Bunuel wrote:

If integer x is greater than 0 but less than 10 and \(k = x^9\), what is the value of integer k?

(1) x^2 has a units digit of 1.

(2) \(x^{(–2)} < \frac{1}{50}\)

Statement 1- Since \(0<x<10\), we have 9 integer options for X.

- From that 9 options, we have two integers with 1 unit digit : \(1^2\) and \(9^2\).

- Therefore, INSUFFICIENT.

Statement 2- \(\frac{1}{x^2} < \frac{1}{50}\).

- Since X is a positive number, we can cross multiply without change the sign.

- \(50 < x^2\), or \(X^2 > 50\). We have different possibilities here. X can be 8 and 9.

- Therefore, INSUFFICIENT.

Statement 1&2- We can conclude that X must be 9.

- SUFFICIENT.

C

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