A cake recipe calls for sugar and flour in the ratio of 2 cups to 1 cu

(1) the cake requires 33 cups of ingredients sufic

S:F=2x:1x; Total = 3x=33cups; x=11cups; S=11*2=22cups

(2) the ratio of the number of cups of flour to the total number of cups used in the recipe is 1:3 insufic

F:T=1/3; F/S+F=1/3; S/F=2/1, S=2F; F/(2F+F)=F/3F=1/3

Ans (A)

A cake recipe calls for sugar and flour in the ratio of 2 cups to 1 cup, respectively. If sugar and flour are the only ingredients in the recipe, how many cups of sugar are used when making a cake?
S:F= 2:1--> S=2F

(Statement1): the cake requires 33 cups of ingredients
S+F =33
--> 3F=33 --> F=11--> S=22 cups

Sufficient

(Statement2): the ratio of the number of cups of flour to the total number of cups used in the recipe is 1:3

\(\frac{F}{(F+S)}= \frac{1}{3}\)
--> \(\frac{F}{(F+2F)}= \frac{F}{3F}= \frac{1}{3}\)
F and S can be anything in this rate.
Insufficient

The answer is A.

given
S/F= 2/1
s= 2f
#1
the cake requires 33 cups of ingredients
s+f=33
3f=33
f=11
and s=22
sufficient
#2
the ratio of the number of cups of flour to the total number of cups used in the recipe is 1:3
f/s+f = 1/3
s=2f
but total cups not know
insufficient
IMO A
A cake recipe calls for sugar and flour in the ratio of 2 cups to 1 cup, respectively. If sugar and flour are the only ingredients in the recipe, how many cups of sugar are used when making a cake?

(1) the cake requires 33 cups of ingredients
(2) the ratio of the number of cups of flour to the total number of cups used in the recipe is 1:3

Given that the ratio of Sugar to Flour = 2:1, we are to determine the number of cups of sugar used in making the cake.

Statement 1: The cake requires 33 cups of ingredients.
Sufficient. Since we can determine the number of cups of sugar used for the cake as 2*33/3 = 22 cups.

Statement 2: the ratio of the number of cups of flour to the total number of cups used in the recipe is 1:3
The information in statement 2 is already provided. Ratio of cups of Sugar to cups of Flour being 2:1 is the same as saying the ratio of cups of Flour to the total cups of ingredients is 1:3. We need information on the total number of cups of ingredients used for preparing the cake. Since statement does not give us any clues to determine this information, statement 2 is insufficient.

The answer is A

OFFICIAL EXPLANATION

Based upon the question, we can set up a few equations:
Equation (1): Sugar/Flour = 2/1

Since one cake could be made from 2 cups of sugar and 1 cup of flour (or different number of cups in the same ratio):
Equation (2): Sugar/(Total Ingredients) = 2/(2+1) = 2/3
Equation (3): Flour/(Total Ingredients) = 1/(2+1) = 1/3

Evaluate Statement (1) alone.
Since the cake requires 33 cups of ingredients, using Equation (2), we know that Total Ingredients = 33:
Sugar/(Total Ingredients) = 2/3
Sugar/33 = 2/3
Therefore: Sugar = 22 cups.

Statement (1) is SUFFICIENT.

Evaluate Statement (2) alone.
Statement (2) does not provide any new information. Based upon the original question, we derived Equation (3). Statement (2) is merely a restatement of Equation (3).

Consider two examples:
If there were 10 cups of flour, the total amount of ingredients would be 30 cups and there would be 20 cups of sugar.
But, if there were 5 cups of flour, the total amount of ingredients would be 15 cups and there would be 10 cups of sugar.

Statement (2) is NOT SUFFICIENT since we cannot determine how many cups of sugar were used in the cake.

Since Statement (1) alone is SUFFICIENT but Statement (2) alone is NOT SUFFICIENT, answer A is correct.