Number Conditions Analysis

The problem asks us to find a single number that meets two specific range conditions:

• Condition 1: The number must be greater than 3 but less than 8. The integers satisfying this are 4, 5, 6, and 7.
• Condition 2: The number must also be greater than 6 but less than 10. The integers satisfying this are 7, 8, and 9.

Finding the Common Number

To find the correct number, we need to identify which number appears in both sets of possibilities.

• Numbers from Condition 1: {4, 5, 6, 7}
• Numbers from Condition 2: {7, 8, 9}

Comparing these two sets, the only number that satisfies both conditions is 7.

Let's check the options:

• Option 1 (8): Satisfies Condition 2 but not Condition 1 (8 is not less than 8).
• Option 2 (6): Satisfies Condition 1 but not Condition 2 (6 is not greater than 6).
• Option 3 (5): Satisfies Condition 1 but not Condition 2 (5 is not greater than 6).
• Option 4 (7): Satisfies Condition 1 (7 > 3 and 7 < 8) and Condition 2 (7 > 6 and 7 < 10).

Therefore, the number that meets both criteria is 7.