Question: The last digit in the expansion of the number (54D)^{100} is 1. What is the value of the digit D? Statement I : D > 5 Statement II: D is a multiple of 3.

A Question is given followed by two Statements I and II. Consider the Question and the Statements. Which one of the following is correct in respect of the above Question and the Statements?

  1. A. The Question can be answered by using one of the Statements alone, but cannot be answered using the other Statement alone
  2. B. The Question can be answered by using either Statement alone
  3. C. The Question can be answered by using both the Statements together, but cannot be answered using either Statement alone ✓
  4. D. The Question can be answered even without using any of the Statements

Correct Answer: C. The Question can be answered by using both the Statements together, but cannot be answered using either Statement alone

Explanation

For (54D)^{100} to end in 1, the digit D can be 1, 3, 7, or 9. Statement I (D > 5) limits it to 7 or 9. Statement II (D is a multiple of 3) limits it to 3 or 9. Combining both statements yields a unique value D = 9.

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