The sequence of s1, s2, s3, . . . , sn of n is such that sk = 2k -1 if

Question

The sequence of s_1, s_2, s_3, . . . , s_n  of n is such that s_k = 2k -1 if k is odd and  s_k = -s_{k-1}  if k is even. Is the sum of the terms in the sequence positive?

(1) The sum of the first 11 terms in the sequence is positive.

(2) n is odd.

chetan2u · Answer

Hi,
 INFO from the Q 
the odd term has a positive value..
the even term immediately after that is -ive of that odd value..
so starting from 1, each pair of even and odd will cancel out each other..

INFERENCE-- 
if we are taking ODD terms, only last term will be left in the sum of all terms as all other will cancel out..
If we are taking EVEN terms, all will cancel out and the SUM will be 0

REQUIREMENT 
 Is the sum of the terms in the sequence positive?
IF ODD TERMS__YES
IF EVEN TERMS__NO

lets see the statements now-- 
 (1) The sum of the first 11 terms in the sequence is positive. 
this has already been INFERRED by us. nothing about number of terms
Insuff

(2) n is odd. 
since terms are odd..
ans is YES
Suff

ans B

Bunuel · Answer

Similar question to practice: the-sequence-a1-a2-a3-an-of-n-integers-is-such-that-51526.html

MathRevolution · Answer

Forget conventional ways of solving math questions. In DS, Variable approach is the easiest and quickest way to find the answer without actually solving the problem. Remember equal number of variables and independent equations ensures a solution.

The sequence ofs1,s2,s3,...,sns1,s2,s3,...,sn of n is such thatsk=2k−1sk=2k−1if k is odd and sk=−sk−1sk=−sk−1 if k is even. Is the sum of the terms in the sequence positive?

(1) The sum of the first 11 terms in the sequence is positive.
(2) n is odd.

When you modify the original condition and the question, they become 1,-1,3,-3,5,-5,.... and sum of up to an odd-number term is always a positive number. However, in 2), since n=odd, sum until the term n is always positive, which is yes and sufficient.
Therefore, the answer is B.

 Once we modify the original condition and the question according to the variable approach method 1, we can solve approximately 30% of DS questions.

stonecold · Answer

Here B is sufficient as ODD value of N will give us a positive result which is a result of the other terms cancelling out..

minustark · Answer

From the stem, we can get the odd terms of the sequence is a positive odd number (eg: 2.1-1=1, 2.3-1=5) and the even terms are negative of its previous term. Either the sum can be 0 when n is even or can be equal to the last odd term of the sequence in case of n is negative.

1) no information about the number of terms. not sufficient

2) the sum will be positive as it will be equal to the last term of the sequence. sufficient.

B is the answer.

zitipiti · Answer

lets say s1 = a
so, s2 = -a
s3 = 6-1 = 5
s4 = -5

kth odd term + (k+1)th even term = 0
so we can say that if n is odd then sum of sequence is +ve and odd
and if n is even, then sum of sequence is 0

Therefore,  statement 2  is enough to answer that the sum of the sequence is neither positive nor negative, it is 0.
Statement 1 tells us nothing that could lead us to the fact that n is even or odd...
 
option B  is correct

zitipiti · Answer

lets say s1 = a
so, s2 = -a
s3 = 6-1 = 5
s4 = -5

kth odd term + (k+1)th even term = 0
so we can say that if n is odd then sum of sequence is +ve and odd
and if n is even, then sum of sequence is 0

Therefore,  statement 2  is enough to answer that the sum of the sequence is neither positive nor negative, it is 0.
Statement 1 tells us nothing that could lead us to the fact that n is even or odd...
 
option B  is correct

The sequence of s1, s2, s3, . . . , sn of n is such that sk = 2k -1 if

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GMAT Data Sufficiency (DS) Questions

The sequence of s1, s2, s3, . . . , sn of n is such that sk = 2k -1 if

Prep Toolkit

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards