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A certain sequence consist of alternating positive and negative number

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A certain sequence consist of alternating positive and negative number  [#permalink]

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New post Updated on: 18 Sep 2016, 02:49
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A certain sequence consist of alternating positive and negative numbers. If the sequence begins with a negative number and contains K numbers, where K is odd, how many positive numbers are in the set?

a) (k+1)/2
b) (k-1)/2
c) k/(2+1)
d) k/(2-1)
e) k/2

Originally posted by alanforde800Maximus on 18 Sep 2016, 02:45.
Last edited by Bunuel on 18 Sep 2016, 02:49, edited 1 time in total.
Renamed the topic and edited the question.
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Re: A certain sequence consist of alternating positive and negative number  [#permalink]

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New post 18 Sep 2016, 03:19
Every even digit of the sequence will be positive number and kth digit will be odd.

The position of last positive digit will be (k-1)

So, total number of digits= \(\frac{(k-1)}{2}\) ==> Ans. B
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Re: A certain sequence consist of alternating positive and negative number  [#permalink]

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New post 18 Sep 2016, 05:13
1
this question can also be solved with putting values for k, say k=7 since it's odd
and first number is neg so sequence will be {neg,pos,neg,pos,neg,pos,neg} we can see that it has 3 positive terms
so putting K=7 in the options, option b = (k-1)/2 => 7-1/2 = 3 , the number of positive integers

So, B is the answer
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Re: A certain sequence consist of alternating positive and negative number  [#permalink]

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New post 18 Sep 2016, 05:33
Take K = 5 and see how many are +ve and how many are -ve.

Substitute the value of K in options, you will get only one option satisfied, which is option B.
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Re: A certain sequence consist of alternating positive and negative number  [#permalink]

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New post 18 Sep 2016, 06:37
Top Contributor
alanforde800Maximus wrote:
A certain sequence consist of alternating positive and negative numbers. If the sequence begins with a negative number and contains K numbers, where K is odd, how many positive numbers are in the set?

a) (k+1)/2
b) (k-1)/2
c) k/(2+1)
d) k/(2-1)
e) k/2


Another approach it to look for a pattern...

k = 1
NEGATIVE
0 positive numbers

k = 3
NEGATIVE, POSITIVE, NEGATIVE
1 positive number

k = 5
NEG, POS, NEG, POS, NEG
2 positive numbers
Notice that if we examine the first 4 numbers, HALF are positive (and the last number is negative).

k = 7
NEG, POS, NEG, POS, NEG, POS, NEG
3 positive numbers
Notice that if we examine the first 6 numbers, HALF are positive (and the last number is negative).

k = 9
NEG, POS, NEG, POS, NEG, POS, NEG, POS, NEG
4 positive numbers
Notice that if we examine the first 8 numbers, HALF are positive (and the last number is negative).

In general, if we examine the first k-1 numbers, HALF will be positive (and the last number is negative).
So, the number of positive numbers = HALF of (k-1)
= (k-1)/2
Answer:
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Re: A certain sequence consist of alternating positive and negative number  [#permalink]

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New post 28 Jan 2018, 14:35
Hi All,

TESTing VALUES is a great approach for this type of question. You can also solve it with a bit of logic (and paying careful attention to how the answer choices are written).

We're told that we have an ODD number of terms in a sequence (represented by the variable "K"), the first term is NEGATIVE and the sequence alternates between negatives and positives. By definition, this means that there will be one more negative term than the total number of positive terms. The question asks for the number of POSITIVE terms.

Notice how all of the answers are written are written as fractions. Based on the description of the sequence, a little less than half of the K terms will be positive. So we should be dividing the total (K) by a little more than 2.

Answer C divides the total by 3, answer D divides the total by 1 and answer E divides the total by exactly 2. None of these answers matches what we're looking for, so they can all be eliminated. Between A and B, answer A INCREASES the total before halving it while Answer B DECREASES the total before halving it. With those two options, the only one that would logically end up with a 'net decrease' leading to a little less than half of the terms is B.

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Re: A certain sequence consist of alternating positive and negative number &nbs [#permalink] 28 Jan 2018, 14:35
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