Distilling the problem down to set notation, you can see that Set B = {n1,n2,n3,n4,n5,n6}

Set A contains everything in Set B, but with an additional number. In essence, Set A = {n1,n2,n3,n4,n5,n6,N}

The additional number, N, is the only thing that can be manipulated in this problem, so that is what you should naturally focus on. The problem then asks you to find out which of the statements given CANNOT be true. Turning this around from the viewpoint of the Testmaker, your job is then to try to discover a condition where each statement IS true.

**Quote:**

Answer choice “A” tells you that the range of set A is equal to the range of set B. Naturally, this could work if N were somewhere in the middle of the set, meaning that it wouldn’t affect the range. Answer choice “A” COULD BE true, and therefore isn’t the right answer.

**Quote:**

Answer choice “B” tells you that the mean of set A is greater than the mean of set B. Naturally, an unusually large value for N would increase the average of set A. Answer choice “B” COULD BE true, and therefore isn’t the right answer.

**Quote:**

Answer choice “C” tells you that the range of set A is less than the range of set B. If the additional number, N, were somewhere in the middle of the set, then it wouldn’t affect the range and set A and set B would have equal ranges. If the number, N, were bigger or smaller than the other numbers, it would increase the range for set A. It could never make the range smaller. Answer choice “C” can NEVER be true, and therefore must be the right answer.

**Quote:**

Answer choice “D” tells you that the mean of set A is equal to the mean of set B. This is a bit trickier to find an example for, but there is one case when this happens. Remember: adding the average of a set to a set doesn’t change the average. If the additional number, N, were equal to the average of set B, then both sets would still have the same average. Answer choice “D” COULD BE true, and therefore isn’t the right answer.

**Quote:**

Answer choice “E” tells you that the median of set A is equal to the median of set B. This, too, is a bit tricky, until you remember how to calculate median. Remember that the median of a set with an even number of elements (like set B) is equal to the average of the two middle numbers; in this case, the median is not contained in the set. If the additional number, N, were equal to the median of set B, it would also fall as the middle number of set A, and the medians would be the same. Answer choice “E” COULD BE true, and therefore isn’t the right answer.

_________________

Please award kudos, If this post helped you in someway.