Quote:
If the sequence S has 300 terms, what is the 293rd term of S?
(1) The 298th term of S is -616, and each term of S after the first is 2 less than the preceding term.
(2) The first term of S is -22.
We are given that sequence S has 300 terms, and we need to determine the 293rd term of S.
Statement One Alone:The 298th term of S is -616, and each term of S after the first is 2 less than the preceding term.
Statement one defines the pattern of the sequence. We are given that each term of S after the first is 2 less than the preceding term. Thus, we know that we can determine the value of the 293rd term.
If we were forced to determine the 293rd term we could determine that value. We know that the 293rd term is 5 terms before the 298th term. Thus, the 298th term is 5(2) = 10 less than the 293rd term, or in other words, the 293rd term is 10 more than -616, the 298th term. So the 293rd term is -606.
Remember, because we are answering a data sufficiency question, we can stop as soon as we know we are able to determine the value of the 293rd term, and so we don't need to perform the math to calculate its actual value.
Statement one is sufficient. We can eliminate answer choices B, C, and E.
Statement Two Alone:The first term of S is -22.
Since we do not have any information about the pattern defining the sequence, statement two is not sufficient to answer the question.
The answer is A.
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