Question

a private college advertised that last year their freshman students, on average, had a score of 1120 on the sat. assume 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 are true, mark the appropriate box. last year some of their freshman students had a score of 1120 or above on the sat. next year some of their freshman students will have a score of at least 1120 on the sat. last year at least one of their freshman students had a score of more than 1000 on the sat. last year at least one of their freshman students had a score of exactly 1120 on the sat. last year more than half of their freshman students had a score of at least 1120 on the sat. none of the above statements are true.

Explanation:

Step1: Analyze average concept

The average SAT - score of freshmen last year was 1120. This is the arithmetic - mean of all the scores.

Step2: Evaluate first statement

It is not necessary that some students had a score of 1120 or above. For example, if all students had a score of 1120, the average is 1120, but there are no scores above 1120. So, the first statement is not necessarily true.

Step3: Evaluate second statement

The information given is about last year's freshmen. There is no way to predict next year's scores based on last year's average. So, the second statement is not true.

Step4: Evaluate third statement

Suppose, for the sake of contradiction, that all students had a score of 1000 or less. Then the average score would be 1000 or less. Since the average score is 1120, at least one student must have had a score more than 1000. So, the third statement is true.

Step5: Evaluate fourth statement

It is not necessary that at least one student had a score of exactly 1120. For example, if half of the students had a score of 1100 and half had a score of 1140, the average is 1120, but no student has a score of 1120. So, the fourth statement is not necessarily true.

Step6: Evaluate fifth statement

It is not necessary that more than half of the students had a score of at least 1120. For example, if a small number of students had very high scores and the rest had relatively low scores, the average can be 1120 without more than half of the students having a score of at least 1120. So, the fifth statement is not necessarily true.

Answer:

Last year at least one of their freshman students had a score of more than 1000 on the SAT.