Critical Reasoning

I ran into this question and was really stumped by the structure and type, I really don't think it is relevant to the GMAT. But if it is, how does one go about it.

Beginning in 1997, high school seniors in State Q have been required to pass a comprehensive proficiency exam before they are allowed to graduate. The exam requirement was intended to ensure that a minimum level of academic quality will be achieved by the students in the state. In 1997, 20 percent of the seniors did not pass the exam and were, therefore, not allowed to graduate. In 1998, the number of seniors who passed the exam decreased by 10% from the previous year.
The argument above, if true, LEAST supports which of the following statement.
A. If the percentage of high school seniors who passed the exam increased from 1997 to 1998 , the number of high schools seniors decreased during that time period.
B. If the percentage of high school seniors who passed the exam decreased from 1997 to 1998 , the number of high schools seniors increased during that time period.
C. Unless the number of high school seniors was lower in 1998 than in 1997, the number of seniors who passed the exam in 1998 was lower than 80 percent.
D. If the number of high school seniors who did not pass the exam decreased by more than 10 percent from 1997 to 1998, the percentage of high school seniors who passed the exam in 1998 was greater than 80 percent.
E. If the percentage of high school seniors who passed the exam in 1998 was less than 70 percent, the number of high school seniors in 1997 was higher than the number in 1998.

An inference is not a matter of opinion. There are only a limited number of conclusions that can be drawn from specific provided evidence. With normal Inference questions, we're used to finding the MOST LIKELY inference. Here we're looking for the LEAST supported Inference.

Question Rephrase: What's the WORST choice?

The WORST choice will likely be something contradicted by the presented facts.

Our next step is to break down the facts:

- 1997 - State Q seniors pass Exam to graduate
- Exam ---> "min academic quality"
- 1997 - 80% passed, 20% did NOT pass
- 1998 - The NUMBER who passed DECREASED 10%

Since this question involved both percents AND numbers, it's worth noting that incorrect answer choices on the GMAT often confuse these two things.

So WITHOUT even looking at the answer choices, we know it's incorrect to assume that 70% passed in 1998. We only know the NUMBER who passed decreased. Let's play with some real-world numbers to make sure we really get this.

For example if 100 students passed in 1997 (and that was 80%, the total would be 125). Then the 1998 number would be 90. But we have NO IDEA what the total number of students who took the 1998 exam is.

I'd expect the CORRECT answer here to try and draw some unfounded inference about 1997 and 1998. Since it's "LEAST," we're looking for the choice that cannot be true in ANY circumstance.

(E) is correct. It says that if 1998 % passed is less than 70%, then total 1997 > total 1998. But we can easily show this to be true.

If 100 passed in 1997, the total is 125.
90 passed in 1998, but the 1998 total could easily be more than 125.

Hi Vivian,

Thanks for your reply. I was just wondering if you have encountered more such questions?
I am generally ok with CR, but this one I just coudnlt wrap my head around.

A

Percents/Numbers questions are kind of rare, but they DO occur. Usually they're designed to be difficult and confusing, so you're not alone! I think your time is best spent focusing on difficult Assumption/Strengthen/Weaken problems, but there's some official percents/number questions you can practice.

Check out this sample question from the GMAT Prep 3 exam. It's a classic example of how we must read carefully to determine what percentage or numbers are being discussed:

Fact: Asthma, a bronchial condition, is much less common ailment than hay fever, an allergic inflammation of the nasal passages.

Fact: Over 95 percent of people who have asthma also suffer from hay fever.

These two facts are almost like a math word problem. We can organize the information using a Venn diagram, just like we would in a Math problem. Let's imagine there are 96% of people with asthma who also have hay fever, and 100 people have asthma. Then 96 would also have hay fever and 4 would only have hay fever. Since the first fact tells us that asthma is less common, then we can expect the total number of people with hay fever to be more than 100. Let's say 102 people have hay fever.

Now we're in a good position to analyze the question-stem and answer choices:

If the information given as facts above is true, which of the following must also be true?

A. Hay fever is a prerequisite for the development of asthma

B. Asthma is a prerequisite for the development of hay fever

C. Those who have neither hay fever nor asthma comprise less than 5 percent of the total population

D. The number of people who have both of these ailments is greater than the number of people who have only one of them

E. The percentage of people suffering from hay fever who also have asthma is lower than 95 percent.

The only safe inference we can make here about these percentages is choice (E). With the sample numbers we picked, there would be 96/102 = 94.1% of people with hay fever who also suffer from asthma. The percentage will always be lower than 95 percent.

VivianKerr wrote:Percents/Numbers questions are kind of rare, but they DO occur. Usually they're designed to be difficult and confusing, so you're not alone! I think your time is best spent focusing on difficult Assumption/Strengthen/Weaken problems, but there's some official percents/number questions you can practice.

Check out this sample question from the GMAT Prep 3 exam. It's a classic example of how we must read carefully to determine what percentage or numbers are being discussed:

Fact: Asthma, a bronchial condition, is much less common ailment than hay fever, an allergic inflammation of the nasal passages.

Fact: Over 95 percent of people who have asthma also suffer from hay fever.

These two facts are almost like a math word problem. We can organize the information using a Venn diagram, just like we would in a Math problem. Let's imagine there are 96% of people with asthma who also have hay fever, and 100 people have asthma. Then 96 would also have hay fever and 4 would only have hay fever. Since the first fact tells us that asthma is less common, then we can expect the total number of people with hay fever to be more than 100. Let's say 102 people have hay fever.

Now we're in a good position to analyze the question-stem and answer choices:

If the information given as facts above is true, which of the following must also be true?

A. Hay fever is a prerequisite for the development of asthma

B. Asthma is a prerequisite for the development of hay fever

C. Those who have neither hay fever nor asthma comprise less than 5 percent of the total population

D. The number of people who have both of these ailments is greater than the number of people who have only one of them

E. The percentage of people suffering from hay fever who also have asthma is lower than 95 percent.

The only safe inference we can make here about these percentages is choice (E). With the sample numbers we picked, there would be 96/102 = 94.1% of people with hay fever who also suffer from asthma. The percentage will always be lower than 95 percent.

Hi Vivian,

I had a doubt. Option E says "the percentage........ Lower than 95 percent".. It's 95 percent of what? Should the not be specifying that? Thanks

Vivek

Hi Vivian

Option E says " The percentage of people suffering from hay fever who also have asthma is lower than 95 percent." The last part lower than 95%. Should the not be mentioning 95 % of what? I mean 95% of total population, or people have hay fever or asthama?

Thanks

Vivek

For the original question posted by akhilsuhag, there is a GREAT explanation on an earlier post of this question. Kudos to Ilyana for an great explanation. https://www.beatthegmat.com/not-convince ... 71905.html

It turns out that neither B nor E is well supported and E is even completed contradicted.

That said, the source of the question posted by akhilsuhag is Princeton Review and I think this question is quite beyond what you would see on test day!

I would not worry too much about that one.

The question posted by Vivian is an official question (retired) and is much better!

Here is the text of that question.

Fact: Asthma, a bronchial condition, is much less common ailment than hay fever, an allergic inflammation of the nasal passages.

Fact: Over 95 percent of people who have asthma also suffer from hay fever.

If the information given as facts above is true, which of the following must also be true?

A. Hay fever is a prerequisite for the development of asthma

B. Asthma is a prerequisite for the development of hay fever

C. Those who have neither hay fever nor asthma comprise less than 5 percent of the total population

D. The number of people who have both of these ailments is greater than the number of people who have only one of them

E. The percentage of people suffering from hay fever who also have asthma is lower than 95 percent.

Notice how much simpler the reasoning is on this official question? It is much easier to actual understand than the convoluted question that began this thread. If you have not attempted the question I have just quoted from Vivian then please attempt it now.

To answer your question vivekvijayan:

Option E says " The percentage of people suffering from hay fever who also have asthma is lower than 95 percent." The last part lower than 95%. Should the not be mentioning 95 % of what? I mean 95% of total population, or people have hay fever or asthama?

The phrase "percentage of people suffering from hay fever" tells you how to set up this fraction. Whenever you have the word "of" "to" or "per" you should draw a fraction line and whatever comes after one of those words goes below the fraction line. The other portion goes above the line.

So kilometers PER hour = k / h

Men TO women = m / w

And "of the total 37 questions on the Quant section he got 28 correct" = 28 / 35


In this case it is like my final example. "Percentage of people suffering from hay fever" mean that you write .../ hay fever. and the the next part fills in the numerator "who also have asthma" tells us that we are looking at " those who have asthma and hay fever / total hay fever is less than 95%".

And of course this is true since hay fever is much more common and 95% of asthma sufferers have hay fever.

Use some quick numbers. Say 100 asthma sufferers in the world. 95% also have hay fever. So 95 people with both hay fever and asthma. Then we see that there are many more than 100 hay fever sufferers since hay fever is "much more common." So that means more than 100 hay fever sufferers.

No set up your fraction. We know that hay fever and asthma together = 95 people. We know hay fever is > 100.

So the fraction has to be 95/ 101+. And 95 / 101 is less than 95%!

Hope that helps!!

David