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

[BTGmoderatorDC]

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.

OA C

Source: Official Guide

[Jay@ManhattanReview]

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.

OA C

Source: Official Guide

Let's take each statement one by one.

(1) The first term of S is −8.

Certainly insufficient as we do not know by what pattern the subsequent terms follow.

(2) Each term of S after the first term is 10 more than the preceding term.

Certainly insufficient. Though we know the pattern the subsequent terms follow, we do not know the first term.

(1) and (2) together

We know both the first term and the pattern. Sufficient. There is no need to calculated the value since we are sure that we will get a unique value.

For your better understanding, let's find out the 105th term.

The sequence would be: -8, 2, 12, 22, 32, 42, ... goes until 120th term. It is clear that we will get a unique value of the 105th term.

Let's relook the above laid-out terms.

The terms -8, 2, 12, 22, 32, 42, ... can be written as -8, 2 [= -8 + (2 - 1)*10], 12 [= -8 + (3 - 1)*10], 22 [= -8 + (4 - 1)*10], 32, 42, ...

Thus, the 105th term = [= -8 + (105 - 1)*10] = -8 + 1040 = 1032.

We can have a formula for an arithmetic sequence:

Tn = a + (n - 1)d; where Tn is the value of the nth term, a = the first term, and d = common difference between the terms

The correct answer: C

Hope this helps!

-Jay
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[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.

OA 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

Cheers,
Brent