Step 1: Understanding the Concept
Tollens' reagent is reduced by aldehydes, and the iodoform test is given by compounds with a \(\text{CH}_{3}\text{CO}-\) group or \(\text{CH}_{3}\text{CH(OH)}-\) group.
Step 2: Use the formula
\(\text{C}_{3}\text{H}_{6}\text{O}\) fits propanal or propanone. The alcohols listed have the formula \(\text{C}_{3}\text{H}_{8}\text{O}\), so they are ruled out.
Step 3: Apply the tests
No reduction of Tollens' reagent rules out propanal. Propanone has a \(\text{CH}_{3}\text{CO}-\) group and gives a positive iodoform test.
Final Answer:
The compound A is acetone, CH3COCH3.
\[ \boxed{\text{(C) }\text{CH}_{3}\text{COCH}_{3}} \]