December 20, 2018 December 20, 2018 10:00 PM PST 11:00 PM PST This is the most inexpensive and attractive price in the market. Get the course now! December 22, 2018 December 22, 2018 07:00 AM PST 09:00 AM PST Attend this webinar to learn how to leverage Meaning and Logic to solve the most challenging Sentence Correction Questions.
Author 
Message 
TAGS:

Hide Tags

Senior Manager
Joined: 18 Sep 2009
Posts: 283

For a finite sequence of non zero numbers, the number of
[#permalink]
Show Tags
22 Feb 2012, 05:33
Question Stats:
74% (00:34) correct 26% (00:39) wrong based on 756 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: 51280

Re: gmat prep
[#permalink]
Show Tags
22 Feb 2012, 05:39
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: Ultimate GMAT Quantitative Megathread  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




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, 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: 51280

Re: For a finite sequence of non zero numbers, the number of
[#permalink]
Show Tags
25 Jul 2012, 07:50



Intern
Joined: 28 Aug 2012
Posts: 43
Location: Austria

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).
Answer C.



Manager
Joined: 28 Feb 2012
Posts: 110
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, 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 (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: 51280

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. 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: Ultimate GMAT Quantitative Megathread  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: 110
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, 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: 51280

Re: For a finite sequence of non zero numbers, the number of
[#permalink]
Show Tags
04 Sep 2012, 03:05
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: Ultimate GMAT Quantitative Megathread  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



Director
Joined: 29 Nov 2012
Posts: 759

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 rearrange the sequence and that's what you are not supposed to do?



Math Expert
Joined: 02 Sep 2009
Posts: 51280

Re: For a finite sequence of non zero numbers, the number of
[#permalink]
Show Tags
21 Jul 2013, 02:34



Manager
Joined: 26 Feb 2013
Posts: 154

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 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: 05 Apr 2015
Posts: 4

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.



EMPOWERgmat Instructor
Status: GMAT Assassin/CoFounder
Affiliations: EMPOWERgmat
Joined: 19 Dec 2014
Posts: 13108
Location: United States (CA)

Re: For a finite sequence of non zero numbers, the number of
[#permalink]
Show Tags
25 Jul 2015, 16:22
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
Special Offer: Save $75 + GMAT Club Tests Free
Official GMAT Exam Packs + 70 Pt. Improvement Guarantee www.empowergmat.com/
*****Select EMPOWERgmat Courses now include ALL 6 Official GMAC CATs!*****



Intern
Joined: 12 Aug 2015
Posts: 6

Re: For a finite sequence of non zero numbers, the number of
[#permalink]
Show Tags
13 Aug 2015, 15:58
It seems to me that the answer is written explicitly in the question since the question says "the number of variations in sign is defined as the number of paires etc now what does it mean the number of variations? Isn't that the 3 negative signs attached the to the number? I don't quiet get what they mean the number of variations in sign



EMPOWERgmat Instructor
Status: GMAT Assassin/CoFounder
Affiliations: EMPOWERgmat
Joined: 19 Dec 2014
Posts: 13108
Location: United States (CA)

Re: For a finite sequence of non zero numbers, the number of
[#permalink]
Show Tags
14 Aug 2015, 08:35
Hi Dreams25, 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.... 1, 3, 2, 5, 4, 6 (1)(3) = 3 this is a negative produce, so we have 1 'variation' (3)(2) = 6 another 'variation' (2)(5) = 10 NOT a variation (since the product is positive) (5)(4) = 20 another 'variation' (4)(6) = 24 NOT a variation Total variations = 3 Final Answer: These types of questions can sometimes take a little time to solve, but they 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
Special Offer: Save $75 + GMAT Club Tests Free
Official GMAT Exam Packs + 70 Pt. Improvement Guarantee www.empowergmat.com/
*****Select EMPOWERgmat Courses now include ALL 6 Official GMAC CATs!*****



Intern
Joined: 12 Aug 2015
Posts: 6

Re: For a finite sequence of non zero numbers, the number of
[#permalink]
Show Tags
14 Aug 2015, 09:39
Thank you for your response, but I still don't get why do you call 1•3= 3 a variation. It's a variation compared to what? I can maybe understand a variation in sign when u take 2 negative numbers and multiply them u get a positive but here the negative 3 was negative already before the multiplication so what is the change that we refer as a variation? Thanks.



EMPOWERgmat Instructor
Status: GMAT Assassin/CoFounder
Affiliations: EMPOWERgmat
Joined: 19 Dec 2014
Posts: 13108
Location: United States (CA)

Re: For a finite sequence of non zero numbers, the number of
[#permalink]
Show Tags
14 Aug 2015, 09:49
Hi Dreams25, In this prompt, we have to follow the specific instructions that we were given: "...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." This defines what a 'variation' is (in this question); you just have to focus on this instruction, and apply it to the given sequence of numbers, to get the correct answer. 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
Special Offer: Save $75 + GMAT Club Tests Free
Official GMAT Exam Packs + 70 Pt. Improvement Guarantee www.empowergmat.com/
*****Select EMPOWERgmat Courses now include ALL 6 Official GMAC CATs!*****



Intern
Joined: 16 Dec 2015
Posts: 1

Re: For a finite sequence of non zero numbers, the number of
[#permalink]
Show Tags
18 Jan 2016, 15:06
(1) Tabulating the problem to see it more clearly.
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 ?
(2) Converting to a more compact version.
For a finite sequence of non zero numbers, V = number of pairs of consecutive terms in {1, 3, 2, 5, 4, 6} when product of the two consecutive terms is negative. What is V=?
The effort is spent in figuring out what V is. Do not get confused with consecutive terms and consecutive integers. Clearly the author of the problem wants you to confuse the concept of consecutive integers and terms, however, resist the temptation. In Set S = {a, b, c}, the terms a and b are consecutive terms, as well as b and c. However, a and c are not consecutive terms. As such, consecutive terms for {1, 3, 2, 5, 4, 6} are: {1, 3, 2, 5, 4, 6} = 1* 3 = 3 (negative) {1, 3, 2, 5, 4, 6} = 3 * 2 = 6 (negative) {1, 3, 2, 5, 4, 6} = 2* 5 = 10 (positive) {1, 3, 2, 5, 4, 6} = 5 * 4 = 20 (negative) {1, 3, 2, 5, 4, 6} = 4 * 6 = 24 (positive)
Note that you do not even need to multiply the numbers, however, you need to realize what happens when you multiply a negative times a positive or vice versa.
As a result of the analysis above, you can conclude that you would have three (3) negative pairs.



Director
Status: Come! Fall in Love with Learning!
Joined: 05 Jan 2017
Posts: 516
Location: India

Re: For a finite sequence of non zero numbers, the number of
[#permalink]
Show Tags
20 Mar 2017, 03:16
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 1, 3, 2, 5, 4, 6 1*3 = 1 3*2 = 6 2*5 = 10 5*4 = 20 4*6 = 24 3 negative terms . Variation is 3
_________________
GMAT Mentors




Re: For a finite sequence of non zero numbers, the number of &nbs
[#permalink]
20 Mar 2017, 03:16



Go to page
1 2
Next
[ 22 posts ]



