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

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In a sequence of terms in which each term is three times the [#permalink]

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15 Feb 2011, 08:28
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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.
[Reveal] Spoiler: OA

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Re: In a sequence of terms in which each term is three times the [#permalink]

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15 Feb 2011, 08:35
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mariyea wrote:
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.

I think the ans should be D. But OA is different.

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.

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Re: In a sequence of terms in which each term is three times the [#permalink]

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15 Feb 2011, 08:59
Bunuel wrote:
mariyea wrote:
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.

I think the ans should be D. But OA is different.

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.

I had to think about that for a bit before I could sincerely agree with you, Bunuel. Thanks!
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Re: In a sequence of terms in which each term is three times the [#permalink]

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15 Feb 2011, 11:03
Bunuel wrote:
mariyea wrote:
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.

I think the ans should be D. But OA is different.

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.

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...

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Re: In a sequence of terms in which each term is three times the [#permalink]

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05 Mar 2011, 21:57
Ans : a , in second statment we dont know where serise start it can start from any no so insuff.
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Re: In a sequence of terms in which each term is three times the [#permalink]

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06 Mar 2011, 13:18
Good question.

First one is sufficient, as we have the rate at which each term is changing and first term which are enough to calculate what is neeed.

Second one is not sufficient , because we dont know the starting term and no of terms.

Hence A is the answer.

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Re: In a sequence of terms in which each term is three times the [#permalink]

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13 Jan 2012, 16:39
Bunuel wrote:
mariyea wrote:
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.

I think the ans should be D. But OA is different.

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?

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Re: In a sequence of terms in which each term is three times the [#permalink]

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16 Jan 2012, 17:24
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SonyGmat wrote:
Bunuel wrote:
mariyea wrote:
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.

I think the ans should be D. But OA is different.

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?

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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Re: In a sequence of terms in which each term is three times the [#permalink]

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09 Jul 2012, 02:54
thanks brunel for pointing out.. you are a jem

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Re: In a sequence of terms in which each term is three times the [#permalink]

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14 Jan 2016, 12:06
Bunuel wrote:
mariyea wrote:
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.

I think the ans should be D. But OA is different.

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.

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?

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Re: In a sequence of terms in which each term is three times the [#permalink]

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14 Jan 2016, 12:14
sarathvr wrote:

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?

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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Re: In a sequence of terms in which each term is three times the [#permalink]

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14 Jan 2016, 18:23
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.
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Re: In a sequence of terms in which each term is three times the [#permalink]

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23 Sep 2016, 21:23
Why is B incorrect? Is it because having the "last term" does not specify a finite value from which we can compute the "last - 1, last -2, ..., 4th" term?

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Re: In a sequence of terms in which each term is three times the [#permalink]

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23 Feb 2017, 05:49
Prompt analysis
A geometric progression following the sequence tn = a. r^(n-1). r= 3

Superset
The answer will be any real number.

Translation
In order to find t4, we need a and r or any two equation to solve for a and r.

Statement analysis

St 1: a =3. r =3. There fore t4 = 3. 3^3 = 81. ANSWER
St 2: ar/ar^(n-1)= 3^10. We don't have any idea about a. INSUFFICIENT.

Option A

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Re: In a sequence of terms in which each term is three times the [#permalink]

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28 May 2017, 20:37
mariyea wrote:
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.

I think the ans should be D. But OA is different.

The goal is to find the fourth term in this sequence. We need to know the first term and the pattern between each term to determine the value of the fourth term.

Statement 1)

x = 3 = first term
9 = second term
27 = third term
81 = fourth term

Sufficient.

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

If there are four total terms, then the value of the fourth term is 3^11.

If there are six total terms, then the value of the fourth term is 3^9.

Insufficient.

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Re: In a sequence of terms in which each term is three times the [#permalink]

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02 Oct 2017, 13:17
St 1: quite clear. T1= 3, T2 = 9, T3 = 27, T4 = 81, SUFF
St2: SECOND last term is 3*10. Last would be 9*10. But what would be the first term? We don't know for sure sure if its 10 or some fraction, because we are multiplying 3 into something, so it should already be a multiple of 3. So NOT SUFF.

Ans A

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Re: In a sequence of terms in which each term is three times the [#permalink]

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10 Oct 2017, 04:44
Quite easy.

3, 9, 27 and 81.

Second data point has no bearing on what's been asked of us.

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Re: In a sequence of terms in which each term is three times the [#permalink]

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12 Oct 2017, 18:17
mariyea wrote:
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.

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.

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Re: In a sequence of terms in which each term is three times the   [#permalink] 12 Oct 2017, 18:17
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# In a sequence of terms in which each term is three times the

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