Is x=1?

Good question. +1.

1234.567

1 - THOUSANDS
2 - HUNDREDS
3 - TENS
4 - UNITS
. - decimal point
5 - TENTHS
6 - HUNDREDTHS
7 - THOUSANDTHS

Is x=1?

(1) If x were rounded to the nearest thousandth, the result would be 1.

This implies that x is of the form 1.000b..., where b can be 0, 1, 2, 3, or 4. So, x can be:
1.0000...
1.0001...
1.0002...
1.0003...
1.0004...

Or x is of the form 0.999b..., where b can be 5, 6, 7, 8, or 9. So, x can be:
0.9995...
0.9996...
0.9997...
0.9998...
0.9999...

Not sufficient.


(2) If x were rounded to the nearest tenth, the result would be equal to the exact value of x.

This statement basically implies that all the digits after the tenth are zeros. Still insufficient. For example, x can be 1.1, or 2.7 or 0.1 or 1.


(1)+(2) Because of (2) we are left with only the first case from (1). So x is 1.000b and from (2) we know that the digits after the tenth in x are zeros, thus x=1. Sufficient.

Answer: C.