All round candles = 60%
All square candles = 100-60= 40%
Target question: what is the probability that a candle selected randomly from the box will be unscented?
Statement 1: If a candle is scented, it has an 80% chance of being round.
The probability of having a round scented candle = 80%
The probability of having a square scented candle = 100-80% = 20%
But the total number of scented and unscented candles is unknown, hence, statement 1 is NOT SUFFICIENT.
Statement 2: If a candle is square, it has a 25% chance of being scented.
A square candle has a 25% probability of being scented and a 75% probability of being unscented from a total of 40 square candles.
The total no of scented square candles = 25% * 40 = 10.
Total no. of unscented square candles = 40-10=30. Hence, the overall scented and unscented candle is still unknown. There is no information about round candles, so, statement 2 is NOT SUFFICIENT.
Combining both statements together
From statement 2, there are 10 square scented candles and 30 square unscented candles.
From statement 1, the probability of having a round scented candle = 80%, and the probability of having a square scented candle = 20%
Therefore, 20% of total scented candles = 10 square scented candles
$$Total\ scented\ candles=\frac{10}{20}=50\%$$
Therefore, total unscented candles = 100-50= 50%, and the probability of having unscented candle=50%. Hence, both statements combined together are SUFFICIENT. The correct answer is option C
