tap to reveal answer
$2:3$. Simplify by dividing both 12 and 18 by their greatest common divisor of 6.
$2:3$. Simplify by dividing both 12 and 18 by their greatest common divisor of 6.
← Didn't Know|Knew It →
What is the value of $x$ if $\frac{x}{15}=\frac{2}{5}$?
What is the value of $x$ if $\frac{x}{15}=\frac{2}{5}$?
Tap to reveal answer
$6$. Solve the proportion by cross-multiplying: $x \cdot 5 = 15 \cdot 2$, so $x=30/5=6$.
$6$. Solve the proportion by cross-multiplying: $x \cdot 5 = 15 \cdot 2$, so $x=30/5=6$.
← Didn't Know|Knew It →
What is the definition of a proportion?
What is the definition of a proportion?
Tap to reveal answer
An equation stating that two ratios are equal. A proportion sets two ratios equal, indicating that the relationships between the pairs are equivalent.
An equation stating that two ratios are equal. A proportion sets two ratios equal, indicating that the relationships between the pairs are equivalent.
← Didn't Know|Knew It →
What is the definition of a rate?
What is the definition of a rate?
Tap to reveal 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.
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.
← Didn't Know|Knew It →
What is the definition of the ratio $a:b$ in fraction form?
What is the definition of the ratio $a:b$ in fraction form?
Tap to reveal answer
$\frac{a}{b}$. The ratio $a:b$ expresses the relative magnitude of $a$ to $b$ as the fraction $\frac{a}{b}$.
$\frac{a}{b}$. The ratio $a:b$ expresses the relative magnitude of $a$ to $b$ as the fraction $\frac{a}{b}$.
← Didn't Know|Knew It →
What is the ratio of volumes of similar solids if the side-length ratio is $2:7$?
What is the ratio of volumes of similar solids if the side-length ratio is $2:7$?
Tap to reveal answer
$8:343$. Volumes of similar solids scale with the cube of the linear dimensions ratio.
$8:343$. Volumes of similar solids scale with the cube of the linear dimensions ratio.
← Didn't Know|Knew It →
What is the ratio of areas of similar figures if the side-length ratio is $3:5$?
What is the ratio of areas of similar figures if the side-length ratio is $3:5$?
Tap to reveal answer
$9:25$. Areas of similar figures scale with the square of the linear dimensions ratio.
$9:25$. Areas of similar figures scale with the square of the linear dimensions ratio.
← Didn't Know|Knew It →
What is the mixture ratio of water to concentrate if $2$ liters of concentrate are added to $8$ liters of water?
What is the mixture ratio of water to concentrate if $2$ liters of concentrate are added to $8$ liters of water?
Tap to reveal answer
$4:1$. The ratio water:concentrate is 8:2, simplified by dividing by 2.
$4:1$. The ratio water:concentrate is 8:2, simplified by dividing by 2.
← Didn't Know|Knew It →
Identify the constant of proportionality $k$ if $y$ is proportional to $x$ and $y=18$ when $x=6$.
Identify the constant of proportionality $k$ if $y$ is proportional to $x$ and $y=18$ when $x=6$.
Tap to reveal answer
$k=3$. In direct proportion $y=kx$, substitute values to solve for $k=18/6$.
$k=3$. In direct proportion $y=kx$, substitute values to solve for $k=18/6$.
← Didn't Know|Knew It →
What is $y$ if $y$ is directly proportional to $x$, $y=10$ when $x=4$, and $x=12$?
What is $y$ if $y$ is directly proportional to $x$, $y=10$ when $x=4$, and $x=12$?
Tap to reveal answer
$30$. Find $k=10/4=2.5$, then $y=2.5 \times 12$ for the new $x$.
$30$. Find $k=10/4=2.5$, then $y=2.5 \times 12$ for the new $x$.
← Didn't Know|Knew It →
State the general equation for inverse variation between $x$ and $y$ with constant $k$.
State the general equation for inverse variation between $x$ and $y$ with constant $k$.
Tap to reveal answer
$y=\frac{k}{x}$. Inverse variation means $y$ decreases as $x$ increases, with product $xy$ constant.
$y=\frac{k}{x}$. Inverse variation means $y$ decreases as $x$ increases, with product $xy$ constant.
← Didn't Know|Knew It →