Data Sufficiency

in a sequence of integer numbers in which each term is the square of the preceeding term, what is the fourth term?


1. last term is 6561
2. first term is 3

qa is b

But I think its a type it looks like qa is d.

book : manhattan review question number 84

I think stmt 2 is sufficient to answer the question. The reasoning follows:

In stsmt 1 only the last term is given. Now if one goes on calculating the square roots he will end up with 1. The catch lies here. Because the series does not exclude repeated numbers so there is a possibility that the series may have infinite no of 1 in the beginning.

While stsmt 2 is simple vanila. sart with 3 and keep squaring to get 4th term

ikant wrote:I think stmt 2 is sufficient to answer the question. The reasoning follows:

In stsmt 1 only the last term is given. Now if one goes on calculating the square roots he will end up with 1. The catch lies here. Because the series does not exclude repeated numbers so there is a possibility that the series may have infinite no of 1 in the beginning.

While stsmt 2 is simple vanila. sart with 3 and keep squaring to get 4th term

Actually, you'll get closer and closer and closer to 1, but you'll never get there.

Just knowing the last term gives us no information at all about the 4th term. For all we know, the sequence only has 4 terms and 6561 is the 4th term. It's also possible that 6561 is the 5th term and that the 4th term is root(6561). Of course, there are infinite other possibilities depending on how many terms the set actually has.

Why isn't it d?

ikant - '...so there is a possibility that the series may have infinite no of 1 in the beginning...'
--- it says that each term is the square of the preceding term, so we can't have ones otherwise we would never have anything but 1s in the sequence.


Stuart, you said that it's also possible that 6561 is the 5th term and that the 4th term is root(6561) or 81, that makes 3rd term 9, 2nd 3, and 1st root(3) which is not an integer anymore. With the last term being 6561, how can we have anything besides (3, 9, 81, 6561) or (-3, 9, 81, 6561)?
Am I seeing this wrong?

xilef wrote:Why isn't it d?


Stuart, you said that it's also possible that 6561 is the 5th term and that the 4th term is root(6561) or 81, that makes 3rd term 9, 2nd 3, and 1st root(3) which is not an integer anymore. With the last term being 6561, how can we have anything besides (3, 9, 81, 6561) or (-3, 9, 81, 6561)?
Am I seeing this wrong?

Doh! I missed the key word "integer" in the stem.

You're 100% correct. If there are at least 4 terms, and if 6561 is the last term, then 6561 would have to be the 4th term.

I guess the issue is "does there have to be a 4th term?" If we can assume that there are at least 4 terms, then 6561 is definitely 4th. However, if a possible answer is "there is no 4th term", then 6561 could be the 3rd and final term of the sequence.

If the answer actually is (b) instead of (d), I'd be interested in the official explanation.

You are right, this only works under the assumption that there is a 4th term in the sequence and since we shouldn't assume on GMAT, the answer might be b after all.

I can see that statement 2 is sufficient but also I see statement 1 being sufficient also.

Hey xilef, what a catch man! Great work...

Stuart Kovinsky wrote:....

I guess the issue is "does there have to be a 4th term?" If we can assume that there are at least 4 terms, then 6561 is definitely 4th. However, if a possible answer is "there is no 4th term", then 6561 could be the 3rd and final term of the sequence.

If the answer actually is (b) instead of (d), I'd be interested in the official explanation.

But Stuart doesn't the question stem ask for a 4th term, So isnt it safe to infer that the sequence has at least 4 terms. I mean, the question and the statement are both obviously referring to the same sequence ... right??.

I too would be really interested in the original explanation ... Enginpasa could you please post the original explanation to this question ..

PS:.. Also do post the source of this question.

gabriel wrote: But Stuart doesn't the question stem ask for a 4th term, So isnt it safe to infer that the sequence has at least 4 terms. I mean, the question and the statement are both obviously referring to the same sequence ... right??.

I too would be really interested in the original explanation ... Enginpasa could you please post the original explanation to this question ..

PS:.. Also do post the source of this question.

Oh, I agree with you - the "there doesn't have to be a 4th term" explanation seems pretty weak to me, but it's the only way I can see that the answer wouldn't be (d).

I'd also be interested in the source of the question - it would be great if everyone always included the source, so we can better decide how valid the question is likely to be.