**Question**

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.

Option A

Option B

Option C

Option D

Option E

(Because of copyrights, the complete question cannot be copied here. The question can be accessed at GMAT Club)

**Solution**

**Introduction**: This question has a 21% accuracy on GMAT Club. So, humans do almost as well as monkeys on this question. If you are one of those who enjoy CR questions around numbers and percentages, you are going to enjoy the challenge in this question. If you are one of those who prefer not to see CR questions around numbers and percentages, this question is going to be a NIGHTMARE for you. I’ve written a detailed solution for this question with as much simplicity as I have in my thought process. Still, I believe that it’s going to be a challenge for many people to understand the nuances in this question.

### The Story

Beginning in 1997, high school seniors in State Q have been required to pass a comprehensive proficiency exam before they are allowed to graduate.

From 1997, there has been a requirement for high school seniors to graduate: they need to pass the mentioned exam.

The exam requirement was intended to ensure that a minimum level of academic quality will be achieved by the students in the state.

This statement mentions the intention behind the requirement. The intention was to ensure a minimum level of academic quality in the students.

In 1997, 20 percent of the seniors did not pass the exam and were, therefore, not allowed to graduate.

1997, 20% of the high school seniors did not pass the exam. That means 80% passed. Were these 80% students allowed to graduate? No idea. We just know that they met this requirement. Probably, some of these students didn’t meet some other requirement.

In 1998, the number of seniors who passed the exam decreased by 10% from the previous year.

This statement compares the number of seniors who passed the exam for two years: 1997 and 1998. If the number of seniors who passed the exam was ‘x’ in 1997, it was 0.9x in 1998.

### The Goal

We are looking for an option that is LEAST supported by the information in the passage. This is not a typical question stem. Therefore, before we jump onto the options, let’s be clear how we are going to evaluate the options.

- Any inference from the given information is going to be INCORRECT. Why? An inference is a statement that is sufficiently supported by the information in the passage.
- A statement that cannot be inferred but could be true can be the correct answer if the remaining four options are inferences.
- A statement that contradicts the given information, if it is present in the options, will definitely be the answer to this question.

*Even though the question stem mentions ‘the argument above’, there is no argument given in the stimulus. The stimulus contains a bunch of facts. This question is not an official question, so there can be some lapse in quality.

### The Evaluation

(A) **Incorrect**. The statement talks about a scenario in which the % of seniors who passed the exam increased from 1997 to 1998. In other words, the % of seniors who passed the exam in 1998 was greater than 80%.

Without getting into any numbers or variables, just think about the situation we have. The **pass percentage** of seniors has **increased** from 1997 to 1998. However, as given in the passage, the **number** of seniors who passed the exam has** gone down** from 1997 to 1998. How can this be possible?

This is possible only if the total number of seniors went down from 1997 to 1998. If the total number of seniors had stayed the same, then, given that the % of seniors who passed has increased, the number of seniors who passed the exam must also have increased. Right?

Thus, given the scenario, we can infer that the number of seniors must have gone down from 1997 to 1998. This is what this option says. Thus, this option can be INFERRED from the passage given.

(B) **Incorrect**. The statement talks about a scenario in which the % of seniors who passed the exam decreased from 1997 to 1998. In other words, the % of seniors who passed the exam in 1998 was less than 80%.

In this scenario, both the **pass percentage** of seniors and the **number** of seniors who passed the exam have gone down. In this scenario, what can we say about the total number of seniors?

The short answer: in this scenario, all three cases are possible:

**The total number of seniors stayed the same**. – It is entirely possible that the number of seniors stayed the same. The number of seniors who passed the exam declined by 10% from 1997 to 1998 since the pass percentage declined from 80% to y%. Can you guess what y will be?The correct answer is 72%. (Select the text after “is” to show the answer)

**The total number of seniors increased**. – It is possible that the total number of seniors increased. The number of seniors who passed the exam declined by 10% from 1997 to 1998 since the pass percentage declined substantially from 80%. If the number of seniors increased by 44% from 1997 to 1998, what was the pass percentage of seniors in 1998?The correct answer is 50%. (Select the text after “is” to show the answer)

**The total number of seniors decreased**. – It is also possible that the total number of seniors decreased. The number of seniors who passed the exam declined by 10% from 1997 to 1998 because of a combination of a smaller total number of seniors and a lower pass percentage. Given that the pass percentage of seniors has gone down, is it possible that the number of seniors decreased by 10% or more?The correct answer is No. (Select the text after “is” to show the answer)

But the total number of seniors can go down by less than 10%.

As we can see, in the scenario presented in this option, all three cases are possible for the total number of seniors. Thus, we CANNOT INFER that the number of high school seniors increased from 1997 to 1998, but it is POSSIBLE that the number of high school seniors increased. If I’m doing this question in the exam, I’ll keep this option on hold. However, after going through all the options, I’ll reject this option since there’s an option that contradicts the information in the passage.

(C) **Incorrect**. Let’s first understand what this statement means. This statement is of the form: Unless X happened, Y happened. This means that if X did not happen, Y happened.

Thus, the statement means that if the number of high school seniors was **NOT** lower in 1998 than in 1997, the number of seniors who passed the exam in 1998 was lower than 80 percent.

The scenario considered in this option is that the number of seniors did not decline from 1997 to 1998 i.e. the number of seniors either increased or remained the same.

Now, we know from the passage that the number of seniors who passed the exam declined from 1997 to 1998. Now think about it. How can it happen that the total number of seniors did not decline but the number of seniors who passed the exam declined?

The only way this could happen was when the pass percentage of seniors delined. Think about it. If the pass percentage of seniors did not decline and the total number of seniors also did not decline, there is NO WAY that the number of seniors who passed the exam could have declined. Right?

Thus, we can infer in this scenario that the pass percentage of seniors declined. Thus, we can infer that the pass percentage of seniors in 1998 was lower than 80%. Thus, this option is also an INFERENCE.

(D) **Incorrect**. This statement talks about a scenario in which the number of seniors who did not pass the exam decreased by more than 10% from 1997 to 1998.

We are already given in the passage that the number of seniors who passed the exam decreased by 10% from 1997 to 1998.

So, we have two types of seniors: seniors who passed the exam (SP) and seniors who did not pass the exam (SNP). We know that SP declined by 10% and that SNP declined by more than 10%.

Think about it. If both SP and SNP had declined by the exact same 10%, then the total number of seniors must also have declined by 10%. Right?

Now, since one component declined by more than 10%, the total number of seniors must also have decreased by more than 10%.

So, we have a scenario in which the total number of seniors went down by more than 10% but the number of seniors who passed the exam went down by only 10%. How is this possible?

The only way this is possible is that the pass percentage went up or increased from 1997 to 1998. Thus, we can infer that the percentage of seniors who passed the exam in 1998 was greater than 80%. This option is, thus, an INFERENCE.

(E) **Correct**. This option talks about a scenario in which the % of seniors who passed the exam in 1998 was <70%. We know that the same % in 1997 was 80%.

Think about it. Given these pass percentages, if the total number of seniors had stayed the same both the years, can we expect a 10% decline in the number of seniors who passed the exam from 1997 to 1998?

The answer is No. If the total number of seniors stayed the same, then for us to have just 10% decline in the number of seniors who passed the exam, the pass percentage in 1998 has to be 72% (we discussed this in option B as well).

Now, since we know that the pass percentage was not 72% but less than 70%, the number of seniors who passed the exam must have declined more than 10% if the total number of seniors stayed the same.

Right?

For the number of seniors to decline just 10% and not more, the total number of seniors has to go up from 1997 to 1998. Right?

Thus, in this scenario, we can infer that the number of seniors was higher in 1998 than in 1997. This is exactly opposite to what this option says.

Therefore, the given option is CONTRADICTING the given information and is thus the right option.

*If you have any doubts regarding any part of this solution, please feel free to ask in the comments section.*

*This solution was created by Chiranjeev Singh and Anish Passi.*

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