Akshit03 wrote:

GMATNinja wrote:

The author concludes that one of two things has happened over the past ten years: either 1) Renston’s schoolchildren have been exposed to greater quantities of the chemicals, or 2) they are more sensitive to the chemicals than schoolchildren were ten years ago. How does the author arrive at this conclusion?

- We are given that exposure to cleaners and pesticides commonly used in schools can cause allergic reactions in some children.
- Over the past ten years, the proportion of schoolchildren sent to school nurses for allergic reactions to THOSE chemicals has increased significantly.

The author states two possible explanations for this increase, but are those the only options? The author's explanation will only hold up if one of the following is assumed:

**Quote:**

(A) The number of school nurses employed by Renston's elementary schools has not decreased over the past ten years.

A change to the number of nurses doesn't impact the number of students sent to see the nurses, so (A) can be eliminated.

**Quote:**

(B) Children who are allergic to the chemicals are no more likely than other children to have allergies to other substances.

We are not concerned with allergies to other substances. Regardless of whether children allergic to the chemicals are more likely to have allergies to other substances, we still need to explain why more students are now sent to the nurses because of reactions to THOSE chemicals. The two theories in the conclusion are only meant to explain the increase in the number of schoolchildren sent to the nurses because of THOSE chemicals, so choice (B) is irrelevant.

**Quote:**

(C) Children who have allergic reactions to the chemicals are not more likely to be sent to a school nurse now than they were ten years ago.

According to the argument, the increase in the proportion of schoolchildren sent to the elementary school nurses is due to either greater exposure to the chemicals or a greater sensitivity to the chemicals. But what if children who have allergic reactions to the chemicals are more likely to be sent to a school nurse now than they were ten years ago? Maybe the amount and severity of the allergic reactions was the same ten years ago but students were simply less likely to be sent to the nurse back then. Maybe ten years ago the teachers simply let the suffering students remain in class with watery eyes and running noses (for example).

That could explain the increase in the proportion of schoolchildren sent to the elementary school nurses, even if students' exposure and sensitivity to the chemicals has not changed. In order for the argument to hold, the author must assume that children who have allergic reactions to the chemicals are NOT more likely to be sent to a school nurse now than they were ten years ago. Choice (C) looks good.

**Quote:**

(D) The chemicals are not commonly used as cleaners or pesticides in houses and apartment buildings in Renston.

Perhaps the cleaners ARE commonly used in houses and apartments, but we don't care about WHERE the students were exposed to the chemicals. If exposure has increased, whether at school or at home, then the author's argument would be valid. The author does not say that exposure has increased AT THE SCHOOLS, so choice (D) can be eliminated.

**Quote:**

(E) Children attending elementary school do not make up a larger proportion of Renston's population now than they did ten years ago.

We are trying to explain an increase in the PROPORTION of students sent to the nurses, not an increase in the TOTAL NUMBER of students sent to the nurses. Thus, an increase in the number of students or the proportion of the population attending elementary schools does not matter. We need to explain the increase in the PROPORTION sent to the nurses for those allergic reactions. Choice (E) is not a required assumption and can be eliminated.

Choice (C) is the best answer.

Hi, great answer.

However, I didn't understand E.

Can you expand a bit more on PROPORTION VS TOTAL?

I think TOTAL has an effect on PROPORTION.

Can you explain with a little example(mathematically or in any way) where I'm wrong?

Always remember: what are we being asked, and what information is

relevant to answering that question? On CR, we could clarify math until a great proportion of cows come home, and still be no closer to picking the right answer choice.

But to avoid any confusion, let's clarify some math! Or at least some terminology.

Generally speaking, "proportion" is a portion, or percentage, of the total. It's typically expressed as a percentage or fraction.

Let's say that I have 10 tomatoes in my garden. I'm asked, "Charles! Did your daughter eat a greater proportion of the tomatoes than you did today?" I look back at our tomato diary, which shows:

- I ate 1 tomato, which is 10% of the tomatoes (1/10).
- My daughter ate 5 tomatoes, which is 50% of the tomatoes (5/10). She loves those things even more than I do. (And for a 20-pound beast, she sure can eat.)

But holy nightshade! I miscounted, and it turns out that my garden actually had 20 tomatoes before we started eating.

- This means that I actually ate 5% of the tomatoes (1/20).
- And my daughter actually ate 25% of the tomatoes (5/20).
- Nobody ate any more tomatoes. But since the total number of tomatoes changed, our measurement of the proportion of tomatoes eaten changed as well.

So yes, the absolute number of tomatoes affects the number used to describe the proportion of tomatoes eaten.

But did this help me answer the question? Nope.I was basically asked, "Who ate a bigger share of however many tomatoes you had?"

And changing the total number of tomatoes will never change the answer: "My daughter ate a bigger proportion of tomatoes. And I'm terrible at counting things in my garden."

Now let's look at choice (E):

**Quote:**

(E) Children attending elementary school do not make up a larger proportion of Renston's population now than they did ten years ago.

This choice basically compares a % measured ten years ago to a % measured today.

The actual numbers are never mentioned. If 5% of Renston's population attended elementary school ten years ago, and 5% of Renston's population attends elementary school today, then any of the following could be true:

- 5 out of 100 people in Renston attended elementary school ten years ago.
- 270 out of 5,400 people in Renston attended elementary school ten years ago.
- 20 out of 400 people in Renston attended elementary school today.
- 250 out of 5,000 people in Renston attended elementary school today.

The assumption presented by (E) doesn't tell us anything about the total number of students in either time period. The total numbers could have grown or shrunk to literally any size with zero impact on what (E) is stating.

More importantly,

the type of proportion that (E) describes is totally irrelevant to the argument we're analyzing.The author is trying to explain the proportion of

elementary school students sent to nurses for treatment of allergic reactions:

- This proportion is a % of elementary school students.
- In a fraction, it would be expressed as [# of elementary students sent to the nurse for treatment of specific allergic reactions] / [total # of elementary students].

Choice (E) describes the proportion of

elementary students in Renston:

- This proportion is a % of people in Renston.
- In a fraction, it would be expressed as [total # of elementary students] / [total number of people in Renston].

I hope this clarifies what I meant when explaining why (E) is not a required assumption! I didn't mean to say that totals have no place in measuring proportion. But in the case of this question, knowing the totals never matters, and in the case of choice (E), the proportions and totals being discussed are simply irrelevant to the author's argument.

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