If sequence S has 120 terms, what is the 105th term of S?

[BTGModeratorVI]

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.

Answer: C
Source: official guide

[Brent@GMATPrepNow]

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.

Answer: C
Source: official guide

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: C

[Scott@TargetTestPrep]

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.

Answer: C
Source: official guide

Solution:

Question Stem Analysis:

We need to determine the 105th term of sequence S, which has 120 terms.

Statement One Alone:

Knowing only the first term does not allow us to determine the 105th term. Statement one alone is not sufficient.

Statement Two Alone:

Since we don’t know the value of any term in the sequence, knowing only that each term of S after the first term is 10 more than the preceding term will not allow us to determine the 105th term. Statement two alone is not sufficient.

Statements One and Two Together:

From the two statements, we see that sequence S is an arithmetic sequence. Furthermore, we see that the first term is -8 and the common difference is 10. With these two pieces of information, we can determine the value of any term of the sequence and in particular, the 105th term. Even though we don’t need to actually perform the calculation, we see that the 105th term is:
a_105 = -8 + (104)(10) = 1032.

Both statements together are sufficient.

Answer: C