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.
Quantity A
Number of other test results in the same
percentile as Dominick’s

Quantity B
Maximum number of other test-takers with the
same result as Dominick

answer is C

To determine the value of Quantity A and Quantity B, we need to first find the number of test results in Dominick's percentile.

Step 1: Calculate the total number of test results in the data set.

The data set includes integers ranging from 15 to 75, inclusive. The range of numbers is given by:

Range = (maximum value) - (minimum value) + 1 = 75 - 15 + 1 = 61

Therefore, there are 61 possible test results in the data set.

Step 2: Calculate the position of Dominick's result within the data set.

Since Dominick's result is in the 80th percentile, it means that 80% of the data set falls below his score. To determine Dominick's score position, we can calculate:

Position = (80/100) * (total number of test results) = (80/100) * 61 ≈ 48.8

Since Position is not an integer, we can round it up to the nearest whole number to find the position of Dominick's score in the data set. Therefore, Dominick's result is the 49th highest score in the data set.

Step 3: Calculate the number of other test results in the same percentile as Dominick's.

Since Dominick's result is the 49th highest score, there are 48 test results higher than his score in the data set. To find the number of other test results in the same percentile, we subtract these 48 results from the total number of test results:

Number of other test results in the same percentile = (total number of test results) - (number of results higher than Dominick's) = 61 - 48 = 13

Therefore, Quantity A is 13.

Step 4: Calculate the maximum number of other test-takers with the same result as Dominick.

Since Dominick's result is unique within the data set, there cannot be any other test-takers with the same result. Therefore, the maximum number of other test-takers with the same result as Dominick is 0.

Therefore, Quantity B is 0.

In conclusion:

Quantity A = 13
Quantity B = 0

To determine the number of other test results in the same percentile as Dominick's, we need to first calculate the position of Dominick's result within the range of test results.

Step 1: Find the range of values:
The range of values is given as integers ranging from 15 to 75. So, the range is 75 - 15 + 1 = 61.

Step 2: Calculate the position of Dominick's result:
Since Dominick's result is in the 80th percentile, it means that 80% of the test results are below Dominick's result. Therefore, we need to find the value of the test result at the 80th percentile.

80% of 300 test results is (80/100) * 300 = 240 test results.

Since Dominick's result is clearly in the 80th percentile, we can conclude that the value at the 80th percentile is greater than Dominick's result. Therefore, the number of other test results in the same percentile as Dominick's is 240 - 1 = 239.

So, Quantity A is 239.

To determine the maximum number of other test-takers with the same result as Dominick, we need to find the number of test results equal to Dominick's result.

Step 1: Calculate the number of test results equal to Dominick's result:
Since Dominick's result is clearly in the 80th percentile, the number of test results equal to Dominick's result cannot be greater than the number of test results in the 80th percentile, which is 239. Therefore, the maximum number of other test-takers with the same result as Dominick is 239.

So, Quantity B is 239.

Therefore, Quantity A and Quantity B are equal.