For a finite sequence of non zero numbers, the number of : GMAT Problem Solving (PS)
Check GMAT Club Decision Tracker for the Latest School Decision Releases http://gmatclub.com/AppTrack

 It is currently 19 Jan 2017, 12:17

### GMAT Club Daily Prep

#### Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized
for You

we will pick new questions that match your level based on your Timer History

Track

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History

# Events & Promotions

###### Events & Promotions in June
Open Detailed Calendar

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

Author Message
TAGS:

### Hide Tags

Senior Manager
Joined: 18 Sep 2009
Posts: 360
Followers: 3

Kudos [?]: 438 [1] , given: 2

For a finite sequence of non zero numbers, the number of [#permalink]

### Show Tags

22 Feb 2012, 05:33
1
KUDOS
12
This post was
BOOKMARKED
00:00

Difficulty:

15% (low)

Question Stats:

72% (01:33) correct 28% (00:49) wrong based on 459 sessions

### HideShow timer Statistics

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
[Reveal] Spoiler: OA
Math Expert
Joined: 02 Sep 2009
Posts: 36567
Followers: 7081

Kudos [?]: 93194 [6] , given: 10553

### Show Tags

22 Feb 2012, 05:39
6
KUDOS
Expert's post
7
This post was
BOOKMARKED
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.

Hope it's clear.
_________________
Intern
Joined: 16 Feb 2012
Posts: 27
GPA: 3.57
Followers: 0

Kudos [?]: 55 [0], given: 0

Re: For a finite sequence of non zero numbers, the number of [#permalink]

### Show Tags

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?
Math Expert
Joined: 02 Sep 2009
Posts: 36567
Followers: 7081

Kudos [?]: 93194 [0], given: 10553

Re: For a finite sequence of non zero numbers, the number of [#permalink]

### Show Tags

25 Jul 2012, 07:50
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.
_________________
Intern
Joined: 28 Aug 2012
Posts: 46
Location: Austria
GMAT 1: 770 Q51 V42
Followers: 3

Kudos [?]: 43 [0], given: 3

Re: For a finite sequence of non zero numbers [#permalink]

### Show Tags

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).

Manager
Joined: 28 Feb 2012
Posts: 115
GPA: 3.9
WE: Marketing (Other)
Followers: 0

Kudos [?]: 42 [0], given: 17

Re: For a finite sequence of non zero numbers, the number of [#permalink]

### Show Tags

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.

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.
_________________

If you found my post useful and/or interesting - you are welcome to give kudos!

Math Expert
Joined: 02 Sep 2009
Posts: 36567
Followers: 7081

Kudos [?]: 93194 [0], given: 10553

Re: For a finite sequence of non zero numbers, the number of [#permalink]

### Show Tags

04 Sep 2012, 02:10
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.

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.

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.
_________________
Manager
Joined: 28 Feb 2012
Posts: 115
GPA: 3.9
WE: Marketing (Other)
Followers: 0

Kudos [?]: 42 [0], given: 17

Re: For a finite sequence of non zero numbers, the number of [#permalink]

### Show Tags

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.
_________________

If you found my post useful and/or interesting - you are welcome to give kudos!

Math Expert
Joined: 02 Sep 2009
Posts: 36567
Followers: 7081

Kudos [?]: 93194 [2] , given: 10553

Re: For a finite sequence of non zero numbers, the number of [#permalink]

### Show Tags

04 Sep 2012, 03:05
2
KUDOS
Expert's post
1
This post was
BOOKMARKED
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.
_________________
Senior Manager
Joined: 13 Aug 2012
Posts: 464
Concentration: Marketing, Finance
GMAT 1: Q V0
GPA: 3.23
Followers: 25

Kudos [?]: 433 [0], given: 11

Re: For a finite sequence of non zero numbers, the number of [#permalink]

### Show Tags

20 Dec 2012, 02:47
There are three pairs with negative product:

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

_________________

Impossible is nothing to God.

Intern
Joined: 08 Jan 2013
Posts: 4
Location: United States
GMAT Date: 03-11-2013
GPA: 3.8
WE: Supply Chain Management (Consumer Products)
Followers: 0

Kudos [?]: 5 [0], given: 3

Re: For a finite sequence of non zero numbers, the number of [#permalink]

### Show Tags

10 Mar 2013, 23:03
Bunuel, thanks for the explanation! + 1 Kudos!
Director
Joined: 29 Nov 2012
Posts: 898
Followers: 14

Kudos [?]: 1044 [0], given: 543

Re: For a finite sequence of non zero numbers, the number of [#permalink]

### Show Tags

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?
_________________

Click +1 Kudos if my post helped...

Amazing Free video explanation for all Quant questions from OG 13 and much more http://www.gmatquantum.com/og13th/

GMAT Prep software What if scenarios http://gmatclub.com/forum/gmat-prep-software-analysis-and-what-if-scenarios-146146.html

Math Expert
Joined: 02 Sep 2009
Posts: 36567
Followers: 7081

Kudos [?]: 93194 [2] , given: 10553

Re: For a finite sequence of non zero numbers, the number of [#permalink]

### Show Tags

21 Jul 2013, 02:34
2
KUDOS
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.
_________________
Manager
Joined: 26 Feb 2013
Posts: 184
Followers: 0

Kudos [?]: 40 [0], given: 25

Re: For a finite sequence of non zero numbers, the number of [#permalink]

### Show Tags

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!
Intern
Joined: 14 Sep 2013
Posts: 9
Followers: 0

Kudos [?]: 0 [0], given: 1

Re: For a finite sequence of non zero numbers, the number of [#permalink]

### Show Tags

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?
Math Expert
Joined: 02 Sep 2009
Posts: 36567
Followers: 7081

Kudos [?]: 93194 [0], given: 10553

Re: For a finite sequence of non zero numbers, the number of [#permalink]

### Show Tags

28 Nov 2013, 05:04
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?

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

Hope this helps.
_________________
GMAT Club Legend
Joined: 09 Sep 2013
Posts: 13456
Followers: 575

Kudos [?]: 163 [0], given: 0

Re: For a finite sequence of non zero numbers, the number of [#permalink]

### Show Tags

05 Apr 2015, 11:34
Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
_________________
Intern
Joined: 05 Apr 2015
Posts: 4
Followers: 0

Kudos [?]: 0 [0], given: 0

Re: For a finite sequence of non zero numbers, the number of [#permalink]

### Show Tags

05 Apr 2015, 16:26
The more natural understanding of the number of variations in sign is the number of times a term in the sequence has the opposite sign of its previous term. Because when the sign changes and a term and its preceding term have opposite signs, their product is necessarily negative, so the definition given is functionally equivalent. Understanding that helped me confirm that I understood what was meant by "number of variations in sign."

Keys to this problem: (1) Have in the front of your mind that the product of a positive and negative number is negative, whereas the product of two numbers of the same sign is positive, and (2) understand what number sequences are.
Manager
Joined: 22 Apr 2015
Posts: 50
Location: United States
GMAT 1: 620 Q46 V27
GPA: 3.86
Followers: 0

Kudos [?]: 14 [0], given: 118

Re: For a finite sequence of non zero numbers, the number of [#permalink]

### Show Tags

25 Jul 2015, 13:01
thats what got me from when I took the practice test what that I reordered the numbers.
EMPOWERgmat Instructor
Status: GMAT Assassin/Co-Founder
Affiliations: EMPOWERgmat
Joined: 19 Dec 2014
Posts: 8296
Location: United States (CA)
GMAT 1: 800 Q51 V49
GRE 1: 340 Q170 V170
Followers: 381

Kudos [?]: 2461 [0], given: 163

Re: For a finite sequence of non zero numbers, the number of [#permalink]

### Show Tags

25 Jul 2015, 16:22
Expert's post
1
This post was
BOOKMARKED
Hi kop,

The GMAT Quant section usually includes at least one "symbolism" question that will either "make up" a math symbol and ask you to perform a calculation with it OR make up a math phrase/concept and ask you to use the concept to answer a question.

These questions are essentially about following instructions.

Here, we're asked to take the PRODUCT of TWO CONSECUTIVE terms. If the product is NEGATIVE, then we have a "variation." So, given the included sequence of numbers, how many "variations" are there? Thankfully the work isn't difficult, but you would need to work through every pair of consecutive terms (and you would find 3 "variations").

These types of questions can sometimes take a little time to solve, but are some of the easiest "math" questions on the exam.

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

# Rich Cohen

Co-Founder & GMAT Assassin

# Special Offer: Save \$75 + GMAT Club Tests

60-point improvement guarantee
www.empowergmat.com/

***********************Select EMPOWERgmat Courses now include ALL 6 Official GMAC CATs!***********************

Re: For a finite sequence of non zero numbers, the number of   [#permalink] 25 Jul 2015, 16:22

Go to page    1   2    Next  [ 25 posts ]

Similar topics Replies Last post
Similar
Topics:
If 'a' and 'b' are non-zero numbers such that their sum is nine times 1 12 Sep 2015, 10:10
49 A sequence of numbers (geometric sequence) is given by the 12 19 Jan 2013, 10:53
16 If S and T are non-zero numbers and 29 04 Nov 2012, 07:20
11 If S and T are non-zero numbers and 1/S + 1/T = S + T, which 8 06 Aug 2008, 06:39
7 If S and T are non zero numbers, and 1/s + 1/t = s + t, 8 08 Nov 2007, 10:52
Display posts from previous: Sort by