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Divisibility Rules Quiz 5 (5 MCQs)

This set of multiple-choice questions evaluates understanding of divisibility rules for 3, 4, 5, 10, and 7. It tests the ability to identify factors, perform integer division, and determine divisibility without a remainder. Concepts such as divisibility by 3, divisibility by 4, divisibility by 5 and 10, and number ending in 0 are covered.

Quiz Instructions

Select an option to see the correct answer instantly.

1. Which of these is not a factor of 12?

Correct Answer: Correct answer is: (D) 8.

Exam Relevance: SAT, ACT, GRE, GMAT

Difficulty: Moderate

Concept notes: A factor of a number is an integer that divides the number without leaving a remainder. To determine if a number is a factor of 12, we check if 12 can be divided by the number without a remainder.

Common Mistakes: A common mistake is to assume that any even number is a factor of 12, but this is not always true. For example, 8 is even but not a factor of 12.

Explanations: To determine if 8 is a factor of 12, we divide 12 by 8. The result is 1.5, which is not an integer. Therefore, 8 is not a factor of 12. The other options (2, 4, and 6) are factors of 12 because 12 can be divided by each of them without leaving a remainder.

Option Analysis:

Option A: 2 is a factor of 12 because 12 ÷ 2 = 6, which is an integer.
Option B: 4 is a factor of 12 because 12 ÷ 4 = 3, which is an integer.
Option C: 6 is a factor of 12 because 12 ÷ 6 = 2, which is an integer.
Option D: 8 is not a factor of 12 because 12 ÷ 8 = 1.5, which is not an integer.

2. The value of P, when 4864 x 9P2 is divisible by 12, is

Correct Answer: Correct answer is: (D) None of these.

Exam Relevance: GMAT, GRE, SAT, ACT

Difficulty: Moderate

Concept notes: To determine if a number is divisible by 12, it must be divisible by both 3 and 4. For divisibility by 3, the sum of the digits must be divisible by 3. For divisibility by 4, the last two digits of the number must form a number divisible by 4.

Common Mistakes: A common mistake is to only check for divisibility by 3 or 4, but not both. Another mistake is to overlook the specific digit placement and its impact on divisibility.

Explanations: To check if 4864 x 9P2 is divisible by 12, we need to ensure it is divisible by both 3 and 4. 1. **Divisibility by 4**: The last two digits of the number must form a number divisible by 4. The last two digits of 9P2 are P2. We need to check if P2 is divisible by 4. - For P = 2, the last two digits are 22, which is not divisible by 4. - For P = 5, the last two digits are 52, which is divisible by 4. - For P = 8, the last two digits are 82, which is not divisible by 4. 2. **Divisibility by 3**: The sum of the digits of the number must be divisible by 3. The sum of the digits of 4864 is 4 + 8 + 6 + 4 = 22. Adding the digits of 9P2, we get 9 + P + 2 = 11 + P. - For P = 2, the sum is 11 + 2 = 13, which is not divisible by 3. - For P = 5, the sum is 11 + 5 = 16, which is not divisible by 3. - For P = 8, the sum is 11 + 8 = 19, which is not divisible by 3. Since none of the values for P (2, 5, 8) satisfy both conditions, the correct answer is (D) None of these.

Option Analysis:

Option A: P = 2 does not satisfy both conditions for divisibility by 12.
Option B: P = 5 does not satisfy both conditions for divisibility by 12.
Option C: P = 8 does not satisfy both conditions for divisibility by 12.
Option D: None of the given values for P satisfy both conditions for divisibility by 12.

Mnemonic: Divisible by 3 and 4, check both, not just one.

3. Which word means able to be divided?

Correct Answer: Correct answer is: (D) Divisible.

Exam Relevance: SAT, GRE, GMAT, ACT

Difficulty: Easy

Concept notes: The term "divisible" means able to be divided without leaving a remainder.

Common Mistakes: A common mistake is confusing "divisible" with other words that sound similar, such as "digestible" or "admissible."

Explanations: The word "divisible" directly relates to the concept of divisibility rules, which are used to determine if a number can be divided by another number without leaving a remainder. The other options do not relate to the concept of divisibility.

Option Analysis:

Option A: Digestible refers to something that can be easily digested, not divided.
Option B: Admissible means something that is allowed or permitted, not related to division.
Option C: Irresistible means something that cannot be resisted, not related to division.
Option D: Divisible means able to be divided without leaving a remainder, which is the correct term in the context of divisibility rules.

Mnemonic: Divisible = Divided without a remainder.

4. Which of the following number is divisible by both 5 & 10

Correct Answer: Correct answer is: (D) 4000.

Exam Relevance: SAT, GRE, GMAT, ACT

Difficulty: Easy

Concept notes: A number is divisible by 5 if it ends in 0 or 5. A number is divisible by 10 if it ends in 0.

Common Mistakes: A common mistake is to assume that a number ending in 5 is divisible by 10, which is incorrect.

Explanations: To be divisible by both 5 and 10, a number must end in 0. Among the given options, only 4000 ends in 0, making it divisible by both 5 and 10.

Option Analysis:

Option A: 1455 ends in 5, so it is divisible by 5 but not by 10.
Option B: 555 ends in 5, so it is divisible by 5 but not by 10.
Option C: 5005 ends in 5, so it is divisible by 5 but not by 10.
Option D: 4000 ends in 0, so it is divisible by both 5 and 10.

Mnemonic: Zero for both, ten and five.

5. Seven is a factor of .....

Correct Answer: Correct answer is: (B) 21, 28, and 42.

Exam Relevance: SAT, ACT, GRE, GMAT

Difficulty: Easy

Concept notes: A number is divisible by 7 if it can be divided by 7 without leaving a remainder.

Common Mistakes: A common mistake is to assume that a number is divisible by 7 based on its last digit, which is incorrect. The divisibility rule for 7 requires checking the entire number.

Explanations: To determine if 7 is a factor of the given numbers, we need to check if each number can be divided by 7 without leaving a remainder. - 21 ÷ 7 = 3 (no remainder) - 28 ÷ 7 = 4 (no remainder) - 42 ÷ 7 = 6 (no remainder) Since all three numbers can be divided by 7 without leaving a remainder, 7 is a factor of 21, 28, and 42.

Option Analysis:

Option A: 14 is divisible by 7, but 27 and 72 are not.
Option B: 21, 28, and 42 are all divisible by 7.
Option C: 1 and 7 are not divisible by 7 (except for 7 itself), and 14 is divisible by 7.
Option D: 37, 47, and 57 are not divisible by 7.

Frequently Asked Questions

What are divisibility rules?

Divisibility rules are shortcuts to determine if a number can be divided by another number without leaving a remainder.

How can I use divisibility rules in everyday life?

Divisibility rules can help in quickly checking if a number is divisible by another, useful for tasks like splitting bills or calculating discounts.

What is the divisibility rule for 3?

A number is divisible by 3 if the sum of its digits is divisible by 3.

Can divisibility rules help with mental math?

Yes, divisibility rules can simplify mental calculations by allowing you to quickly determine if a number can be evenly divided by another.

What is the divisibility rule for 5 and 10?

A number is divisible by 5 if it ends in 0 or 5, and by 10 if it ends in 0.

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