Author 
Message 
TAGS:

Hide Tags

Math Expert
Joined: 02 Sep 2009
Posts: 45422

Is the product of three consecutive integers negative? [#permalink]
Show Tags
28 Feb 2014, 04:14
3
This post received KUDOS
Expert's post
1
This post was BOOKMARKED
Question Stats:
43% (00:57) correct 57% (01:06) wrong based on 153 sessions
HideShow timer Statistics



Math Expert
Joined: 02 Sep 2009
Posts: 45422

Re: Is the product of three consecutive integers negative? [#permalink]
Show Tags
28 Feb 2014, 04:14
1
This post received KUDOS
Expert's post
3
This post was BOOKMARKED
SOLUTIONIs the product of three consecutive integers negative?(1) The sum of the integers is equal to the product of the integers. Let the three consecutive integers be \((x1)\), \(x\), and \(x+1\), so we are given that \((x1)+x+(x+1)=(x1)x(x+1)\) > \(3x=x(x^21)\) > \(x(x^24)=0\) > \(x=2\), \(x=0\), or \(x=2\). The set can be: {3, 2, 1}, {1, 0, 1}, or {1, 2, 3}. Not sufficient. (2) At least one of the integers is negative. We can have three cases: (i) All three integers are negative. In this case the product will obviously be negative. (ii) Two of the integers are negative: {2, 1, 0}. In this case the product will be zero. (iii) Only one of the integers is negative: {1, 0, 1}. In this case the product will be zero. Not sufficient. (1)+(2) We still can have 2 sets: {3, 2, 1} and {1, 0, 1}. So, the product can be negative as well as zero. Not sufficient. Answer: E.
_________________
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: 24 Sep 2011
Posts: 1

Re: Is the product of three consecutive integers negative? [#permalink]
Show Tags
28 Feb 2014, 06:38
1
This post received KUDOS
Consider consecutive integers as a1, a, a+1 1. According to statement 1 , Sum = product so 3a= a ( a^2 1) solving we get a=0, a=2 , +2 three values of a so , integers are 1, 0, 1 3,2,1, and 1, 2 , 3 as we cannot answer the target question with certainty ..Statement is insufficient 2. Second statement : clearly insufficient , as when 1 is negative = product is ve 2 are ve = product is +ve So 2nd statement is also insufficient
Combining both we get consecutive integers as : 1, 0 , 1 ===product is zero 3, 2, 1 ===product is ve
E is the answer



Intern
Joined: 30 Nov 2013
Posts: 29

Re: Is the product of three consecutive integers negative? [#permalink]
Show Tags
28 Feb 2014, 07:09
My Answer is "C"
Statement 1 is insufficient for example 1,2,3 have product and sum and product of 6 While 1,2,3 have a sum and product of 6 so there are two possibilities.
Statement 2 is insufficient because at least one negative means that there could be 1,2 or 3 numbers negative and each will have a different outcome and in the case of 1,0,1 the product is 0.
However, statement 1 and 2 taken together mean that the three numbers have to be negative and have a sum and product that is equal . So yes "C" means the product is negative !!
What is OA !!



Intern
Joined: 02 Oct 2013
Posts: 12

Re: Is the product of three consecutive integers negative? [#permalink]
Show Tags
28 Feb 2014, 15:07
1
This post received KUDOS
Statement 1: can be satisfied with (1,2,3) sum =6, product = 6 can be satisfied with (1,2,3) sum = 6, product = 6
Insufficient
Statement 2: clearly insufficient
1 and 2: can be satisfied with (1,2,3) can be satisfied with (1,0,1) product is not negative
E



Math Expert
Joined: 02 Sep 2009
Posts: 45422

Re: Is the product of three consecutive integers negative? [#permalink]
Show Tags
03 Mar 2014, 12:22
SOLUTIONIs the product of three consecutive integers negative?(1) The sum of the integers is equal to the product of the integers. Let the three consecutive integers be \((x1)\), \(x\), and \(x+1\), so we are given that \((x1)+x+(x+1)=(x1)x(x+1)\) > \(3x=x(x^21)\) > \(x(x^24)=0\) > \(x=2\), \(x=0\), or \(x=2\). The set can be: {3, 2, 1}, {1, 0, 1}, or {1, 2, 3}. Not sufficient. (2) At least one of the integers is negative. We can have three cases: (i) All three integers are negative. In this case the product will obviously be negative. (ii) Two of the integers are negative: {2, 1, 0}. In this case the product will be zero. (iii) Only one of the integers is negative: {1, 0, 1}. In this case the product will be zero. Not sufficient. (1)+(2) We still can have 2 sets: {3, 2, 1} and {1, 0, 1}. So, the product can be negative as well as zero. Not sufficient. Answer: E.
_________________
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



Retired Moderator
Joined: 20 Dec 2013
Posts: 180
Location: United States (NY)
GMAT 1: 640 Q44 V34 GMAT 2: 710 Q48 V40 GMAT 3: 720 Q49 V40
GPA: 3.16
WE: Consulting (Venture Capital)

Re: Is the product of three consecutive integers negative? [#permalink]
Show Tags
03 Mar 2014, 20:54
great example of why you can't blindly reduce equations [e.g. (x1)x(x+1)=3x > (x1)(x+1)=3] thanks Bunuel.
_________________
MY GMAT BLOG  ADVICE  OPINIONS  ANALYSIS



Math Revolution GMAT Instructor
Joined: 16 Aug 2015
Posts: 5452
GPA: 3.82

Is the product of three consecutive integers negative? [#permalink]
Show Tags
08 Sep 2015, 07:24
Forget conventional ways of solving math questions. In DS, Variable approach is the easiest and quickest way to find the answer without actually solving the problem. Remember equal number of variables and equations ensures a solution. Is the product of three consecutive integers negative? (1) The sum of the integers is equal to the product of the integers. (2) At least one of the integers is negative. In the original condition we have three consecutive integers thus we just need to know the first term, thus we have 1 variable. Since we need 1 equation, D is likely the answer. In case of 1), for (3,2,1) the answer is yes, for (1,0,1) the answer is no, and same for (1,2,3). The answer is not unique, therefore it is not sufficient. In case of 2), for (1,0,1) the answer is no, and for (3,2,1) the answer is yes. Thus the condition is not sufficient. Using both 1) & 2) together, for (1,0,1) the answer is no, for (3,2,1) the answer is yes. therefore the conditions are not sufficient. The answer is E.
_________________
MathRevolution: Finish GMAT Quant Section with 10 minutes to spare The oneandonly World’s First Variable Approach for DS and IVY Approach for PS with ease, speed and accuracy. "Only $79 for 3 month Online Course" "Free Resources30 day online access & Diagnostic Test" "Unlimited Access to over 120 free video lessons  try it yourself"



NonHuman User
Joined: 09 Sep 2013
Posts: 6851

Re: Is the product of three consecutive integers negative? [#permalink]
Show Tags
13 Mar 2018, 02:01
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




Re: Is the product of three consecutive integers negative?
[#permalink]
13 Mar 2018, 02:01






