2025 · Q83
A Question is given followed by two Statements I and II.
Question: The last digit in the expansion of (54D)^100 is 1. What is D?
Statement ID>5.
Statement IID is a multiple of 3.
Which one of the following is correct?
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
The last digit of (54D)^100 is D^100 mod 10, which is 1 for D in {1,3,7,9} - four possibilities, so the question alone does not fix D. Statement I (D>5) leaves {7,9}; Statement II (D multiple of 3) leaves {3,9}; together they pin D=9. Hence both statements together (not either alone, not neither) are needed. The stored key D was wrong; corrected to C.