The outcome of a standardized test is an integer between 151 and 200, inclusive. The percentiles of 400 test

scores are calculated, and the scores are divided into corresponding percentile groups.
Quantity A

Minimum number of integers between 151 and 200,
inclusive, that include more than one percentile group

Quantity B
Minimum number of percentile
groups that correspond to a score of
200

To find the minimum number of integers between 151 and 200 that include more than one percentile group, we need to determine the number of integers that have duplicates among the percentile groups.

Since there are 400 test scores and the percentiles are divided into corresponding percentile groups, we can assume that each percentile group contains either 1 or 2 integers. If every integer is in a unique percentile group, then there would be a total of 400 percentile groups.

To determine the minimum number of integers that include more than one percentile group, we need to find the largest number of distinct percentile groups possible. If we assume that there are only 2 integers per percentile group, then there would be 200/2 = 100 percentile groups that correspond to a range of 2 integers each.

Since the percentile groups for the range of integers from 151 to 200 need to be maximized, the remaining 50 integers from 151 to 200 can be placed in pairs within the 100 groups. This means that there would be 50/2 = 25 pairs that include integers from more than one percentile group.

Therefore, the minimum number of integers between 151 and 200 that include more than one percentile group is Quantity A = 25.

To find the minimum number of percentile groups that correspond to a score of 200, we need to determine the maximum number of percentile groups that can have a score of 200.

Since there are 400 test scores, the score 200 can be placed in different percentile groups. Additionally, each percentile group can contain either 1 or 2 scores.

To maximize the number of percentile groups that correspond to a score of 200, we can assume that there is only 1 score of 200 per percentile group. Therefore, the minimum number of percentile groups that correspond to a score of 200 is equal to the total number of scores of 200, which is 1.

Therefore, the minimum number of percentile groups that correspond to a score of 200 is Quantity B = 1.

In conclusion, Quantity A = 25 and Quantity B = 1.

To calculate the minimum number of integers between 151 and 200 that include more than one percentile group, we can start by examining each individual integer from 151 to 200.

To be included in more than one percentile group, an integer must fall at the border of two groups. The percentile groups are determined by dividing the range of 400 scores evenly. So, if we divide the range of scores (200-151+1 = 50) by the number of groups (400), we get the size of each group, which is approximately 0.125.

For an integer to fall on the border of two groups, it would need to be at a distance of 0.125 from the upper or lower bounds of each group. Therefore, we can calculate the number of integers at the border by multiplying the number of groups (400) by 2, since there are two borders for each group. In this case, the minimum number of integers at the border is 800.

However, we should note that the range of scores (151-200) does not include a solid integer for each possible percentile group. This means that some of the percentile groups may not have a corresponding score in this range. So, in order to find the minimum number of integers between 151 and 200 that include more than one percentile group, we need to subtract the number of incomplete groups.

Since the scores range from 151 to 200, there are only 50 possible integers. We can subtract this number from 400 (the total number of groups) to find the number of incomplete groups, which is 400 - 50 = 350.

Now, we can subtract the number of incomplete groups from the number of integers at the border to find the minimum number of integers between 151 and 200 that include more than one percentile group:

800 - 350 = 450

Therefore, the minimum number of integers between 151 and 200 that include more than one percentile group is 450. This corresponds to Quantity A.

Now, let's move on to Quantity B: the minimum number of percentile groups that correspond to a score of 200.

Since the scores are divided into 400 percentile groups, we can assume that each integer between 151 and 200 corresponds to a unique percentile group. Therefore, the minimum number of percentile groups that correspond to a score of 200 is 1.

Therefore, Quantity B is equal to 1.

Comparing the two quantities, we have:

Quantity A = 450
Quantity B = 1

Quantity A is greater than Quantity B.

this is easy. quantity A=1 quantity B=0. So A is greater