Hi @aaronhma! Basically, Dr. Loh figured out an approximate answer for "how many breaths someone takes in a minute": it's around 15 to 20 breaths.
But the question asks how many breaths 327.2 million people take in 1 year. So to go from the number of breaths taken by 1 person in 1 day to the number of breaths taken by lots of people in lots of days, you would multiply by some number.
For example, if X is "number of breaths taken by 1 person in 1 day," then 20X is "number of breaths taken by 20 people in 1 day." And then, (20X) * 30 = 600X is "number of breaths taken by 20 people in 30 days." So essentially, to solve the problem, we multiply "number of breaths taken by 1 person in 1 day" by a really big number. Call that really big number K.
So we have established that the final answer is KX. But remember, X is some number from 15 to 20, because those were the bounds we established! This means that the minimum answer is 15K and the maximum answer is 20K. Now, 20K = (4/3) * 15K... in other words, 20K is about 33% bigger than 15K.
Therefore, if we have two answer choices A and B, with A>B, and A is more than 33% bigger than B, they both can't be right! ("Proof": if B would work, we can assume that it's the absolute minimum possible. But then, the absolute maximum possible would be 33% more than B, which is less than A, so A can't be right too!) That's why Prof. Loh says we can probably guess which one is right.
Essentially, the big picture is that all the answer choices are "spaced out" enough so that ambiguity is avoided.
I hope this was helpful, and let me know if I could clarify something!
So, both buckets are being filled up at the same rate. But, since the 4-pound bucket holds less, it's going to dump more often than the 7-pound bucket. How much more often? Well, since the 4-pound bucket is \(\frac47\) of the size of the 7-pound, it's going to have to dump \(\frac74\) as often in order to take the same amount of corn.
Thus, since it dumps \(\frac74\) more often, \(\frac74\cdot112\) is the answer.
Let me know if this makes sense!
Thinking about how to solve questions in unique ways takes practice. One of the goals of this course is to equip you with the experience necessary to view problems in new ways. Focus on the lesson of each video. For example, this video shows us that there is more than one way to think about fractions. In the future, we'd be able to apply this knowledge to different problems. Always take a step back and consider if there is a different way to think of a problem than the first way you think of it. Keep practicing, and you'll be able to find the most efficient solution to a problem in no time!