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# What is the 999th term of the series S ? (1) The first four terms of S

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What is the 999th term of the series S ? (1) The first four terms of S [#permalink]

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06 Jan 2018, 14:22
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What is the 999th term of the series S ?

(1) The first four terms of S are (1 + 1)^2, (2 + 1)^2, (3 + 1)^2, and (4 + 1)^2.
(2) For every x, the xth term of S is (x + 1)^2
[Reveal] Spoiler: OA

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What is the 999th term of the series S ? (1) The first four terms of S [#permalink]

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06 Jan 2018, 20:37
What is the 999th term of the series S ?

(1) The first four terms of S are (1 + 1)^2, (2 + 1)^2, (3 + 1)^2, and (4 + 1)^2.
(2) For every x, the xth term of S is (x + 1)^2

Statement 1: we know the first $$4$$ terms but what about terms after that? They could be anything. Hence insufficient

Statement 2: This clearly mentions the value of each term in the series.

So 999th term will be $$(999+1)^2=1000^2$$. Sufficient

Option B
Intern
Joined: 25 Mar 2017
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Re: What is the 999th term of the series S ? (1) The first four terms of S [#permalink]

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16 Jan 2018, 11:11
Can someone explain why A as well cannot provide an answer?
The first four terms of the series are given and we are asked to find the 999th term. If we see a pattern in a series(and we know at least two terms), can we not find the nth term?

Or did I not get the question correctly?
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Joined: 22 Aug 2013
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Re: What is the 999th term of the series S ? (1) The first four terms of S [#permalink]

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16 Jan 2018, 11:23
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NiruSinghal wrote:
Can someone explain why A as well cannot provide an answer?
The first four terms of the series are given and we are asked to find the 999th term. If we see a pattern in a series(and we know at least two terms), can we not find the nth term?

Or did I not get the question correctly?

Hi

First four terms are given. But there is no pattern given in the question. I know from the first four terms there seems to be a pattern, but we cannot conclude that just by looking at the first four terms.

Eg, If we are given first three terms of a series as 3, 5, 7... we cannot conclude that next term would be 9. It might be 11 (series of prime numbers) or the fourth term might just be 10 (so no pattern). A specific pattern is not necessary unless its specified in the question.

But the second statement generalises a pattern by specifying that x, the xth term of S is (x + 1)^2. So we can find the 999th term
Intern
Joined: 25 Mar 2017
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What is the 999th term of the series S ? (1) The first four terms of S [#permalink]

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16 Jan 2018, 12:01
1
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amanvermagmat wrote:
NiruSinghal wrote:
Can someone explain why A as well cannot provide an answer?
The first four terms of the series are given and we are asked to find the 999th term. If we see a pattern in a series(and we know at least two terms), can we not find the nth term?

Or did I not get the question correctly?

Hi

First four terms are given. But there is no pattern given in the question. I know from the first four terms there seems to be a pattern, but we cannot conclude that just by looking at the first four terms.

Eg, If we are given first three terms of a series as 3, 5, 7... we cannot conclude that next term would be 9. It might be 11 (series of prime numbers) or the fourth term might just be 10 (so no pattern). A specific pattern is not necessary unless its specified in the question.

But the second statement generalises a pattern by specifying that x, the xth term of S is (x + 1)^2. So we can find the 999th term

Thanks for the response

I understand it's not an arithmetic series but when I look at the terms, I do find a pattern:
2^2, 3^2, 4^2, 5^2. Can I assume that the xth term is (x+1)^2 ?

Also, if I expand the terms:
4, 9, 16, 25. the common difference increases by 2. And if we apply this pattern, the 5th term is 25+11=36, which is equal to 6^2(5+1)^2.

Just trying to understand where I'm going wrong.

TIA
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Re: What is the 999th term of the series S ? (1) The first four terms of S [#permalink]

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16 Jan 2018, 23:00
1
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NiruSinghal wrote:
amanvermagmat wrote:
NiruSinghal wrote:
Can someone explain why A as well cannot provide an answer?
The first four terms of the series are given and we are asked to find the 999th term. If we see a pattern in a series(and we know at least two terms), can we not find the nth term?

Or did I not get the question correctly?

Hi

First four terms are given. But there is no pattern given in the question. I know from the first four terms there seems to be a pattern, but we cannot conclude that just by looking at the first four terms.

Eg, If we are given first three terms of a series as 3, 5, 7... we cannot conclude that next term would be 9. It might be 11 (series of prime numbers) or the fourth term might just be 10 (so no pattern). A specific pattern is not necessary unless its specified in the question.

But the second statement generalises a pattern by specifying that x, the xth term of S is (x + 1)^2. So we can find the 999th term

Thanks for the response

I understand it's not an arithmetic series but when I look at the terms, I do find a pattern:
2^2, 3^2, 4^2, 5^2. Can I assume that the xth term is (x+1)^2 ?

Also, if I expand the terms:
4, 9, 16, 25. the common difference increases by 2. And if we apply this pattern, the 5th term is 25+11=36, which is equal to 6^2(5+1)^2.

Just trying to understand where I'm going wrong.

TIA

I understand where you are coming from. We have done those sort of questions. Given a series 1^2, 2^2, 3^2, 4^2.. then automatically the next thing which comes to mind is 5^2. It seems that there cannot be anything else, because from the first four terms, it seems that the pattern for each term is n^2.

But since this is a GMAT data sufficiency question, we cannot assume that would be the case. Its possible that i decide to make a series where the first four terms follow the rule n^2, next four terms follow (n+1)^2, next four terms follow (n+2)^2 and so on.. In that case the series will look like this:
1, 4, 9, 16, 36, 49, 64, 81, 121, 144,...

So how do we know that the given series (as per first statement) is not something like this. How do we know that ALL terms will follow n^2 or (n+1)^2?
That is what is specified only in second statement.
Intern
Joined: 25 Mar 2017
Posts: 8
Re: What is the 999th term of the series S ? (1) The first four terms of S [#permalink]

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16 Jan 2018, 23:28
1
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I understand where you are coming from. We have done those sort of questions. Given a series 1^2, 2^2, 3^2, 4^2.. then automatically the next thing which comes to mind is 5^2. It seems that there cannot be anything else, because from the first four terms, it seems that the pattern for each term is n^2.

But since this is a GMAT data sufficiency question, we cannot assume that would be the case. Its possible that i decide to make a series where the first four terms follow the rule n^2, next four terms follow (n+1)^2, next four terms follow (n+2)^2 and so on.. In that case the series will look like this:
1, 4, 9, 16, 36, 49, 64, 81, 121, 144,...

So how do we know that the given series (as per first statement) is not something like this. How do we know that ALL terms will follow n^2 or (n+1)^2?
That is what is specified only in second statement.[/quote]

Thanks, Aman.

Indeed, it's one of those lessons learned in school to assume based on the first few terms.
Will keep this in mind, thanks again
Re: What is the 999th term of the series S ? (1) The first four terms of S   [#permalink] 16 Jan 2018, 23:28
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# What is the 999th term of the series S ? (1) The first four terms of S

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