If a < 5 and b > 2, which of the following must be true?

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Question: If a < 5 and b > 2, which of the following must be true?

Options:

Correct Answer: a / b < 3

Solution:

Since a < 5 and b > 2, a / b can be less than 3 if a is close to 5 and b is just above 2. The other options do not hold true in all cases.

If a < 5 and b > 2, which of the following must be true?

If a < 5 and b > 2, which of the following must be true?

Step 1: Understand the inequalities given: a < 5 means a can be any number less than 5, and b > 2 means b can be any number greater than 2.
Step 2: Think about the possible values for a and b. For example, if a is 4.9 (close to 5) and b is 2.1 (just above 2), we can calculate a / b.
Step 3: Calculate a / b using the example values: 4.9 / 2.1 = approximately 2.33, which is less than 3.
Step 4: Consider other possible values for a and b. If a is 1 and b is 3, then a / b = 1 / 3 = approximately 0.33, which is also less than 3.
Step 5: Check if a / b can be greater than or equal to 3. If a is 4.9 and b is 3, then a / b = 4.9 / 3 = approximately 1.63, which is still less than 3.
Step 6: Conclude that a / b can be less than 3 in the cases we checked, but it cannot be guaranteed to be greater than or equal to 3 in all cases.

Inequalities – Understanding and manipulating inequalities to determine relationships between variables.
Fraction Comparison – Analyzing the behavior of fractions given constraints on the numerator and denominator.