Key points: We need to see whether the variables in the question are
consecutive, as in 1, 2, 3; do not be afraid to calculate an
average.
Statements: The first statement tells us that \(\frac{(x + z)}{2} = y\); the second is a basic equation relating x to z.
Breakdown: I typically like to start with what appears to be the easier of the two statements in order to help with timing. I would say statement (2) seems like an easier point of entry. If x = -z, then we can
use some easy numbers to test for sufficiency. How about -1 and 1 for x and z, respectively? That would give us -1 and 1, but does y have to equal 0 in that case? Of course not! It could be, but it could just as easily be anything else. With a quick substitution, then, we have ruled out (B) and (D). Onto statement (1).
If the average of x and z is y, then they could be consecutive, as in 1, 2, 3: \(\frac{(1 + 3)}{2} = 2\). Does that have to be the case, though? Since we have already dealt with statement (2), we could test values for x and z that are equidistant from y, which we can set to 0, and see what happens. For instance, let x = -4 and z = 4. Now, we have
\(\frac{(-4 + 4)}{2} = 0\) True.
Since we have tested two valid combinations of integers x and z that average to y, one in which the three are consecutive, and the other in which they are not, we know that statement (1) is NOT sufficient. Together, the two statements achieve nothing more than what we just tested above for the first statement. (We could test -1, 0, and 1 to see that the integers could be consecutive, but there is no need.) Choice (E) must be the answer.
Guessing: Because statement (2) takes little in the way of interpretation to figure out, it should be pretty simple to arrive at an (A), (C), or (E) split. Statement (1), for all its words, deals with nothing more than an average, and with three variables that represent
integers, intuitive numbers can crack the problem fairly quickly, as demonstrated above. With a 50/50 between (C) or (E), I would like to think that anyone who had spent a little time figuring out statement (1) would immediately see that putting (1) and (2) together will shed no new light on the problem. Choice (C) is just a trap, NOT to be used as a crutch because you do not want to do a little work. Remember, this is a test of
reasoning ability more than one that measures mathematical prowess.
As always, good luck with your studies.
- Andrew
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Please use
official questions from the Official Guide or Verbal Review to practice for the Verbal section.