Number properties are a fundamental concept tested in the ASVAB exam. Understanding number properties is crucial for answering various math questions efficiently and accurately. From prime numbers to integers, knowing the ins and outs of number properties can give you a significant advantage on test day. In this guide, we will explore essential tips and tricks for mastering number properties in the ASVAB exam. We will cover topics such as divisibility rules, even and odd numbers, prime factorization, and more. By sharpening your skills in number properties, you can improve your overall performance on the ASVAB and increase your chances of achieving your desired score. Whether you are just starting your studying or looking to fine-tune your knowledge, this guide will provide valuable insights to help you succeed in the number properties section of the ASVAB exam.

ASVAB

Which of the following statements is TRUE?

It is true that if a number is divisible by both 2 and 3, it is also divisible by 6. For example, 108 is divisible by 2 (108 ÷ 2 = 54) and by 3 (1 + 0 + 8 = 9 ÷ 3 = 3), and therefore is also divisible by 6.

If a number is divisible by 1, it is also divisible by 2.

If the last 3 digits of a number are divisible by 2, then the number is divisible by 4.

If a number is divisible by 2 and 3, it is also divisible by 6.

If a number is divisible by 5, it is also divisible by 10.

How many prime numbers are there between 25 and 35, inclusive?

Prime numbers are not divisible by anything other than themselves and 1. The only prime numbers in this set are 29 and 31. 25, 30, and 35 can be excluded because they are divisible by 5. 26, 28, 30, 32, and 34 are divisible by 2. 27, 30, and 33 are divisible by 3.

An integer is any positive or negative whole number or zero. Therefore, -9 is an integer. 

@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@ and 0.5 are not integers because they are not whole numbers. 

The square root of 42 is approximately 6.48 and therefore not an integer.

Which of the following numbers is divisible by 3?

If the sum of the digits of a number is divisible by 3, then the number itself is divisible by 3. 
 8 + 5 + 0 + 1 + 9 + 4 + 5 + 7 = 39. 
 39 divided by 3 is 13 with no remainders, so the number is divisible by 3.

Laura goes to the grocery store every 5 days and Tim goes to the same grocery store every 6 days. If Laura and Tim both went to the grocery store today, when is the next time they will both go to the grocery store on the same day?

To determine when Laura and Tim will both go to the grocery store on the same day again, we need to find the least common multiple of the two intervals: 5 days and 6 days.

Calculate the least common multiple using the following steps:

- Find the prime factorization of each number: 5 = 5 and 6 = 2 × 3

- Find the highest power of each prime factor: @@@@@@@ and @@@@@@@@@@@@@@@@@

- Multiply the prime factors together: @@@@@@@@@@@@@@@@@@@@@@@@@@@ = 30

The least common multiple of 5 and 6 is 30. 

This means that after 30 days, both Laura and Tim will go to the grocery store on the same day again.

There is not enough information to answer the question.

What is the absolute value of the quantity two minus seven?

The absolute value of the quantity two minus seven” should be written as |2-7| = |-5| = 5. Absolute value is the distance of a number from zero, and since distances cannot be negative, absolute values are always positive numbers. To take the absolute value, simplify the expression between the absolute value bars and then take the positive value of it.
 |2-7| = |-5| = 5 .

If @@@@@@@@@@@, which of the following best describes a?

The absolute value is the positive magnitude of a particular number or variable and is indicated by two vertical lines: |−7|=7. In the case of a variable absolute value (|a|=7) the value of a can be either positive or negative (a = -7 or a = 7).

What is the LEAST common multiple of 2 and 8?

The first few multiples of 2 are [2, 4, 6, 8, 10, 12, 14, 16, 18, 20] and the first few multiples of 8 are [8, 16, 24, 32, 40, 48, 56, 64, 72, 80]. The first few multiples they share are [8, 16, 24, 32, 40] making 8 the smallest multiple 2 and 8 have in common.

Which of the following is NOT an integer?

An integer is any whole number, including zero. An integer can be either positive or negative. Examples include -77, -1, 0, 55, 119.

All of the following are examples of composite numbers EXCEPT which one?

A composite number is a whole number that can be divided by itself, 1, and one or more other whole numbers. 6 is a composite number because it can be divided by 1, 2, 3, and 6; 9 is a composite number because it can be divided by 1, 3, and 9; and 12 is a composite number because it can be divided by 1, 2, 3, 4, 6, and 12.
 A prime number is a whole number that can only be divided by itself and 1. 2 is a prime number because its factors are only 1 and 2. A prime number is a whole number that can only be divided by itself and 1. 2 is a prime number because its factors are only 1 and 2.

Which of the following is NOT a factor of 90?

A factor of a number is a whole number that divides the given number without leaving a remainder. In other words, if you can divide a number 𝐴 by another number 𝐵 and the result is an integer, then 𝐵 is a factor of 𝐴.
 Let's test each option:
 90 ÷ 15 = 6 (No remainder, therefore 15 is a factor)
 90 ÷ 5 = 18 (No remainder, therefore 5 is a factor)
 90 ÷ 6 = 15 (No remainder, therefore 6 is a factor)
 90 ÷ 12 = 7.5 (Leaves a remainder of 0.5)
 Therefore, 12 is not a factor of 90.

Which of the following is equivalent to 4×4×4×4?

An exponent is a method of indicating repeated multiplication. For example, 4×4×4×4 can also be expressed as @@@@@@@, which is also known as “4 to the fourth power.” The small number written slightly above and to the right of a number is the exponent, and it indicates the number of times you multiply the number it accompanies by itself.

Which of the following is a prime number: 13, 15, 4, or 12?

A prime number is one that can be divided evenly only by itself and 1. All of the other choices can be divided by numbers other than just 1 and the given number.

The absolute value of the quantity of 5 plus a number equals 10. Which of the following options is the CORRECT solution set for the above equation?

The absolute value of 5 plus a number equals 10 should be written as |5 + x| = 10. 
 Absolute value means the distance of a number from zero, so whenever you solve for the number inside absolute value bars, you must consider both the positive and negative values. 
 Take away the bars and set the expression equal to both 10 and -10. 5 + x = 10 gives you x = 5, and 5 + x = -10 gives you x = -15. 
 The solution set is x = {-15, 5}.

ASVAB Number Properties: Tips and Tricks for Success

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ASVAB Number Properties: Tips and Tricks for Success

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