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For a finite sequence of non zero numbers, the number of

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For a finite sequence of non zero numbers, the number of [#permalink] New post 22 Feb 2012, 05:33
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For a finite sequence of non zero numbers, the number of variations in sign is defined as the number of pairs of consecutive terms of the sequence for which the product of the two consecutive terms is negative. What is the number of variations in sign for the sequence 1, -3, 2, 5, -4, -6 ?

A. 1
B. 2
C. 3
D. 4
E. 5
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Re: gmat prep [#permalink] New post 22 Feb 2012, 05:39
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TomB wrote:
For a finite sequence of non zero numbers, the number of variations in sign is defined as the number of pairs of consecutive terms of the sequence for which the product of the two consecutive terms is negative. What is the number of variations in sign for the sequence 1, -3, 2, 5, -4, -6 ?
A. 1
B. 2
C. 3
D. 4
E. 5

this problem is already posted in the forum. My doubt is every body multiplying the negative number with positive number to find the variations. but the question asked for "number of pairs of consecutive terms of the sequence for which the product of the two consecutive terms is negative." for ex:1,-3 are not consecutive . please explain


You are probably mixing consecutive terms in a sequence and consecutive integers: 1 and -3 are not consecutive integers, but they are consecutive terms in the sequence given. See complete solution below.

For a finite sequence of non zero numbers, the number of variations in the sign is defined as the number of pairs of consecutive terms of the sequence for which the product of the two consecutive terms is negative. What is the number of variations in sign for the sequence 1, -3, 2, 5, -4, -6?
A. 1
B. 2
C. 3
D. 4
E. 5

Given sequence: {1, -3, 2, 5, -4, -6}

The questions basically asks: how many pairs of consecutive terms are there in the sequence such that the product of these consecutive terms is negative.

1*(-3)=-3=negative;
-3*2=-6=negative;
2*5=10=positive;
5*(-4)=-20=negative;
(-4)*(-6)=24=positive.

So there are 3 pairs of consecutive terms of the sequence for which the product is negative.

Answer: C.

Hope it's clear.
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Re: For a finite sequence of non zero numbers, the number of [#permalink] New post 24 Jul 2012, 05:56
Hi Bunuel,
Why is -4*1, -4*2 not considered?? You are only taking 1*-3, -3*2 only consecutive terms? Would you please clearify it?
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Re: For a finite sequence of non zero numbers, the number of [#permalink] New post 25 Jul 2012, 07:50
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rajman41 wrote:
Hi Bunuel,
Why is -4*1, -4*2 not considered?? You are only taking 1*-3, -3*2 only consecutive terms? Would you please clearify it?


Because 1 and -4 are NOT consecutive terms in the sequence.
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Re: For a finite sequence of non zero numbers [#permalink] New post 02 Sep 2012, 07:58
We can take two consecutive numbers of this sequence and the product of those two numbers has to be negative.
There are 5 pairs, we can build:
(1, -3), (-3, 2), (2, 5), (5, -4), (-4, -6)

1 * (-3) = negative
(-3) * 2 = negative
2 * 5 = positive
5 * (-4) = negative
(-4) * (-6) = positive

So there are three pairs (1, -3), (-3, 2), and (5, -4).

Answer C.
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Re: For a finite sequence of non zero numbers, the number of [#permalink] New post 03 Sep 2012, 21:42
Bunuel wrote:
TomB wrote:
For a finite sequence of non zero numbers, the number of variations in sign is defined as the number of pairs of consecutive terms of the sequence for which the product of the two consecutive terms is negative. What is the number of variations in sign for the sequence 1, -3, 2, 5, -4, -6 ?
A. 1
B. 2
C. 3
D. 4
E. 5

this problem is already posted in the forum. My doubt is every body multiplying the negative number with positive number to find the variations. but the question asked for "number of pairs of consecutive terms of the sequence for which the product of the two consecutive terms is negative." for ex:1,-3 are not consecutive . please explain


You are probably mixing consecutive terms in a sequence and consecutive integers: 1 and -3 are not consecutive integers, but they are consecutive terms in the sequence given. See complete solution below.

For a finite sequence of non zero numbers, the number of variations in the sign is defined as the number of pairs of consecutive terms of the sequence for which the product of the two consecutive terms is negative. What is the number of variations in sign for the sequence 1, -3, 2, 5, -4, -6?
A. 1
B. 2
C. 3
D. 4
E. 5

Given sequence: {1, -3, 2, 5, -4, -6}

The questions basically asks: how many pairs of consecutive terms are there in the sequence such that the product of these consecutive terms is negative.

1*(-3)=-3=negative;
-3*2=-6=negative;
2*5=10=positive;
5*(-4)=-20=negative;
(-4)*(-6)=24=positive.

So there are 3 pairs of consecutive terms of the sequence for which the product is negative.

Answer: C.

Hope it's clear.


I have answered correctly, but my pairs were: (2, -3) (-4,5) (5,-6). My question is, Bunuel, why do we consider (1-3) as pair while (5;-6) not?
Thanks.
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Re: For a finite sequence of non zero numbers, the number of [#permalink] New post 04 Sep 2012, 02:10
Expert's post
ziko wrote:
Bunuel wrote:
TomB wrote:
For a finite sequence of non zero numbers, the number of variations in sign is defined as the number of pairs of consecutive terms of the sequence for which the product of the two consecutive terms is negative. What is the number of variations in sign for the sequence 1, -3, 2, 5, -4, -6 ?
A. 1
B. 2
C. 3
D. 4
E. 5

this problem is already posted in the forum. My doubt is every body multiplying the negative number with positive number to find the variations. but the question asked for "number of pairs of consecutive terms of the sequence for which the product of the two consecutive terms is negative." for ex:1,-3 are not consecutive . please explain


You are probably mixing consecutive terms in a sequence and consecutive integers: 1 and -3 are not consecutive integers, but they are consecutive terms in the sequence given. See complete solution below.

For a finite sequence of non zero numbers, the number of variations in the sign is defined as the number of pairs of consecutive terms of the sequence for which the product of the two consecutive terms is negative. What is the number of variations in sign for the sequence 1, -3, 2, 5, -4, -6?
A. 1
B. 2
C. 3
D. 4
E. 5

Given sequence: {1, -3, 2, 5, -4, -6}

The questions basically asks: how many pairs of consecutive terms are there in the sequence such that the product of these consecutive terms is negative.

1*(-3)=-3=negative;
-3*2=-6=negative;
2*5=10=positive;
5*(-4)=-20=negative;
(-4)*(-6)=24=positive.

So there are 3 pairs of consecutive terms of the sequence for which the product is negative.

Answer: C.

Hope it's clear.


I have answered correctly, but my pairs were: (2, -3) (-4,5) (5,-6). My question is, Bunuel, why do we consider (1-3) as pair while (5;-6) not?
Thanks.


Please read the question and the thread carefully. This question is answered here: for-a-finite-sequence-of-non-zero-numbers-the-number-of-127949.html#p1107497

Again, we are told that "the number of variations in sign is defined as the number of pairs of consecutive terms of the sequence ..." 1 and -3 are consecutive terms in the sequence while 5 and -6 are not.
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Re: For a finite sequence of non zero numbers, the number of [#permalink] New post 04 Sep 2012, 02:58
Thank you Bunuel, i got it, i did not realised that 1, -3, 2, 5, -4, -6 is a given finite sequence, for some reason i understood it as a set. Although now i see that if it were a set then the answer would be 0, since there are no pair with negative signs in a normal consequtive sequence.
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Re: For a finite sequence of non zero numbers, the number of [#permalink] New post 04 Sep 2012, 03:05
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ziko wrote:
Thank you Bunuel, i got it, i did not realised that 1, -3, 2, 5, -4, -6 is a given finite sequence, for some reason i understood it as a set. Although now i see that if it were a set then the answer would be 0, since there are no pair with negative signs in a normal consequtive sequence.


1. Even if we consider the terms in ascending order {-6, -4, -3, 1, 2, 5} still one pair of consecutive terms will make negative product: -3*1=-1=negative. But in this case, ANY sequence of non-zero integers which have both negative and positive numbers will have variation of 1 and the question does not make sense any more.

2. A sequence by definition is already an ordered list of terms. So if we are given the sequence of 10 numbers: 5, 6, 0, -1, -10, -10, -10, 3, 3, -100 it means that they are exactly in that order and not in another.

Hope it's clear.
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Re: For a finite sequence of non zero numbers, the number of [#permalink] New post 20 Dec 2012, 02:47
There are three pairs with negative product:

1,-3
-3,2
5,-4

Answer: C
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Re: For a finite sequence of non zero numbers, the number of [#permalink] New post 10 Mar 2013, 23:03
Bunuel, thanks for the explanation! + 1 Kudos!
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Re: For a finite sequence of non zero numbers, the number of [#permalink] New post 20 Jul 2013, 23:58
So the only thing different about this question is that people might re-arrange the sequence and that's what you are not supposed to do?
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Re: For a finite sequence of non zero numbers, the number of [#permalink] New post 21 Jul 2013, 02:34
Expert's post
fozzzy wrote:
So the only thing different about this question is that people might re-arrange the sequence and that's what you are not supposed to do?


People might do a lot of things. The point is to read the stem carefully.
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Re: For a finite sequence of non zero numbers, the number of [#permalink] New post 16 Sep 2013, 08:54
Bunuel wrote:
fozzzy wrote:
So the only thing different about this question is that people might re-arrange the sequence and that's what you are not supposed to do?


People might do a lot of things. The point is to read the stem carefully.


Ok it took me like 5 reads to understand what the question is about. I understood Bunuel's explanation (straight forward) but didn't get that GMAT declared a fancy way of saying the product of each pair of integers... I wonder how many of these does it take to drop you off your seat! :evil:
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Re: For a finite sequence of non zero numbers, the number of [#permalink] New post 27 Nov 2013, 18:57
I don't understand what the question is asking for... Could someone please break it down better on what the question is asking?
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Re: For a finite sequence of non zero numbers, the number of [#permalink] New post 28 Nov 2013, 05:04
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haotian87 wrote:
I don't understand what the question is asking for... Could someone please break it down better on what the question is asking?


Please check below posts:
for-a-finite-sequence-of-non-zero-numbers-the-number-of-127949.html#p1048083
for-a-finite-sequence-of-non-zero-numbers-the-number-of-127949.html#p1118541

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Re: For a finite sequence of non zero numbers, the number of   [#permalink] 28 Nov 2013, 05:04
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