Is This Sufficient Data?

Number Theory Level 3

Are statements I and II sufficient to determine the answer to the following question?

"Suppose $x$ is an integer larger than 10. What is the last digit of $x^4?$ "

Statement I: $x$ is prime.

Statement II: $x$ is even.

Statement I is sufficient alone, but II alone is not sufficient alone. Statement II is sufficient alone, but I alone is not sufficient alone. Both statements together are sufficient, but neither alone is sufficient. Each statement alone is sufficient. Both statements together are not sufficient.

1 solution

Dripto Biswas
Nov 20, 2015

the second statement is obviously false. Just consider the numbers 12 and 100. They end in different digits. the first one is sufficient, since any prime greater that 10, ends in 1,3,7,9 (trivial). each of them raised to the 4th power has '1' as the last digit. hence proved.

Is This Sufficient Data?

1 solution

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