A private college advertised that last year their freshman students, on average, had a score of 1140 on the college entrance exam. Assuming that average refers to the mean, which of the following claims must be true based on this information? Note: More than one statement could be true. If none of the statements is true, mark the appropriate box. A. Last year, the number of their freshman students who had a score of 1140 or above on the exam was equal to the number of their freshman students who had a score of 1140 or below on the exam. Last year at least one of their freshman students had a score of less than 1280 on the exam. B. Last year some of their freshman students had a score of 1140 or above on the exam. C. Next year at least one of their freshman students will have a score of at least 1140 on the exam. D. Last year some of their freshman students had a score of exactly 1140 on the exam. E. None of the above statements is true.

(B)

(A) has two statements, the second of which is correct

Step-by-step explanation:

The mean of a set of numbers can be described thus: the differences between the mean and each number all add up to 0. These differences are called deviations.

Take these sample set of numbers: 2, 2, 2, 14. The mean is (2+2+2+14) / 4 = 5.

Note that there is no 5 in the list. Note also that three of the numbers are lesser than 5 while only one is higher.

Note this, however: the difference between the mean and 14 is 9; the difference between 5 and the three 2s is 3+3+3 = 9. So all the numbers above the mean have the sum of their deviations equal to those of the lower numbers.

If all the numbers in a list are not the same, then some will be lesser than the mean, some will be higher while some might be equal to the mean.

Hence, (B) is correct.

(C) is not correct because it is predicting using last year's average. They are different situations because they won't be the same students.

(D) is not necessarily true as the mean doesn't have to be in the list of numbers as illustrated previously.

The first statement in (A) follows also from the previous illustration: the mean does not divide the list into two equal parts. The second statement, however, is true because a score less than 1280 could be less than 1140 (say 1000) or more than 1140 (say 1200). Both ranges are certainly plausible in the set.

(E) is certainly not true because (B) is true.