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

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Note that nowhere in the original question is it mentioned that the sequence S is some kind of a particular sequence (Arithmetic, Geometric etc). 105th term= \(S_{105}\)

Per statement 1, a=first term =-8. Still do not know what kind of a sequence is this.

Per statement 2, Given that the sequence is an arithmetic progression (difference between 2 consecutive terms is constant) \(a_n\)=nth term in the sequence = \(a+(n-1)*d\) where n=105 and d =10. Thus, 105th term = a+(105-1)*10 = a+1040. Still no information on 'a' or the first term. Not sufficient.

Combining the 2 statements, a=-8 and thus, \(S_{105}\) = \(a+(n-1)*d\) = -108+1040=932. C is thus the correct answer.
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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:

Here is a visual that should help.

Hi All,

This question is another great example of a 'concept' question - if you understand the concept(s) involved, then you can get to the correct answer without doing much (if any) math.

We're told that a sequence has 120 terms. We're asked for the 105th term in the sequence.

1) The first term of S is -8.

While this Fact tells us the 1st term in the sequence, it does NOT tell us how the sequence progresses. The sequence might increase, decrease or 'oscillate', so there's no way to determine the 105th term.
Fact 1 is INSUFFICIENT.

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

Fact 2 tells us how the sequence progresses (each term is 10 greater than the term that precedes it), BUT we don't know any of the individual terms, so there's no way to determine the exact value of any of them.
Fact 2 is INSUFFICIENT.

Combined, we know:
-The first term is -8
-Each term is 10 greater than the one that precedes it.

Thus, we could figure out the 105th term (either algebraically or y just "adding 10s" until we get to that term). Either way, we CAN determine the value of the 105th term.
Combined, SUFFICIENT.

Final Answer:

GMAT assassins aren't born, they're made,
Rich

hello pushpitkc, can you please point out my mistake

\(S_{105}\) = \(-8+(105-1)*10\) ----> -8+1050-40 = 1032

even if I do so \(-8+(n-1)*10\) I get 10n-18 ---> plug in 105 I get the same result 1032

Hello

There is no mistake, the 105th term will be 1032 only.

-8 became -108 in your calculation. Please correct the post.

= -8+1040= 1032. C is thus the correct answer

Hey dave13,
The problem lies in here;

When you open the brackets it will be = -8 + 1050 - 10 = 1032. According to the calculation in RED, it should have been 1002.

Well, in both the cases you mentioned, the solution is correct and it will be 1032 anyway.

Answer: Option C

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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
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The 105th term is 1032 and not 932. Check your calculations brother.

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