Data Sufficiency

jjjinapinch wrote:If the sequence S has 300 terms, what is the 293rd term of S?

(1) The 298th term of S is -616, and each term of S after the first is 2 less than the preceding term.
(2) The first term of S is -22.

Official Guide question
Answer: A

Target question: What is the 293rd term of S?

Statement 1: The 298th term of S is -616, and each term of S after the first is 2 less than the preceding term.
So, each term is 2 less than the previous term.
Since term_298 = -616, we can conclude that:
term_297 = -614
term_296 = -612
term_295 = -610
So, we COULD keep going to determine the value of term_293 (which happens to be -606)
Since we can answer the target question with certainty, statement 1 is SUFFICIENT

Statement 2: The first term of S is -22.
Since this statement tells us nothing about the NATURE of the sequence, there's no way to determine the value of term_293
Since we cannot answer the target question with certainty, statement 2 is NOT SUFFICIENT

Answer: A

Cheers,
Brent

jjjinapinch wrote:If the sequence S has 300 terms, what is the 293rd term of S?

(1) The 298th term of S is -616, and each term of S after the first is 2 less than the preceding term.
(2) The first term of S is -22.

Official Guide question
Answer: A

This is a typical sequence question. For a sequence question, you need to know the pattern or the logic behind the subsequent term.

Statement 1:

We have T_298 = -616;

It is given that each term of S after the first is 2 less than the preceding term.

Thus,

T_298 = T_297 - 2;

Thus, T_297 = -616 + 2 = -614

On a similar basis, we can certainly reach to any term whether it is the 293rd term of the first term. We are sure to get the unique answer. Sufficient.

Statement 1:

We only know the value of the first term; we must know how the sequence is arranged to get the answer Insufficient.

The correct answer: A

Hope this helps!

Download free ebook: Manhattan Review GMAT Quantitative Question Bank Guide

-Jay
_________________
Manhattan Review GMAT Prep

Locations: New York | Singapore | Doha | Lausanne | and many more...

Schedule your free consultation with an experienced GMAT Prep Advisor! Click here.

Hi All,

We're told that sequence S has 300 terms. We're asked for the value of the 293rd term of S. With 'sequence' questions, there is always some type of mathematical 'relationship' among the terms, so we'll need to know that 'formula' - and the value of at least one of the terms - to properly answer this question.

1) The 298th term of S is -616, and each term of S after the first is 2 less than the preceding term.

Fact 1 gives us the value of one of the terms in the sequence AND how the sequence progresses. Thus, we could figure out ALL of the terms in the sequence. While you don't have to do that work at this point, you could figure out the 293rd sequence by working backwards from the 298th term and adding 2 to each term....
298th = -616
297th = -614
296th = -612
295th = -610
294th = -608
293rd = -606
Fact 1 is SUFFICIENT

2) The first term of S is -22.

The information in Fact 2 does not define how the sequence progresses, so there's no way to determine the value of the 293rd term.
Fact 2 is INSUFFICIENT

Final Answer: A

GMAT assassins aren't born, they're made,
Rich

jjjinapinch wrote:If the sequence S has 300 terms, what is the 293rd term of S?

(1) The 298th term of S is -616, and each term of S after the first is 2 less than the preceding term.
(2) The first term of S is -22.

We are given that sequence S has 300 terms, and we need to determine the 293rd term of S.

Statement One Alone:

The 298th term of S is -616, and each term of S after the first is 2 less than the preceding term.

Statement one defines the pattern of the sequence. We are given that each term of S after the first is 2 less than the preceding term. Thus, we know that we can determine the value of the 293rd term.

If we were forced to determine the 293rd term we could determine that value. We know that the 293rd term is 5 terms before the 298th term. Thus, the 298th term is 5(2) = 10 less than the 293rd term, or in other words, the 293rd term is 10 more than -616, the 298th term. So the 293rd term is -606.

Remember, because we are answering a data sufficiency question, we can stop as soon as we know we are able to determine the value of the 293rd term, and so we don't need to perform the math to calculate its actual value.

Statement one is sufficient.

Statement Two Alone:

The first term of S is -22.

Since we do not have any information about the pattern defining the sequence, statement two is not sufficient to answer the question.

Answer: A