Author 
Message 
TAGS:

Hide Tags

Senior Manager
Joined: 18 Sep 2009
Posts: 355

For a finite sequence of non zero numbers, the number of [#permalink]
Show Tags
22 Feb 2012, 06:33
1
This post received KUDOS
15
This post was BOOKMARKED
Question Stats:
73% (01:34) correct
27% (00:48) wrong based on 517 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
Official Answer and Stats are available only to registered users. Register/ Login.



Math Expert
Joined: 02 Sep 2009
Posts: 39622

Re: gmat prep [#permalink]
Show Tags
22 Feb 2012, 06:39
6
This post received KUDOS
Expert's post
10
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. Answer: C. Hope it's clear.
_________________
New to the Math Forum? Please read this: All You Need for Quant  PLEASE READ AND FOLLOW: 12 Rules for Posting!!! Resources: GMAT Math Book  Triangles  Polygons  Coordinate Geometry  Factorials  Circles  Number Theory  Remainders; 8. Overlapping Sets  PDF of Math Book; 10. Remainders  GMAT Prep Software Analysis  SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS)  Tricky questions from previous years.
Collection of Questions: PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.
What are GMAT Club Tests? Extrahard Quant Tests with Brilliant Analytics



Math Expert
Joined: 02 Sep 2009
Posts: 39622

Re: For a finite sequence of non zero numbers, the number of [#permalink]
Show Tags
04 Sep 2012, 04:05
2
This post received KUDOS
Expert's post
2
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 nonzero 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.
_________________
New to the Math Forum? Please read this: All You Need for Quant  PLEASE READ AND FOLLOW: 12 Rules for Posting!!! Resources: GMAT Math Book  Triangles  Polygons  Coordinate Geometry  Factorials  Circles  Number Theory  Remainders; 8. Overlapping Sets  PDF of Math Book; 10. Remainders  GMAT Prep Software Analysis  SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS)  Tricky questions from previous years.
Collection of Questions: PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.
What are GMAT Club Tests? Extrahard Quant Tests with Brilliant Analytics



Math Expert
Joined: 02 Sep 2009
Posts: 39622

Re: For a finite sequence of non zero numbers, the number of [#permalink]
Show Tags
21 Jul 2013, 03:34



Intern
Joined: 16 Feb 2012
Posts: 27
GPA: 3.57

Re: For a finite sequence of non zero numbers, the number of [#permalink]
Show Tags
24 Jul 2012, 06:56
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: 39622

Re: For a finite sequence of non zero numbers, the number of [#permalink]
Show Tags
25 Jul 2012, 08:50



Intern
Joined: 28 Aug 2012
Posts: 46
Location: Austria

Re: For a finite sequence of non zero numbers [#permalink]
Show Tags
02 Sep 2012, 08:58
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.



Manager
Joined: 28 Feb 2012
Posts: 115
Concentration: Strategy, International Business
GPA: 3.9
WE: Marketing (Other)

Re: For a finite sequence of non zero numbers, the number of [#permalink]
Show Tags
03 Sep 2012, 22:42
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 (13) 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: 39622

Re: For a finite sequence of non zero numbers, the number of [#permalink]
Show Tags
04 Sep 2012, 03:10
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. 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 (13) as pair while (5;6) not? Thanks. Please read the question and the thread carefully. This question is answered here: forafinitesequenceofnonzeronumbersthenumberof127949.html#p1107497Again, 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.
_________________
New to the Math Forum? Please read this: All You Need for Quant  PLEASE READ AND FOLLOW: 12 Rules for Posting!!! Resources: GMAT Math Book  Triangles  Polygons  Coordinate Geometry  Factorials  Circles  Number Theory  Remainders; 8. Overlapping Sets  PDF of Math Book; 10. Remainders  GMAT Prep Software Analysis  SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS)  Tricky questions from previous years.
Collection of Questions: PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.
What are GMAT Club Tests? Extrahard Quant Tests with Brilliant Analytics



Manager
Joined: 28 Feb 2012
Posts: 115
Concentration: Strategy, International Business
GPA: 3.9
WE: Marketing (Other)

Re: For a finite sequence of non zero numbers, the number of [#permalink]
Show Tags
04 Sep 2012, 03:58
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!



Senior Manager
Joined: 13 Aug 2012
Posts: 464
Concentration: Marketing, Finance
GPA: 3.23

Re: For a finite sequence of non zero numbers, the number of [#permalink]
Show Tags
20 Dec 2012, 03:47
There are three pairs with negative product: 1,3 3,2 5,4 Answer: C
_________________
Impossible is nothing to God.



Intern
Joined: 08 Jan 2013
Posts: 4
Location: United States
Concentration: International Business, Marketing
GMAT Date: 03112013
GPA: 3.8
WE: Supply Chain Management (Consumer Products)

Re: For a finite sequence of non zero numbers, the number of [#permalink]
Show Tags
11 Mar 2013, 00:03
Bunuel, thanks for the explanation! + 1 Kudos!



Director
Joined: 29 Nov 2012
Posts: 878

Re: For a finite sequence of non zero numbers, the number of [#permalink]
Show Tags
21 Jul 2013, 00:58
So the only thing different about this question is that people might rearrange 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/gmatprepsoftwareanalysisandwhatifscenarios146146.html



Manager
Joined: 26 Feb 2013
Posts: 177

Re: For a finite sequence of non zero numbers, the number of [#permalink]
Show Tags
16 Sep 2013, 09:54
Bunuel wrote: fozzzy wrote: So the only thing different about this question is that people might rearrange 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

Re: For a finite sequence of non zero numbers, the number of [#permalink]
Show Tags
27 Nov 2013, 19:57
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: 39622

Re: For a finite sequence of non zero numbers, the number of [#permalink]
Show Tags
28 Nov 2013, 06:04



GMAT Club Legend
Joined: 09 Sep 2013
Posts: 15932

Re: For a finite sequence of non zero numbers, the number of [#permalink]
Show Tags
05 Apr 2015, 12:34
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.
_________________
GMAT Books  GMAT Club Tests  Best Prices on GMAT Courses  GMAT Mobile App  Math Resources  Verbal Resources



Intern
Joined: 05 Apr 2015
Posts: 4

Re: For a finite sequence of non zero numbers, the number of [#permalink]
Show Tags
05 Apr 2015, 17:26
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: 51
Location: United States
GPA: 3.86

Re: For a finite sequence of non zero numbers, the number of [#permalink]
Show Tags
25 Jul 2015, 14:01
thats what got me from when I took the practice test what that I reordered the numbers.



EMPOWERgmat Instructor
Status: GMAT Assassin/CoFounder
Affiliations: EMPOWERgmat
Joined: 19 Dec 2014
Posts: 9257
Location: United States (CA)
GRE 1: 340 Q170 V170

Re: For a finite sequence of non zero numbers, the number of [#permalink]
Show Tags
25 Jul 2015, 17:22
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
_________________
760+: Learn What GMAT Assassins Do to Score at the Highest Levels Contact Rich at: Rich.C@empowergmat.com
Rich Cohen
CoFounder & GMAT Assassin
***********************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, 17:22



Go to page
1 2
Next
[ 28 posts ]




