I have big problem with this question, the word "clearly" might mean that for 80 percentile would have the same test result, then for Quant A "Number of other test results in the same percentile as Dominick’s" might be 0.

Or the "other test result" can mean other people get the same result as Dominick? VERY confusing.

I am not able to understand this question, Is there an easy way to understand?

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Regards

The question is asking you to compare the number of scores in a particular percentile rank (the 80th) with the maximum number of scores that match a given score.

You can think of percentiles as "bins" of 1% each, going from the lowest possible score (15) to the highest (75).

To figure out the value in choice A:

Although we don't know the actual distribution of scores, we can take the 300 total scores and imagine they are distributed evenly into the 100 *bins*, which would mean that the 80th percentile (bin) contains 3 students, or two in addition to Dominick.

To figure out the value in choice B:

We need to find the maximum number of other scores that match Dominick's. If the scores were evenly distributed (3 per percentile "bin"), we know that there will be two other scores equivalent to Dominick's in the 80th percentile. Even though we don't actually know the score distribution, we can't have any more than three equal scores, or we could no longer determine that they would remain in the 80th percentile.

The maximum is two other scores equal to Dominick's, and the categories are equal.

Answer: C

May you please clarify this question because I didn't understand the upper explanations ?

Now in the GRE scores ( someone could score 170 which = to 97 percentile) which means that he is better than the 97 percent of the people who took the test.
Coming to this question,
I know that 1 percentile represents 1 % of the data, so each percentile = 3 students. How does this exist that each percentile represents equal amount of data ?

Why we can't say that 80 percentile could represent the best score and the rest 59 student are in the same percentile for example?

GIVEN: 300 test results are integers ranging from 15 to 75, inclusive. Dominick’s result is clearly in the 80th percentile of those results, not the 79th or the 81st.
I'm not a huge fan of this question.
The idea is that the word "clearly" is supposed to tell us that the other scores in the 80th percentile are all equal.

If the 300 scores consisted of...
240 scores of 15
Dominick's score of 25
and 59 scores of 75,
...I'd say that Dominick's score is an 80th percentile score (since 240/300 = 80%)
I can also be certain that his score isn't in the 79th or the 81st percentile.

It's unclear to me (unless I'm missing something) why the word CLEARLY excludes the above scenario.

I suggest you skip this question and move on.

The question is testing the concept of a percentile? 300 test results which can take values from 15-75 inclusive.
If we had 100 test results Dominick test result would have been at 81th position out of 100.
since 300 test results he is at 241 position(percentile gives the precise location of each result in a distribution arranged in ascending order) said so , Qty A and Qty B are asking the result at 241th position , there can be none , both are zero
Hence C.

how can you assume that the data is linear and is not of any other type of distribution?

Step 1: Understanding the 80th percentile in a set of 300
- The 80 th percentile means Dominick's result is higher than or equal to $\(80\) %$ of the other results.

The position of the 80th percentile in an ordered list of 300 results can be found as:

$$
\(P_{80}=0.80 \times 300=240\)
$$


This means the 240th value (in sorted order) corresponds to the 80th percentile position.
- Dominick's result is at the 240 th rank (or position).
- Because it's clearly 80th percentile, Dominick's rank corresponds exactly to the 240th position - not 239th (79th percentile) or 241st (81st percentile).

Step 2: Quantities involved
- Quantity A: Number of other test results in the same percentile as Dominick's.

Since it is exactly the 80th percentile, everybody who shares Dominick's percentile has test scores equal to his.

That is, all test-takers with the same score as Dominick are the group at the 80th percentile.
The "same percentile" includes Dominick and others having the same score.
So, Quantity A = (number of test-takers with same test result as Dominick) - 1 (excluding Dominick himself).

Step 3: Estimating Quantity B
Quantity B is the maximum number of other test-takers with the same result as Dominick.
We want to find the maximum possible number of test-takers with the same score at the 80th percentile.

Step 4: Reconciling the 80th percentile with potentially repeated scores
To ensure Dominick's result is exactly at position 240, all test-takers with scores less than Dominick's must total exactly 239.

Dominick's result is at rank 240 , so-
- Number of test results < Dominick's score $=239$.
- Number of test results $\geq$ Dominick's score $=300-239=61$.

Since Dominick's score is integer-valued and there may be multiple people sharing his score, the number of test-takers with his score (including Dominick) is equal to:
\text\{\# with Dominick's score\} = 300-239 = 61
- Therefore, 61 test-takers have Dominick's score, including Dominick.

So,
- Number of other test results with Dominick's percentile (= Quantity A) =61-1=60
- Maximum number of other test-takers with Dominick's score (= Quantity B) = 60

Step 5: Comparing Quantity A and Quantity B
- Quantity A = 60
- Quantity B $=60$

Final conclusion:
Both quantities are equal.