GMAT Question of the Day - Daily to your Mailbox; hard ones only

It is currently 20 Sep 2018, 01:57

Close

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
Your Progress

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

Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.

Close

Request Expert Reply

Confirm Cancel

Is the product of three consecutive integers negative?

  new topic post reply Question banks Downloads My Bookmarks Reviews Important topics  
Author Message
TAGS:

Hide Tags

Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 49271
Is the product of three consecutive integers negative?  [#permalink]

Show Tags

New post 28 Feb 2014, 04:14
3
6
00:00
A
B
C
D
E

Difficulty:

  95% (hard)

Question Stats:

43% (01:06) correct 57% (01:15) wrong based on 218 sessions

HideShow timer Statistics

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.

_________________

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?
Extra-hard Quant Tests with Brilliant Analytics

Most Helpful Expert Reply
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 49271
Re: Is the product of three consecutive integers negative?  [#permalink]

Show Tags

New post 28 Feb 2014, 04:14
1
4
SOLUTION

Is 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 \((x-1)\), \(x\), and \(x+1\), so we are given that \((x-1)+x+(x+1)=(x-1)x(x+1)\) --> \(3x=x(x^2-1)\) --> \(x(x^2-4)=0\) --> \(x=-2\), \(x=0\), 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?
Extra-hard Quant Tests with Brilliant Analytics

General Discussion
Intern
Intern
avatar
Joined: 24 Sep 2011
Posts: 1
Re: Is the product of three consecutive integers negative?  [#permalink]

Show Tags

New post 28 Feb 2014, 06:38
1
Consider consecutive integers as
a-1, 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
Intern
avatar
Joined: 30 Nov 2013
Posts: 27
Re: Is the product of three consecutive integers negative?  [#permalink]

Show Tags

New post 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
Intern
avatar
Joined: 02 Oct 2013
Posts: 12
Re: Is the product of three consecutive integers negative?  [#permalink]

Show Tags

New post 28 Feb 2014, 15:07
1
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
User avatar
V
Joined: 02 Sep 2009
Posts: 49271
Re: Is the product of three consecutive integers negative?  [#permalink]

Show Tags

New post 03 Mar 2014, 12:22
1
SOLUTION

Is 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 \((x-1)\), \(x\), and \(x+1\), so we are given that \((x-1)+x+(x+1)=(x-1)x(x+1)\) --> \(3x=x(x^2-1)\) --> \(x(x^2-4)=0\) --> \(x=-2\), \(x=0\), 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?
Extra-hard Quant Tests with Brilliant Analytics

Retired Moderator
User avatar
Joined: 20 Dec 2013
Posts: 179
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)
GMAT ToolKit User Premium Member Reviews Badge
Re: Is the product of three consecutive integers negative?  [#permalink]

Show Tags

New post 03 Mar 2014, 20:54
great example of why you can't blindly reduce equations [e.g. (x-1)x(x+1)=3x --> (x-1)(x+1)=3]
thanks Bunuel.
_________________

MY GMAT BLOG - ADVICE - OPINIONS - ANALYSIS

Math Revolution GMAT Instructor
User avatar
V
Joined: 16 Aug 2015
Posts: 6214
GMAT 1: 760 Q51 V42
GPA: 3.82
Premium Member
Is the product of three consecutive integers negative?  [#permalink]

Show Tags

New post 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 one-and-only World’s First Variable Approach for DS and IVY Approach for PS with ease, speed and accuracy.
"Only $99 for 3 month Online Course"
"Free Resources-30 day online access & Diagnostic Test"
"Unlimited Access to over 120 free video lessons - try it yourself"

Intern
Intern
avatar
B
Joined: 30 Apr 2018
Posts: 19
CAT Tests
Re: Is the product of three consecutive integers negative?  [#permalink]

Show Tags

New post 18 Jun 2018, 12:03
Hi Bunuel , great question - but can you please explain why we cannot blindly cancel upon the "x's" on both sides of the equation you used ( i.e. (x−1)x(x+1)(x−1)+x+(x+1)=(x−1)x(x+1) --> 3x )

I have noticed you not cancelling out such scenarios in multiple questions (including not drawing direct conclusions in ratio based questions as well) - any reason why? and any guidance on when not to cancel out such cases??

TIA!
Manager
Manager
avatar
B
Status: Student
Joined: 07 Jun 2018
Posts: 61
Location: India
Concentration: Finance, Marketing
GPA: 4
GMAT ToolKit User
Re: Is the product of three consecutive integers negative?  [#permalink]

Show Tags

New post 18 Jun 2018, 14:03
NidSha wrote:
Hi Bunuel , great question - but can you please explain why we cannot blindly cancel upon the "x's" on both sides of the equation you used ( i.e. (x−1)x(x+1)(x−1)+x+(x+1)=(x−1)x(x+1) --> 3x )

I have noticed you not cancelling out such scenarios in multiple questions (including not drawing direct conclusions in ratio based questions as well) - any reason why? and any guidance on when not to cancel out such cases??

TIA!


Because that cancels out one result. You will notice that if you cut that x out, you will not get X=0 and thus believe that there is only one answer.

Posted from my mobile device
Manager
Manager
User avatar
B
Joined: 07 Feb 2017
Posts: 179
Re: Is the product of three consecutive integers negative?  [#permalink]

Show Tags

New post 18 Jun 2018, 14:49
I.
x+x+1+x+2=x(x+1)(x+2)
3(x+1)=x(x+1)(x+2)
x=-1 then cancel x+1
3=x(x+2)
x=1, -3
1, 2, 3 Product is positive
-1, 0, 1 Product is zero
-3, -2, -1 Product is negative
Insufficient

II.
Insufficient

I and II.
Insufficient

Answer E
Intern
Intern
avatar
B
Joined: 30 Apr 2018
Posts: 19
CAT Tests
Re: Is the product of three consecutive integers negative?  [#permalink]

Show Tags

New post 18 Jun 2018, 17:33
Antreev - so should i generalize that each time we are trying to find solutions for an unknown variable, such cases should not be cancelled ?

Though this confuses me - don't we usually arrive to such equations to find possible solutions for an unknown variable?
DS Forum Moderator
avatar
P
Joined: 22 Aug 2013
Posts: 1343
Location: India
Premium Member
Re: Is the product of three consecutive integers negative?  [#permalink]

Show Tags

New post 18 Jun 2018, 20:58
1
NidSha wrote:
Antreev - so should i generalize that each time we are trying to find solutions for an unknown variable, such cases should not be cancelled ?

Though this confuses me - don't we usually arrive to such equations to find possible solutions for an unknown variable?


Hello Nidsha

If you could take particular example then it would be better to discuss question by question
It varies from question to question. Eg, if we have:
3x(x-1) = x(x+1)

then we cannot cancel x from both sides, because x could be '0' also, and cancellation by '0' (division by 0) is not permissible.

But in the above equation if we know that x is a non-zero number, then we can cancel x from both sides.

I would request you to take example of that particular question that you are talking about so we could discuss it in detail.
Intern
Intern
avatar
B
Joined: 30 Apr 2018
Posts: 19
CAT Tests
Re: Is the product of three consecutive integers negative?  [#permalink]

Show Tags

New post 19 Jun 2018, 20:27
amanvermagmat - thank you so much for this explanation - i think i was hugely missing the '0' based fact/' exception while looking at such equations - explains it all now - thank you so much again!
Re: Is the product of three consecutive integers negative? &nbs [#permalink] 19 Jun 2018, 20:27
Display posts from previous: Sort by

Is the product of three consecutive integers negative?

  new topic post reply Question banks Downloads My Bookmarks Reviews Important topics  

Events & Promotions

PREV
NEXT


GMAT Club MBA Forum Home| About| Terms and Conditions and Privacy Policy| GMAT Club Rules| Contact| Sitemap

Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne

Kindly note that the GMAT® test is a registered trademark of the Graduate Management Admission Council®, and this site has neither been reviewed nor endorsed by GMAC®.