Easy GRE Integer Questions Practice Questions

Concept Explanation

Integers are whole numbers that include all positive counting numbers, their negative counterparts, and the number zero.

On the GRE, integer properties form the bedrock of the Quantitative Reasoning section. An integer is any member of the set $\{..., -3, -2, -1, 0, 1, 2, 3, ...\}$. It is vital to remember that zero is an integer, and it is neither positive nor negative, but it is even. Fractions, decimals, and mixed numbers like $1.5$ or $\frac{3}{4}$ are not integers. Key concepts often tested include parity (even vs. odd), divisibility, prime numbers, and remainders. For instance, an even number is any integer divisible by 2, expressed as $2n$, while an odd number is expressed as $2n + 1$. When you encounter Easy GRE Integer Questions, you are often being tested on your ability to apply these fundamental rules without making "careless" errors. For more foundational practice, you can explore free GRE practice questions to build your confidence.

Understanding the rules of operations is also essential. For example, the product of two odd integers is always odd, while the sum of two odd integers is always even. You can find detailed breakdowns of these patterns in the GRE Prep hub. Additionally, the Wikipedia page on integers provides a deep dive into the mathematical theory if you wish to see the formal proofs behind these arithmetic properties.

Solved Examples

Review these examples to understand how basic integer rules are applied in a test format.

1. Example 1: Parity Rules
   If $n$ is an odd integer, which of the following must be an even integer?
   1. $n + 2$
   2. $2n + 1$
   3. $3n + 1$
   Solution:
   1. Pick a sample odd integer, such as $n = 3$.
   2. Test option (a): $3 + 2 = 5$ (Odd).
   3. Test option (b): $2(3) + 1 = 7$ (Odd).
   4. Test option (c): $3(3) + 1 = 10$ (Even).
   5. Since $3n + 1$ resulted in an even number, (c) is the correct answer.
2. Example 2: Divisibility
   Is the sum of three consecutive integers always divisible by 3? Solution:
   1. Represent three consecutive integers as $x$, $x + 1$, and $x + 2$.
   2. Add them together: $x + (x + 1) + (x + 2) = 3x + 3$.
   3. Factor out the 3: $3(x + 1)$.
   4. Since the sum can be written as 3 times an integer, it is always divisible by 3.
3. Example 3: Prime Numbers
   What is the sum of the prime numbers between 10 and 20? Solution:
   1. List the integers between 10 and 20: 11, 12, 13, 14, 15, 16, 17, 18, 19.
   2. Identify the primes: 11, 13, 17, and 19. (Note: 15 is not prime because $3 \times 5 = 15$).
   3. Calculate the sum: $11 + 13 + 17 + 19 = 60$.
   4. The sum is 60.

Practice Questions

Test your skills with these Easy GRE Integer Questions. Use a scratchpad and try to solve them within 60 seconds each.

1. If $x$ is an even integer and $y$ is an odd integer, what is the parity of $(x + y) \times y$?
2. How many integers between 2 and 10 (inclusive) are prime?
3. If $k$ is an integer and $0 < k < 10$, for how many values of $k$ is $\frac{12}{k}$ an integer?

4. What is the smallest prime number greater than 40?
5. If $m$ is an even integer, which of the following must be odd: $m^2$, $m+1$, or $m-2$?
6. What is the remainder when $53$ is divided by $7$?
7. List all factors of 18.
8. If the product of two integers is 24 and their sum is 11, what are the two integers?
9. Is zero an even or an odd integer?
10. If $p$ is a prime number, how many factors does $p^2$ have?

Answers & Explanations

1. Odd. The sum of an even and an odd integer is always odd ($E + O = O$). Multiplying an odd number by another odd number results in an odd number ($O \times O = O$).
2. 4. The integers are 2, 3, 4, 5, 6, 7, 8, 9, 10. The primes are 2, 3, 5, and 7.
3. 5. We need the factors of 12 that are between 0 and 10. These are 1, 2, 3, 4, and 6.
4. 41. 41 has no divisors other than 1 and itself. 42 is even, and 43 is also prime, but 41 is the smallest greater than 40.
5. $m+1$. Adding 1 to any even integer always results in an odd integer. $m^2$ will be even, and $m-2$ will be even.
6. 4. $7 \times 7 = 49$. Then $53 - 49 = 4$.
7. 1, 2, 3, 6, 9, 18. These are all the integers that divide 18 without a remainder.
8. 3 and 8. $3 \times 8 = 24$ and $3 + 8 = 11$.
9. Even. An integer $n$ is even if there exists an integer $k$ such that $n = 2k$. Since $0 = 2(0)$, zero is even.
10. 3. The factors of $p^2$ are $1$, $p$, and $p^2$.
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1. Which of the following is NOT an integer?

• A-5
• B0
• C2.5
• D1,000

Frequently Asked Questions

Is zero considered a positive integer on the GRE?

No, zero is neither positive nor negative, although it is an even integer. You should treat it as its own category when a question specifies "positive integers" or "negative integers."

What is the difference between a factor and a multiple?

A factor is an integer that divides into another integer evenly, while a multiple is the product of that integer and another integer. For example, 3 is a factor of 12, and 12 is a multiple of 3.

Are negative numbers allowed to be prime?

By mathematical definition used on the GRE, prime numbers must be integers greater than 1. Therefore, negative numbers, 0, and 1 are not prime numbers.

How do I handle "consecutive integers" in algebra?

You should represent them as $n, n+1, n+2, ...$ to solve for unknown values. If the question specifies consecutive even or odd integers, use $n, n+2, n+4, ...$.

What does the term "inclusive" mean in integer ranges?

The term inclusive means you must include the start and end numbers of the range in your calculations. If a question asks for integers from 1 to 5 inclusive, you count 1, 2, 3, 4, and 5.