Let total number of flowers = x
carnations = x/2
lilies = x/3
roses = x/6
Question=> The total price of which the 3 types of flowers in the arrangement is the greatest?
Statement 1: The prices per flower for carnations, lilies, and roses are in the ratio 1:3:4 respectively.
$$Total\ price\ of\ carnation=1\cdot\frac{x}{2}=\frac{x}{2}$$
$$Total\ price\ of\ lilies=3\cdot\frac{x}{3}=x$$
$$Total\ price\ of\ roses=4\cdot\frac{x}{6}=\frac{2x}{3}$$
From the expression above, the price of lillies are the greatest, hence, statement 1 is SUFFICIENT.

Statement 2: The price of one rose is $0.75 more than the price of one carnation and the price of one rose is $0.25 more than the price of one lily.
Let the price of one carnation = y
Therefore, one rose = y + $0.75
one lily = y + $0.75 - $0.25 = y + $0.5
Total price of carnation = xy/2
$$Total\ price\ of\ rose=\frac{x\left(y+0.75\right)}{6}$$
$$Total\ price\ of\ lillies=\frac{x\left(y+0.5\right)}{3}$$
The value of x and y is unknwon, so , we cannot decipher the flower with the greatest price between rose and lillies.
Therefore, statement 2 is NOT SUFFICIENT.

Since statement 1 alone is SUFFICIENT, then this validates option A as the correct option.