Easy GRE Algebra Word Problems Practice Questions

Concept Explanation

Easy GRE algebra word problems are mathematical challenges that require translating short, descriptive scenarios into basic linear equations or inequalities to find an unknown value. These problems typically focus on single-variable relationships, simple ratios, or direct arithmetic applications where the setup is straightforward. Understanding how to identify the "variable"—the quantity you are looking for—is the first step toward success. Often, the word "is" acts as an equal sign, while words like "more than" or "product" signal addition and multiplication, respectively. By breaking down the text into manageable mathematical components, you can solve these problems quickly and accurately. This skill is a foundational component of GRE Prep, ensuring you have the speed required for more complex quantitative sections.

Solved Examples

Review these examples to see how common phrasing translates into algebraic notation.

1. Example 1: A certain number is 12 more than three times 5. What is the number?

   1. Identify the operations: "3 times 5" is $3 \times 5$, and "12 more than" means adding 12.

   2. Set up the equation: Let the number be $x$. So, $x = (3 \times 5) + 12$.

   3. Calculate: $x = 15 + 12 = 27$.

   4. The answer is 27.

2. Example 2: If Sarah's age is twice Mark's age and the sum of their ages is 36, how old is Mark?

   1. Define variables: Let Mark's age be $m$. Then Sarah's age is $2m$.

   2. Create the equation: $m + 2m = 36$.

   3. Combine like terms: $3m = 36$.

   4. Divide by 3: $m = 12$.

   5. Mark is 12 years old.

3. Example 3: A store sells apples for $0.50 each and oranges for $0.75 each. If a customer buys 4 apples and some oranges for a total of $5.00, how many oranges did they buy?

   1. Calculate the cost of apples: 4 x 0.50 = $2.00.

   2. Set up the equation for the remaining cost: Let $n$ be the number of oranges. $2.00 + 0.75n = 5.00$.

   3. Subtract 2.00 from both sides: $0.75n = 3.00$.

   4. Divide by 0.75: $n = 4$.

   5. The customer bought 4 oranges.

Practice Questions

Test your skills with these easy GRE algebra word problems. Start with the basics and work your way through the list.

1. If a taxi charges a flat fee of $3.00 plus $1.50 per mile, what is the total cost for a 6-mile ride?

2. The product of a number and 4 is 10 less than 50. What is the number?

3. A baker has 24 cupcakes. If he gives 3 cupcakes to each of his $x$ friends and has 6 cupcakes left over, what is the value of $x$?

4. A rectangle has a perimeter of 40 cm. If the length is 12 cm, what is the width?

5. James has $150. He spends $15 per week on coffee. After how many weeks will he have $45 remaining?

6. The sum of three consecutive integers is 72. What is the smallest of these integers?

7. A car travels at a constant speed of 55 miles per hour. How many hours will it take to travel 220 miles?

8. If $5x - 7 = 18$, what is the value of $2x$?

9. A jacket is on sale for 20% off the original price. If the sale price is $80, what was the original price?

10. A water tank contains 500 gallons and is leaking at a rate of 5 gallons per hour. How many gallons are in the tank after 12 hours?

For more variety in your study sessions, you can explore free GRE practice questions or use an AI Exam Simulator to mimic the actual test environment.

Answers & Explanations

1. Answer: $12.00. The equation is $\text{Cost} = 3.00 + 1.50(6)$. Calculating the multiplication first, $1.50 \times 6 = 9.00$. Then, $3.00 + 9.00 = 12.00$.

2. Answer: 10. Translate to $4n = 50 - 10$. This simplifies to $4n = 40$. Dividing by 4 gives $n = 10$.

3. Answer: 6. The equation is $24 - 3x = 6$. Subtract 24 from both sides to get $-3x = -18$. Dividing by -3 yields $x = 6$.

4. Answer: 8 cm. Perimeter $P = 2l + 2w$. Substitute the values: $40 = 2(12) + 2w$, which is $40 = 24 + 2w$. Subtracting 24 gives $16 = 2w$, so $w = 8$.

5. Answer: 7 weeks. Let $w$ be the number of weeks. $150 - 15w = 45$. Subtracting 150 gives $-15w = -105$. Dividing by -15 results in $w = 7$.

6. Answer: 23. Let the integers be $n, n+1, n+2$. Their sum is $3n + 3 = 72$. Subtract 3 to get $3n = 69$. Dividing by 3 gives $n = 23$.

7. Answer: 4 hours. Use the formula $\text{Distance} = \text{Rate} \times \text{Time}$. So, $220 = 55t$. Dividing 220 by 55 gives $t = 4$.

8. Answer: 10. First, solve for $x$: $5x = 18 + 7$, so $5x = 25$ and $x = 5$. The question asks for $2x$, which is $2 \times 5 = 10$.

9. Answer: $100. If the jacket is 20% off, the sale price is 80% of the original price ($P$). $0.80P = 80$. Dividing 80 by 0.80 gives $P = 100$.

10. Answer: 440 gallons. The amount lost is $5 \times 12 = 60$ gallons. Subtracting from the total: $500 - 60 = 440$.

If you are looking for more specific practice, check out these GRE practice questions with explanations or improve your verbal skills with GRE text completion practice questions.

1. A number increased by 7 is equal to twice the same number decreased by 3. What is the number?

• A4
• B10
• C15
• D20

Frequently Asked Questions

How do I translate "less than" in algebra word problems?

The phrase "less than" indicates subtraction, but the order is reversed. For example, "5 less than $x$" is written as $x - 5$, not $5 - x$.

What does the word "is" mean in a math word problem?

In almost all algebra word problems, the word "is" (or "was", "will be", "results in") functions as the equal sign ($=$) in your equation.

Should I use one variable or two for GRE algebra word problems?

For easy problems, it is usually simpler to use one variable by expressing the second quantity in terms of the first. However, setting up a system of two equations is also a valid and often clear method.

How can I check my answer for an algebra word problem?

Plug your numerical answer back into the original text of the problem to see if the scenario makes logical sense and the numbers add up as described.

Are easy algebra word problems common on the GRE?

Yes, while the GRE contains difficult questions, the first quantitative section includes several easy to medium word problems to establish your baseline performance level. You can use the Retrieval Challenge tool to keep these basic rules fresh in your mind.

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