请教一道 pre上面的数学题

Maimai.

The positive integer k has exactly two positive prime factors, 3 and 7. If k has a total of 6 positive factors, including 1 and k, what is the value of k ?

(1)  3^{2} is a factor of K.
(2) 7^{2} is not a factor of K.

Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.

Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.

BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.

EACH statement ALONE is sufficient.

Statements (1) and (2) TOGETHER are NOT sufficient.

答案是d EACH statement ALONE is sufficient.

Puddingjiang

已知k有2个prime factors，3和7。然后又有6个positive factors，包括了1，3，7个k（已经占了4个了），那另外2个因子要么是3*3和3*7，要么是7*3和7*7，其他都会超出题目的范围。

所以k就2种可能性：1）3*3*7；2）3*7*7

EACH statement ALONE 都排除了另一种可能，所以可以确定唯一的value k。