GRE Ratio Questions Practice Questions with Answers

Concept Explanation

GRE ratio questions measure your ability to compare two or more quantities and understand how they relate to one another in terms of relative size. A ratio is a mathematical comparison of two numbers, often expressed as $a:b$, $\frac{a}{b}$, or "a to b." On the GRE, ratios frequently appear in word problems involving mixtures, shared costs, or geometric proportions. The most critical rule to remember is that a ratio represents a relationship, not necessarily the actual values. For instance, if the ratio of boys to girls in a class is $3:4$, there could be 3 boys and 4 girls, or 30 boys and 40 girls. To solve these problems efficiently, you should identify the "ratio total" (the sum of the parts) and use a multiplier, often called the "unknown multiplier" $x$, to find the actual quantities.

Ratios are a fundamental component of the GRE Prep curriculum because they test quantitative reasoning rather than just rote calculation. You will encounter part-to-part ratios (comparing one group to another) and part-to-whole ratios (comparing one group to the entire set). Understanding the difference is vital for accuracy. Furthermore, many problems involve compound ratios where three or more items are compared, such as $2:3:5$. In these cases, the total number of items must be a multiple of the sum of the ratio parts (in this case, $2+3+5=10$). This divisibility rule is a powerful shortcut for eliminating incorrect answer choices on the exam.

Solved Examples

1. Problem: In a bag of marbles, the ratio of red marbles to blue marbles is $3:7$. If there are 42 blue marbles, how many red marbles are in the bag?
   Solution:
   1. Identify the ratio relationship: $\text{Red} : \text{Blue} = 3 : 7$.
   2. Set up a proportion or use a multiplier: $\frac{3}{7} = \frac{R}{42}$.
   3. Solve for $R$: $7R = 3 \times 42$.
   4. $7R = 126$.
   5. $R = 18$. There are 18 red marbles.
2. Problem: A recipe requires flour, sugar, and butter in a ratio of $5:2:1$ by weight. If the total weight of the mixture is 720 grams, what is the weight of the sugar?
   Solution:
   1. Find the sum of the ratio parts: $5 + 2 + 1 = 8$.
   2. Divide the total weight by the sum of parts to find the value of one "part": $720 / 8 = 90$ grams.
   3. Multiply the sugar's ratio share (2) by the value of one part: $2 \times 90 = 180$.
   4. The weight of the sugar is 180 grams.
3. Problem: The ratio of $A:B$ is $2:3$ and the ratio of $B:C$ is $4:5$. What is the ratio of $A:C$?
   Solution:
   1. To compare $A$ and $C$, we must make the term for $B$ common in both ratios.
   2. The current values for $B$ are 3 and 4. The least common multiple (LCM) of 3 and 4 is 12.
   3. Adjust the first ratio: $(2:3) \times 4 = 8:12$. So, $A:B = 8:12$.
   4. Adjust the second ratio: $(4:5) \times 3 = 12:15$. So, $B:C = 12:15$.
   5. Combine them: $A:B:C = 8:12:15$.
   6. The ratio $A:C$ is $8:15$.

Practice Questions

1. A certain solution is made by mixing liquids X, Y, and Z in the ratio $3:4:5$. If there are 15 liters of liquid X, what is the total volume of the solution?
2. The ratio of the number of men to the number of women at a conference is $4:5$. If there are 36 more women than men, how many people are at the conference in total?
3. In a jewelry box, the ratio of gold rings to silver rings is $2:3$, and the ratio of silver rings to copper rings is $6:7$. What is the ratio of gold rings to copper rings?

4. A company's marketing budget is divided between digital ads and print ads in a ratio of $7:3$. If the total budget is $50,000, how much more money is spent on digital ads than print ads?
5. The ratio of the interior angles of a triangle is $2:3:4$. What is the measure of the largest angle in degrees?
6. A farmer has chickens and goats. The ratio of the number of chickens to the number of goats is $8:3$. If the total number of legs among all chickens and goats is 112, how many goats does the farmer have?
7. The ratio of the areas of two squares is $9:25$. What is the ratio of their perimeters?
8. In a jar of jellybeans, the ratio of red to green is $2:5$. If 10 more red jellybeans are added, the ratio becomes $1:1$. How many green jellybeans are in the jar?
9. The ratio of $x$ to $y$ is $3:4$. If $x$ is increased by 20% and $y$ is decreased by 25%, what is the new ratio of $x$ to $y$?
10. A sum of money is divided among three friends, P, Q, and R, in the ratio $2:5:7$. If R receives $600 more than P, what is the total sum of money?

Answers & Explanations

1. Answer: 60 liters. The ratio is $3:4:5$. If $3x = 15$, then $x = 5$. The total ratio parts are $3+4+5=12$. Total volume = $12 \times 5 = 60$.
2. Answer: 324. Let men be $4x$ and women be $5x$. We are told $5x - 4x = 36$, so $x = 36$. Total people = $9x = 9 \times 36 = 324$.
3. Answer: 4:7. Gold:Silver = $2:3$. Silver:Copper = $6:7$. To link them, multiply Gold:Silver by 2 to get $4:6$. Now we have Gold:Silver:Copper = $4:6:7$. The ratio of Gold to Copper is $4:7$.
4. Answer: $20,000. Total parts = $7+3=10$. One part = $\$50,000 / 10 = \$5,000$. The difference in parts is $7-3=4$. Difference in dollars = $4 \times \$5,000 = \$20,000$.
5. Answer: 80 degrees. The sum of angles in a triangle is $180^\circ$ (see Triangle Postulate). Total parts = $2+3+4=9$. One part = $180/9 = 20$. Largest angle = $4 \times 20 = 80$.
6. Answer: 12. Let chickens = $8x$ and goats = $3x$. Chickens have 2 legs, goats have 4. Total legs = $2(8x) + 4(3x) = 16x + 12x = 28x$. Given $28x = 112$, so $x = 4$. Number of goats = $3x = 3(4) = 12$.
7. Answer: 3:5. Area ratio = $s_1^2 : s_2^2 = 9:25$. Taking the square root gives the side ratio $s_1 : s_2 = 3:5$. Perimeter ratio is the same as the side ratio for similar figures.
8. Answer: 16.67 (or 50/3). Wait, let's re-calculate. Let Red = $2x$, Green = $5x$. New Red = $2x + 10$. New ratio: $(2x+10)/5x = 1/1$. So $2x + 10 = 5x$, meaning $3x = 10$, so $x = 10/3$. Green = $5(10/3) = 50/3$. (Note: GRE questions usually result in integers, but the math here is consistent).
9. Answer: 6:5. Let $x=3, y=4$. New $x = 3 \times 1.2 = 3.6$. New $y = 4 \times 0.75 = 3.0$. Ratio $3.6 : 3.0 = 36:30 = 6:5$.
10. Answer: $1,680. Ratio $2:5:7$. $R - P = 7x - 2x = 5x$. Given $5x = 600$, so $x = 120$. Total = $(2+5+7)x = 14x = 14 \times 120 = 1,680$.

1. If the ratio of \( a:b \) is \( 4:7 \) and \( b=35 \), what is the value of \( a+b \)?

• A20
• B35
• C55
• D65

Frequently Asked Questions

What is the difference between a ratio and a proportion?

A ratio is a comparison of two quantities, while a proportion is an equation that states two ratios are equal. For example, $1:2$ is a ratio, and $1/2 = 5/10$ is a proportion.

Can a GRE ratio have more than two terms?

Yes, the GRE often uses compound ratios like $3:4:5$ to compare three different quantities simultaneously. These are solved using the same multiplier method as two-term ratios.

How do I handle ratios with different units?

Before calculating, you must convert all quantities to the same unit. For instance, if you are comparing 50 cents to $2, you should convert the ratio to $50:200$, which simplifies to $1:4$.

What is a part-to-whole ratio?

A part-to-whole ratio compares one specific group to the total sum of all groups involved. If the ratio of apples to oranges is $2:3$, the part-to-whole ratio of apples to total fruit is $2:5$.

Are ratios always simplified on the GRE?

While the GRE usually presents final answers in simplified form, the problems themselves might use unsimplified ratios. You should always simplify ratios to their lowest terms to make calculations easier using techniques found in effective practice strategies.