2024 · Q64
A question is given followed by two statements I and II. Consider the Question and the Statements and mark the correct option. Question : Is 327n + 173n divisible by 500?
Statement In is odd natural number
Statement IIn is a positive integer Which one of the following is correct in respect of the above Question and the Statements?
Elementary MathematicsNumber System
- AThe Question can be answered by using one of the Statements alone, but cannot be answered using the other Statement alone
- BThe Question can be answered by using either Statement alone
- CThe Question can be answered by using both the Statements together, but cannot be answered using either Statement alone
- DThe Question can be answered even without using any of the Statements
Explanation
327+173 = 500, and a^n+b^n is divisible by a+b for odd n. Statement I (n odd) alone settles it as divisible; statement II (n a positive integer) alone does not (e.g. n = 2 gives remainder 358). One statement alone suffices — option A.