4) Are the integers x, y and z consecutive?

I. The arithmetic mean (average) of x, y and z is y.

II. y-x = z-y

A. statement 1 alone is sufficient, but statement 2 alone is not sufficient to answer the question

B. statement 2 alone is sufficient, but statement 1 alone is not sufficient to answer the question

C. both statements taken together are sufficient to answer the question, but neither statement alone is sufficient

D. each statement alone is sufficient

E. statements 1 and 2 together are not sufficient, and additional data is needed to answer the question

Show Answer

**Correct Answer : **Answer: E.

The mean of three numbers will equal the middle number for any set of evenly spaced numbers (1,2,3 or 2,4,6, or -1, -4, -7 for example) and so we cannot assume that x, y and z are consecutive. Hence the answer cannot be A or D. If x, y and z were 2, 4, and 6, for example, the equation in (2) would be valid, so once again the numbers do not have to be consecutive, and the answer cannot be B. From the numbers we have just substituted, we should be able to see that putting (1) and (2) together will still not give a situation in which the numbers are always consecutive or always not consecutive, and so the best answer is E.