The nth term, where n 1, in a series S of positive integers is

Question

The sequence  x_1,x_2 ....x_n  is such that  x_1 = 5,  x_2 = - 5,  x_3 = 0 ,  x_4  = - 2,  x_5  = 4 and  x_n  =  x_{n - 5} . P is an integer greater than 5. P= ?

(1) Sum of the first P terms in the given sequence is 10. 
(2) Sum of the first P + 3 terms in the given sequence is 10.

gmatophobia · Answer

The question as originally presented was not correctly formatted, hence I have corrected the same.

Let's write a few terms in the sequence

A = { 5, \quad -5, \quad 0, \quad -2, \quad 4, \quad 5, \quad -5, \quad 0, \quad -2, \quad 4 ....  }

Statement 1

(1) Sum of the first P terms in the given sequence is 10.

The addition of the first five terms in the sequence yields the sum = 2

So P can be 5 such sets, i.e. P can be 25.

However, if we take the sum of the first two, or the first three terms the sum adds to 0.

Hence, if P = 25, 27, or 28 the sum will still be 0.

The statement is not sufficient.

Statement 2

(2) Sum of the first P + 3 terms in the given sequence is 10

Similar to statement 1, P+3 can be 25, 27, or 28 or we can further and P + 3 can be 34.

As we are getting multiple values of P we can eliminate B.

Combined

P + 3 = 28

Hence, P = 25

Sufficient.

Option C

Fictional26 · Answer

After combining both statements,
P+3=28
can you please explain this part?

Bunuel · Answer

Pure algebraic questions are no longer a part of the  DS syllabus  of the GMAT.

DS questions in GMAT Focus encompass various types of word problems, such as:

Word Problems 
 Work Problems 
 Distance Problems 
 Mixture Problems 
 Percent and Interest Problems 
 Overlapping Sets Problems 
 Statistics Problems 
 Combination and Probability Problems

While these questions may involve or necessitate knowledge of algebra, arithmetic, inequalities, etc., they will always be presented in the form of word problems. You won’t encounter pure "algebra" questions like, "Is x > y?" or "A positive integer n has two prime factors..."

Check  GMAT Syllabus for Focus Edition

You can also visit the  Data Sufficiency forum  and filter questions by  OG 2024-2025, GMAT Prep (Focus), and Data Insights Review 2024-2025 sources  to see the types of questions currently tested on the GMAT.

So, you can ignore this question.

Hope it helps.

The nth term, where n > 1, in a series S of positive integers is

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