If the sequence S has 100 terms, what is the 7th term of S?

Question

(1) The 93rd term of S is -100, and each term of S after the first is 7 less than the preceding term.

(2) The first term of S is 544.

Bunuel · Answer

Kinshook · Answer

Given:  The sequence S has 100 terms

Asked:  What is the 7th term of S?

(1) The 93rd term of S is -100, and each term of S after the first is 7 less than the preceding term.
 t_{93} = -100 
 t_n = t_{n-1} - 7 
 t_{n-1} = t_{n} + 7 
 t_{92} = t_{93}+7 = -100 +7 = -93

t__{7} = t_{93} +7*(93-7) = -100 + 7*86 = -100 + 602 = 502 
SUFFICIENT

(2) The first term of S is 544
NOT SUFFICIENT

IMO A

Bunuel · Answer

Official Explanation

Since this sequence has 100 terms, and we want the 7th term of the sequence, it's not clear whether we will be able to compute the 7th in a reasonable amount of time, even if it's possible. Possibly, we will need to confirm that the term can be computed without actually computing it. Indeed, turning to the statements, separately first, Statement (1) is giving us an idea that we can count backward. If the 93rd term is -100, then the 92nd term is -93, and the 91st term is -86. We could make an algebraic expression to figure out what the 7th term is, or list it out. So Statement (1) is sufficient. Statement (2), alone, gives us nothing, because without Statement (1), we don't know how to get from one term of the sequence to the next. So Statement (2) is insufficient. The correct answer is (A). This question is a good example of how the data statements may essentially try to lure you into evaluating them together before you have evaluated them separately.

The correct answer is (A).

Bunuel · Answer

Video Explanation

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bumpbot · Answer

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If the sequence S has 100 terms, what is the 7th term of S?

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GMAT Data Sufficiency (DS) Questions

If the sequence S has 100 terms, what is the 7th term of S?

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