This morning, a certain sugar container was full. Since then some of

Forget conventional ways of solving math questions. In DS, Variable approach is the easiest and quickest way to find the answer without actually solving the problem. Remember equal number of variables and independent equations ensures a solution.

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

We only have one variable as we only need to know the percentage of sugar if we let the total be 100%. There are 2 equations given from the 2 conditions, so there is high chance (D) will be our answer.
From condition 1, if we let the amount of sugar left be X, 1.3X=100%, so this is sufficient.
For condition 2, there is no relationship between percentage and number, so this is insufficient and the answer is (A).

from con 1) and con 2), if one of the conditions is given by numbers and the other is given by ratio (percent,fraction), then the condition with ratio (percent,fraction) value has higher chance of being the answer

here everything talking in percentage..it is better to take any comfortable value i take 100gms of sugar is initially in container.
(1)let x gms is removed so adding 30% to 100-x gms will again be 100
(100-x)(1+30/100)=100
it will yield into some value of x gms.
so we can give a YES to our ans to the ques .asked.
(2) no info about quantity of cups..
insuff...
Ans A

Can someone solve this completely!

Hi All,

Given:

+Morning = Full = x

+Change = Amount of sugar used = Unknown

+After = y (y < x)

Asked: [(x-y)/x]*100 =?

(1) The amount of sugar in the container after making the cookies would need to be increased by 30 percent to fill the container

=> Change = 30% of x = 0.3x => y = x - 0.3x = 0.7x

=> [(x-y)/x]*100 = [(x - 0.7x)/x]*100 => Sufficient

(2) Six cups of sugar from the container were used to make the cookies

What is total amount of six cups of sugar? We do not know => Insufficient

Answer = A.

Not sure my reasoning is correct. Please help.

Many thanks.

Please let me know if my confusion/logic makes sense. I'd assumed that Statement 1 would be insufficient because since X could be anything, the percentage decrease itself could be anything. So since the percentage decrease for a cup with 100mg and a cup with 130mg are different, I thought it would be insufficient because you'd then get two different numbers.

Statement 1: The % decrease from A (one value) to B (other value) will always yield a unique % increase from B to A. This is because you can express A and B in terms of the same variable. Sufficient

Statement 2: This one could have been helpful if we knew the absolute volume of the container in terms of total number of cups. Not Sufficient.

Hi

When we say 'a decrease of 20% in X', it means a decrease of 20% only, and nothing else.
Now if X=100, then a decrease of 20% would mean = 20% of 100 = 20
If X=120, then a decrease of 20% would mean = 20% of 120 = 24

So while the amounts of decrease (20 and 24) in the above two cases are different, the percentage decrease is same = 20%

Now in our given question, statement 1, after decreasing the sugar by a certain amount, remaining sugar needs to be increased by 30% to get back to the original value. So lets say remaining sugar is now = y. It needs to be increased by 30% of y = 0.3 y to get back to the its original value. This means original value of sugar was = y + 0.3y = 1.3y

So original value = 1.3y and final value = y, so the percentage decrease that took place was = (1.3y - y)/1.3y * 100 = 3/13 * 100 = 23% approximately
As you can see, the variable y is eliminated and the answer is independent of the value of y. Here it doesnt matter what the original value of y was.. whether y was 120 or 250 or 34.. the percentage decrease in sugar which took place was 23% only, this is fixed

This is a fantastic explanation, thank you so much! So the key is that we are asked for a percentage decrease, which would be the same regardless of what y would be.

As this is DS question we need not solve for values but still..

Statement 1 : Amount of sugar to be added to get the original quantity = 30%

Let X be the original amount of sugar and Y be the amount after removal.
-> X = Y + 0.3Y
-> X = 1.3 Y

Percent by which the amount of sugar decreased = \(\frac{Sugar Removed}{Sugar Present Initially}*100\) = \(\frac{0.3Y}{1.3Y}*100\) = 23.07 % approx

Sufficient

Statement 2 : We do know 6 cups of sugar was removed , but we do not know the size of the cup or the relation between the cup and the original amount of sugar present

Not Sufficient

Option : A

Percent change is a crucial subject to know for the GMAT, and this question offers a lot of good learning opportunities.

Here's an explanation on YouTube

https://www.youtube.com/watch?v=R1jLoBu ... E49y4ykEnU

The answer is (A)

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