Question

a private college advertised that last year their freshman students, on average, had a score of 1160 on the sat. 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 are true, mark the appropriate box. last year, the number of their freshman students who had a score of 1160 or below on the sat was equal to the number of their freshman students who had a score of 1160 or above on the sat. last year at least one of their freshman students had a score of more than 950 on the sat. next year some of their freshman students will have a score of at least 1160 on the sat. last year all of their freshman students had a score of 1160 or above on the sat. last year at least one of their freshman students had a score of exactly 1160 on the sat. none of the above statements are true.

Explanation:

Step1: Analyze first statement

The mean (average) doesn't imply equal - number of values above and below it. For example, in a set {1000, 1160, 1160}, the mean is 1106.67, but the number of values above and below the mean is not equal. So the first statement is false.

Step2: Analyze second statement

If the average SAT score of fresh - man students is 1160, it is impossible for all students to have a score of 950 or less. Because if all scores were 950 or less, the average would be 950 or less. So at least one student must have a score more than 950. This statement is true.

Step3: Analyze third statement

The average score of last year's fresh - man students gives no information about the scores of next year's fresh - man students. So this statement is false.

Step4: Analyze fourth statement

If the average is 1160, it is possible to have some students with scores below 1160 and some above 1160. For example, in a set {1000, 1320}, the average is 1160. So this statement is false.

Step5: Analyze fifth statement

The average being 1160 doesn't mean that there is a student with exactly 1160 score. For example, in a set {1000, 1320}, the average is 1160 but no value is 1160. So this statement is false.

Answer:

Last year at least one of their freshman students had a score of more than 950 on the SAT.