#12 - The number of North American children who are

[Eric Ockert]

John

Your example of Rum and Coke is a great one! Let's use your numbers.

So if I were to write your numbers in a stimulus that is worded similarly to this problem it would read:
"The number of ounces of rum in John's Bar and Grill's famous Rum and Coke - a drink made up of 50% rum and 50% coke- has increased over the past year."

Notice the definition of a Rum and Coke hasn't changed. It's still 50/50. This is similar to the definition of obesity in the question you cited. It's 15% of the population no matter what.

So if the number of ounces of rum in the Rum and Coke is going up, but the recipe is unchanged,this means the drink is getting larger (i.e. more ounces). And if the drink is larger, but is still 50% Coke, then you MUST put more Coke in the drink as well.

The same with the obesity question. If 15% of the total population is a higher number now than it was before, that means the total number of children is going up. And if the number of children is higher, 85% of that higher number (the non-obese children) has to translate to a higher total number of non obese children as well.

[biskam]

I'm struggling to understand why the total # of children has to go up if the total number of kids in the top 15% goes up.


Couldn't it be that the number of kids in NA are staying the same, but just more kids fit into the top 15%??? Meaning then that the number of obese kids could be decreasing?

[biskam]

I'm struggling to understand why the total # of children has to go up if the total number of kids in the top 15% goes up.


Couldn't it be that the number of kids in NA are staying the same, but just more kids fit into the top 15%??? Meaning then that the number of obese kids could be decreasing?

I'm trying to work out a hypothetical to make "If 15% of the total population is a higher number now than it was before, that means the total number of children is going up" true...

15 years ago, the number of kids in the top 15% was 15 kids and the number of kids in the bottom 85% was 85 kids, giving us a total population of 100 kids.

15 years later, the number of kids in the top 15% increased to 50 kids...
so if more kids fit into the top 15% then... This is where I'm struggling.

If 15% of x is 50, not 15, that x or that total must be larger.

Here that x or the total number of kids must be 333 kids. that means the # of kids in the bottom 85% must have increased too.

I think I worked it out as a hypothetical. But can someone explain to me without math why the total must increase too? Thank you!

[AthenaDalton]

Hi Biskam,

You're on the right track.

In this stimulus, "obese" Is defined as "being in the top 15 percent" in terms of bodyfat. Here's how a hypothetical would look:

15 years ago: 100 children, top 15 percent obese = 15 obese children
Today: 1000 children, top 15 percent obese = 150 obese children

Since the definition of "obese" is always limited to the top 15 percent of children, the only way for there to be more children who fit into that top 15 percent category is if there are more children overall.

I think part of the reason this question is tough to process is that in normal discourse we think of "obese" as meaning having a high percentage of bodyfat, not just having more fat than the rest of the population. It may help to think of this in a different context:

To be admitted to the Order of the Coif, a student must graduate in the top 10 percent of his class in law school. In the year 2000, let's assume that 20,000 students graduated from law school. Only the top 10 percent were admitted to the Order of the Coif, so a total of 2,000 lucky students made Order of the Coif that year. Now let's say that it's the year 2015 and we learn that this year 3,000 students were admitted to the Order of the Coif.

What can we conclude from this? Assuming that the criteria for making the Order of the Coif hasn't changed, the only way for more students to have earned this achievement is if there were more law school graduates overall -- in this example, 30,000 nationwide.

I hope that helps clarify things for you. Good luck studying!

Athena Dalton

[biskam]

Really helpful!! Thanks!

[Legallyconfused]

Hi!

Does this make sense?

• obese: more body fat than the majority (85%) of the total kids
• obese is 15% of the population
• average or anything under obese is 85% of the population

2004: 100 kids total: 85 kids are average and 15 have more body fat (obese) than those 85 average kids.
2019: 200 kids total: 170 kids are average and 30 have more body fat (obese) than those 170 average kids.

The stimulus said the number of kids who are obese is increasing...so if that number is increasing it results in both the total and the number of average kids increasing as well. In order for that increasing number of obese kids still to be 15% of the whole (total kids)?

So if the amount of obese children rises from 15 to 30, they still need to be 15% of a whole, which also makes the average amount of kids rise to meet the 85% of the whole.

It took me way too long to write all oft his math out when I am reviewing the test. How would someone be able to do this quickly during the actual testing time?!? It just didn't click...

I had a problem deciding not to change the percentages. I was thinking during the test that if more kids were becoming obese then it would go form 15% of the population to maybe 20% of the population. At the time I didn't consider the total population growing...Is it because it said the NUMBER increased instead of the PERCENTAGE increased?
Thanks!!!

[Jeremy Press]

Hi Legallyconfused,

Yes, that's the right understanding of the issue in the stimulus. I fully agree with you that in an ideal testing scenario, you wouldn't be sketching out a complete hypothetical like that. You just don't have time! So what can you do? Try to find a general principle being exhibited by the stimulus that can then be applied simply, in order to prephrase an appropriate answer. The principle is this: if the number of people within a certain percentile changes (i.e. if the size of a slice of a pie changes) without the percentile changing (i.e. without the proportion of the pie the slice occupies changing), the number of people in the remainder percentile has to change as well (i.e. the size of the rest of the pie has to change as well). Here, that principle would tell you to prephrase essentially what answer choice C says. It's not an easy principle to internalize, so spend some time thinking about some different scenarios, so that on a future question you can see the principle in action more easily!

I hope this helps,

Jeremy

[haganskl]

Hello.

I was able to use process of elimination to get to the correct answer (C). However, I dont have a solid understanding of how the numbers work together so based on my understanding of the above explanations, I created a rule.

If a percentage of a total number is used to set the standard for a non existent VS an existent determination then any increase or decrease in the non existent number will result in a corresponding increase or decrease in the existent number and vice versa.

Does this rule accurately depict the foundation of how these numbers work together for this type of situation?

TIA!

[Adam Tyson]

I'm not sure what you mean here by an existent number, haganskl, but I'll give you a rule that might help and may be simpler:

If a number increases, but its percentage of the total stays the same, then the total must have also increased.

This rule would also require that the number of things that are NOT in that percentage also increased. So in this question, if the number of kids in the 15% went up, but it's still 15% of the total, then the total went up, and that also means that the number of kids in the other 85% also went up.

[haganskl]

OMG So much simpler.
Thank you!