swerve wrote:This morning, a certain sugar container was full. Since then some of the sugar from this container was used to make cookies. If no other sugar was removed from or added to the container, by what percent did the amount of sugar in the container decrease?

1) The amount of sugar in the container after making the cookies would need to be increased by 30 percent to fill the container.
2) Six cups of sugar from the container were used to make the cookies.

The determine the percent decrease, we need to know the RATIO between the remaining amount of sugar after cookie-making and the original amount of sugar.

Statement 1:
Case 1: Remaining sugar after cookie-making = 10 pounds
Since the remaimning amount of sugar would need to increase by 30% to fill the container, the original amount of sugar = 10 + (30% of 10) = 10 + 3 = 13 pounds.
Resulting ratio:
(remaining sugar)/(original sugar) = 10/13.

Case 2: Remaining sugar after cookie-making = 20 pounds
Since the remaining amount of sugar would need to increase by 30% to fill the container, the original amount of sugar = 20 + (30% of 20) = 20 + 6 = 26 pounds.
Resulting ratio:
(remaining sugar)/(original sugar) = 20/26 = 10/13.

Since the resulting ratio in each case is the same, SUFFICIENT.

Statement 2:
Case 1: Original amount of sugar = 10 pounds, remaining amount after cookie-making = 10-6 = 4 pounds
Resulting ratio:
(remaining sugar)/(original sugar) = 4/10 = 2/5.

Case 2: Original amount of sugar = 20 pounds, remaining amount after cookie-making = 20-6 = 14 pounds
Resulting ratio:
(remaining sugar)/(original sugar) = 14/20 = 7/10.

Since the two cases yield different ratios, INSUFFICIENT.

The correct answer is A.

Let amount of sugar in container = x

Statement 1
The amount of sugar in the container after making the cookies would need to be increased by 30% to fill the container.
Let amount of sugar removed from the container = r
Sugar needs to be increased by 30% to fill the container
Therefore,
$$\left(x-r\right)30\%\ +\left(x-r\right)=x$$
$$\frac{\left(x-r\right)30}{100}+\left(x-r\right)=x$$ $$\left(x-r\right)0.3+\left(x-r\right)=x$$ $$0.3x-0.3r+x-r=x$$ $$1.3x-1.3r=x$$ $$1.3x-x=1.3r$$ $$\frac{0.3x}{1.3}=r$$ $$r=0.23x$$
hence 0.23*100=23% of x ;23% of the total amount of sugar in the container has been removed, hence statement 1 is INSUFFICIENT.

Statement 2
Six cups of sugar from the container were used to make cookies.
There is no relationship between the number of cups used to make cookies and the percentage of of sugar decrease, moreover we are not given the specific quantity of cups in the amount of sugar in the container, hence Statement 2 is INSUFFICIENT.
$$answer\ is\ OptionA$$