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Each statement alone is not sufficient (pretty obvious).
Both statements together are sufficient. x=10 and y=180 are the only numbers that fulfill both properties.
(1) states that 10 is a common factor (and that it is the largest common factor). Therefore x and y must be multiples of 10.
Because of (2) we need to consider the factors of 180, that are multiples of 10. These are 10, 30, 60, 90 and 180. The least common multiple of two of these numbers is always lower than 180, except for 10 and 180 (easy to check) .
Therefore only 10 and 180 fulfill both properties.