"Finding the fourth" problem

[ajafari]

This problem showed up in my CAT #3.

I chose answer D but the correct answer is A.

I don't see why #2 can't be considered as sufficient. Can't it be backed out?


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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.

[2amitprakash]

Technically it is a "geometric" progression but that is not important here. From question you derive that
nth term = (1st term) *(3^(n-1))
1 - since you know the 1st term, you know the 4th term. SUFFICIENT.
4th term = 3*(3^3) = 81

2 - second-to-last term is known but we don't know about last term or total number of terms? Basically you have 2 unknowns and only one equation, so impossible to know.
Knowing 2 terms or knowing the number of total terms and then the second-to-last term would be sufficient to know the sequence and hence any term in the sequence.
Try putting some number:
case 1: there are 12 terms in sequence. so second-to-last term will mean 11th term.
11th term = (1st term)*(3^10)
so 1st term will be 1.
4th term = 3^3
case 2: there are 11 terms in sequence, so second-to-last term will be 10th term.
10th term = (1st term)*(3^9)
so 1st term will be 3.
4th term = 3*3^3 = 3^4
INSUFFICIENT.

So the answer will be A.

[RonPurewal]

I don't see why #2 can't be considered as sufficient. Can't it be backed out?

if you knew which NUMBERED term was 3^10, then yes, you could just run it backwards, dividing by 3 rather than multiplying.

but, you don't. "second-to-last" could be fifth, or hundredth, or millionth.

careful!

[nocheivyirene]

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.

This is trap question. But one thing will help you realize that it is a trap.

1. The question tells us that the sequence is an = (an-1) * 3.
2. The question asks us about the fourth term. WE don't know because we don't know any of the term. Knowing either the first, third or second term will help us know the 4th.
3. Test STATEMENT 1. a1 = 3. This then tells us that the sequence goes like this: 3,9,27,81. SUFFICIENT!
Please not that in the GMAT. If both STATEMENT 1 and 2 are sufficient on its own, the statements give the same answer.
4. Test STATEMENT 2. second-to-the-last is 3^10. Let's say you misunderstood the question and thought the fourth term is the last term. If you think that, the fourth term would be 3^11 which is not equal to the result we derived from STATEMENT 1. This is a trap. WE DO NOT REALLY KNOW THE LAST TERM. Perhaps it is the 1000th term. We don't know.
Remember, statements if sufficient alone, give duplicate answers to the question.

Answer: A

[jlucero]

Correct.