futuremba96
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.
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