BrainLab wrote:
If sequence S has 120 terms, what is the 105th term of S?
(1) The first term of S is −8.
(2) Each term of S after the first term is 10 more than the preceding term.
Source: [
OG 2016]
Target question: What is the 105th term of S? Given: Sequence S has 120 terms Statement 1: The first term of S is −8. We have no information about the nature of the sequence.
So, knowing the value of term 1 won't help is determine the value of term 105
Since we cannot answer the
target question with certainty, statement 1 is NOT SUFFICIENT
Statement 2: Each term of S after the first term is 10 more than the preceding term.This statement provides information about the nature of the sequence, but we don't know the first term.
For example, the 105th term of the sequence {10, 20, 30, 40, ....} will be different from the 105th term of the sequence {3310, 3320, 3330, 3340, ....}
Since we cannot answer the
target question with certainty, statement 2 is NOT SUFFICIENT
Statements 1 and 2 combined Statement 1 tells us that term 1 = -8
Statement 2 tells us that every term (after term 1) is 10 more than the preceding term
So, the sequence is as follows: -8, 2, 12, 22, 32, 42, 52, 62, .....
At this point we COULD determine
the value of the 105th term of the sequence . For example, we could keep listing every term until we get to the 105th term. However, we don't need to do that, since our sole objective is to determine whether we have sufficient information to answer the target question (which we DO)
Since we can answer the
target question with certainty, the combined statements are SUFFICIENT
Answer:
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