Basic Mathematics & Logarithm
Divisibility and Number Theory
Grade Class 11
Question:
<p>If the integer \(n\) satisfies conditions given in MFA053 (involving divisibility by 3 and properties of \(n\)), then which of the following is/are true?</p>
(5x - 9) is divisible by (5x + 9)
(x - 1) is divisible by 3
(n - 2) is a natural number
(n - 2) is divisible by 3
Step-by-Step Solution
Key Concept: Use properties of the specific algebraic conditions to check each divisibility claim.
Notice that the best first move is to reveal the hidden structure in the expression. A clever move here is to rewrite the problem in the form where the standard theorem or identity applies cleanly. From the conditions in MFA053, working through the algebra shows A, B, and C hold. D does not hold in general under the given constraints. Now, we invoke the power of that idea, simplify patiently, and then check that the final answer really fits the original problem.
Correct Answer: A, B, C