In a sequence of terms in which each term is three times the

In a sequence of terms in which each term is three times the previous term, what is the fourth term?

(1) The first term is 3 --> sequence is: 3, 9, 27, 81, ... so the fourth term is 81. Sufficient.

(2) The second-to-last term is 3^10 --> since we don't know how many terms are there in the sequence then we don't know which term is second-to-last. For example: if it's third term then fourth (and last) will be 3^11, if it's fifth term then the fourth term is 3^9, ... Not sufficient.

Answer: A.
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Responding to a pm.

If it were the case it would have been something like "the ratio of second to last term is ..."

Also on the GMAT, two data sufficiency statements always provide TRUE information and these statements never contradict each other. So if on the GMAT your interpretation of the statements leads you to conclude that the statements are impossible/incorrect or contradict each other then the case would be that your interpretation is wrong not the statements.
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You are truly awesome .. with DS.... i kinda assumed it to be 2nd term when said 2nd to last assuming that there r only 4 terms...thanks bunuel...

The first term is 3.

Our terms are as follows:

3, 9, 27, 81…

So, the fourth term is 81. Statement one alone is sufficient to answer the question.

Statement Two Alone:

The second-to-last term is 3^10.

Since we do not know the number of terms in the set, statement two alone is not sufficient to answer the question.

For example, if there are 4 terms in the set, the fourth term is 3^11. However, if there are 5 terms in the set, the fourth term is 3^10.

Answer: A
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I had to think about that for a bit before I could sincerely agree with you, Bunuel. Thanks!

regarding the second statement. Someone could interpret the second-to-last term as the ratio between the second and the last term.

Since we know that it is an exponential expression dividing the second with the last term should result a fraction smaller than 1. Therefore, someone could assume that the second statement is wrong.

is my reasoning valid?

thanks brunel for pointing out.. you are a jem

Hi Bunuel, since the question states that each term is 3 times another term, it means that for the nth term, the value will be 3^n. So I assumed that the 10th term is 3^10, last term is 3^11 and 4th term is 3^4. What was the flaw in my logic?
Thanks in advance.

You are not interpreting the text in red above correctly.

When you say "3 times the other term", it means that if the 1st term is a, then the 2nd term is 3a, 3rd term is 3a*3=9a etc. Thus the sequence becomes

a,3a,9a,27a .... and NOT 3^n as you have mentioned.

This is where you are making a mistake.

Hope this helps.
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Forget conventional ways of solving math questions. In DS, Variable approach is the easiest and quickest way to find the answer without actually solving the problem. Remember equal number of variables and independent equations ensures a solution.

In a sequence of terms in which each term is three times the previous term, what is the fourth term?

(1) The first term is 3.

(2) The second-to-last term is 3^10.

Modify the original condition and the question and suppose the sequence A_n. Then it becomes A_(n+1)=3A_(n) and once you figure out A_(1), you can figure out everything. So there is 1 variable, which should match with the number of equations. So you need 1 equation. For 1) 1 equation, for 2) 1 equation, which is likely to make D the answer.
For 1), A_(1)=3 -> A_(2)=3^2, A_(3)=3^3, A_(4)=3^4, which is unique and sufficient.
For 2), you can’t figure out where the last term comes, which is not sufficient. Therefore, the answer is A.


 For cases where we need 1 more equation, such as original conditions with “1 variable”, or “2 variables and 1 equation”, or “3 variables and 2 equations”, we have 1 equation each in both 1) and 2). Therefore, there is 59 % chance that D is the answer, while A or B has 38% chance and C or E has 3% chance. Since D is most likely to be the answer using 1) and 2) separately according to DS definition. Obviously there may be cases where the answer is A, B, C or E.

Hi Bunuel

Can u pls explain

The second-to-last term is 3^10--> since we don't know how many terms are there in the sequence then we don't know which term is second-to-last. For example: if it's third term then fourth (and last) will be 3^11, if it's fifth term then the fourth term is 3^9, ... Not sufficient.

what is the meaning of second to last term? I thought it means the last but second term, which means the 3rd term

The second-to-last term means the term before the last term.
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