Summer is Coming! Join the Game of Timers Competition to Win Epic Prizes. Registration is Open. Game starts Mon July 1st.

 It is currently 17 Jul 2019, 02:25

### 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

# If a·b≠0, and (x+a)(x+b)=0, is x=a?

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

### Hide Tags

Intern
Joined: 17 Jun 2013
Posts: 4
If a·b≠0, and (x+a)(x+b)=0, is x=a?  [#permalink]

### Show Tags

21 Jul 2014, 10:32
2
13
00:00

Difficulty:

75% (hard)

Question Stats:

51% (01:48) correct 49% (02:00) wrong based on 249 sessions

### HideShow timer Statistics

If a·b≠0, and (x+a)(x+b)=0, is x=a?

(1) x−b=0

(2) a=−b
Math Expert
Joined: 02 Sep 2009
Posts: 56267
Re: If a·b≠0, and (x+a)(x+b)=0, is x=a?  [#permalink]

### Show Tags

21 Jul 2014, 11:43
2
5
If a·b≠0, and (x+a)(x+b)=0, is x=a?

a·b≠0 implies that none of them is 0.

$$(x+a)(x+b)=0$$ --> $$x=-a$$ or $$x=-b$$.

(1) x−b=0 --> $$x=b$$. Since b is not 0, then x cannot be b and -b simultaneously (x=b and x=-b would mean that b=-b --> b=0), hence $$x\neq{-b}$$. So, $$x=-a$$. The question asks whether $$x=a$$: again since a is not 0, then x cannot be a and -a simultaneously, hence $$x\neq{a}$$. We have a NO answer to the question. Sufficient.

(2) a=−b --> $$x=-a$$ or $$x=-b=a$$. So, x may or may not equal to a. Not sufficient.

_________________
##### General Discussion
Intern
Joined: 03 Feb 2014
Posts: 2
Location: Russian Federation
If a·b≠0, and (x+a)(x+b)=0, is x=a?  [#permalink]

### Show Tags

11 Aug 2014, 02:53
1
If a·b≠0, and (x+a)(x+b)=0, is x=a?

(1) x−b=0

(2) a=−b

Struggle to understand the concept behind elimination of possible roots, which lead to Suff/Insuff...
Director
Joined: 25 Apr 2012
Posts: 668
Location: India
GPA: 3.21
WE: Business Development (Other)
If a·b≠0, and (x+a)(x+b)=0, is x=a?  [#permalink]

### Show Tags

11 Aug 2014, 03:27
PikkuMyy wrote:
If a·b≠0, and (x+a)(x+b)=0, is x=a?

(1) x−b=0

(2) a=−b

Struggle to understand the concept behind elimination of possible roots, which lead to Suff/Insuff...

Give $$a,b \neq{0}$$ and x=-a or x=-b...we need to find whether x=a

St 1 says x=b and we also know that x=-a or-b...Now if x=-b then b=-b or 2b=0 but we are told that$$b\neq{0}$$

Hence x =-a and $$x\neq{a}$$

St 2 says a=-b and we have x=-b or -a.
If x=-b then x=a...
but if x=-a then $$x\neq{a}$$

since x can be equal to a or not equal to a therefore St 2 is not sufficient
Ans is A
_________________

“If you can't fly then run, if you can't run then walk, if you can't walk then crawl, but whatever you do you have to keep moving forward.”
Manager
Joined: 05 Jun 2014
Posts: 61
GMAT 1: 630 Q42 V35
Re: If a·b≠0, and (x+a)(x+b)=0, is x=a?  [#permalink]

### Show Tags

11 Aug 2014, 08:53
As the question tells that x+a =0
Replace a with -b, so x-b=0 and x=b.............equation 1
Now st(2) is a=-b therefore -a=b
Replace in eq 1 x= -a.
Where am I going wrong???
Manager
Joined: 05 Jun 2014
Posts: 61
GMAT 1: 630 Q42 V35
Re: If a·b≠0, and (x+a)(x+b)=0, is x=a?  [#permalink]

### Show Tags

11 Aug 2014, 09:22
Or x=-a
and st 2 tells that a=-b so -a=b
Replacing above equation becomes x=b, so (x+b) isnt equal to 0 in the given equation.
Which means x+a =0 and x=-a.
Intern
Joined: 03 Feb 2014
Posts: 2
Location: Russian Federation
Re: If a·b≠0, and (x+a)(x+b)=0, is x=a?  [#permalink]

### Show Tags

11 Aug 2014, 09:35
WoundedTiger wrote:
PikkuMyy wrote:
If a·b≠0, and (x+a)(x+b)=0, is x=a?

(1) x−b=0

(2) a=−b

Struggle to understand the concept behind elimination of possible roots, which lead to Suff/Insuff...

Give $$a,b \neq{0}$$ and x=-a or x=-b...we need to find whether x=a

St 1 says x=b and we also know that x=-a or-b...Now if x=-b then b=-b or 2b=0 but we are told that$$b\neq{0}$$

Hence x =-a and $$x\neq{a}$$

St 2 says a=-b and we have x=-b or -a...a=-b so we have a+b=0 or or a=-a or 2a=0 but a\neq{0}...so a+b=0 so a=-b but we don't know whether x=-a or -b....if x=-b then x=a but x=-a then x\neq{a}

St1 is sufficient as st2 does not tell you relation between x,a and b

Thanks! It clears up St.1.
As per St.2, does your comment mean that no need to dive in checking possibilities if there is no x mentioned in the statement stem?
Director
Joined: 25 Apr 2012
Posts: 668
Location: India
GPA: 3.21
WE: Business Development (Other)
Re: If a·b≠0, and (x+a)(x+b)=0, is x=a?  [#permalink]

### Show Tags

11 Aug 2014, 10:23
PikkuMyy wrote:
WoundedTiger wrote:
PikkuMyy wrote:
If a·b≠0, and (x+a)(x+b)=0, is x=a?

(1) x−b=0

(2) a=−b

Struggle to understand the concept behind elimination of possible roots, which lead to Suff/Insuff...

Give $$a,b \neq{0}$$ and x=-a or x=-b...we need to find whether x=a

St 1 says x=b and we also know that x=-a or-b...Now if x=-b then b=-b or 2b=0 but we are told that$$b\neq{0}$$

Hence x =-a and $$x\neq{a}$$

St 2 says a=-b and we have x=-b or -a...a=-b so we have a+b=0 or or a=-a or 2a=0 but a\neq{0}...so a+b=0 so a=-b but we don't know whether x=-a or -b....if x=-b then x=a but x=-a then x\neq{a}

St1 is sufficient as st2 does not tell you relation between x,a and b

Thanks! It clears up St.1.
As per St.2, does your comment mean that no need to dive in checking possibilities if there is no x mentioned in the statement stem?

I have edited my post...can you please check now.....and let me know if you have any doubt
_________________

“If you can't fly then run, if you can't run then walk, if you can't walk then crawl, but whatever you do you have to keep moving forward.”
Intern
Joined: 14 May 2014
Posts: 20
Concentration: Finance, General Management
Re: If a·b≠0, and (x+a)(x+b)=0, is x=a?  [#permalink]

### Show Tags

13 Aug 2014, 00:36
a.b≠0 means a≠0 and b≠0.Now , let's move to ptions

<1>x-b=0
It means if we apply x=b in given equation (x+a)(x+b)=0 then (x+a)*2b=0
Implies x+a=0 as b≠0
implies x=-a
if a would have been 0 then x=-a=a=0. But a≠0
so x=-a imples x≠a
Hence,Option 1 is duffienct to answer the question

<2>a=-b
It means if we apply a=-b in given equation (x+a)(x+b)=0 then (x+a)(x-a)=0
Implies x=-a or x=a
Implies can not be determined whether x=a

So , A is the answer
Intern
Joined: 17 Jun 2014
Posts: 15
GMAT 1: 760 Q51 V42
GPA: 3.3
WE: Engineering (Manufacturing)
Pls explain this Question.  [#permalink]

### Show Tags

06 Sep 2014, 04:12
1
Givens:
1. a*b =/= 0 means that neither a nor b can be 0.
2. (x+a)(x+b) = 0

1) x - b = 0

step 1) x = b
step 2) plug into given 2: (b+a)(b+b) = 0
step 3) simplify: (b+a)(2*b) = 0, (b+a) = 0, a = -b
step 4) substitute: a = -x

SUFFICIENT

2) a = -b

step 1) substitute into given 2: (x+a)(x-a) = 0
step 2) simplify: x^2-a^2 = 0, x^2 = a^2
step 3) x = a, x = -a

INSUFFICIENT

Manager
Joined: 21 Sep 2012
Posts: 212
Location: United States
Concentration: Finance, Economics
Schools: CBS '17
GPA: 4
WE: General Management (Consumer Products)
Re: Pls explain this Question.  [#permalink]

### Show Tags

06 Sep 2014, 08:32
(x+a)(x+b)=0...given
so x=-a and b can take any value or
x=-b and a can take any value or
x=-a=-b

statement 1 : x-b=0
x=b, since x=b then x=-a in order to make (x+a)(x+b)=0
Therefore x can't be equal to a.
Statement is sufficient

statement 2 : a=−b
substitute in x=-a or x=-b
so x=b or x=a
we don't have definite answer. statement is insufficient.

Ans- A
Math Expert
Joined: 02 Sep 2009
Posts: 56267
Re: If a·b≠0, and (x+a)(x+b)=0, is x=a?  [#permalink]

### Show Tags

06 Sep 2014, 08:52
vivekvijayan wrote:
Q. If a•b≠0, and (x+a)(x+b)=0, is x=a?
(1) x−b=0
(2) a=−b

Merging similar topics. Please refer to the discussion above.

Also, please read carefully and follow: rules-for-posting-please-read-this-before-posting-133935.html Pay attention to rule 3. Thank you.
_________________
Intern
Joined: 15 Apr 2017
Posts: 8
Location: India
GMAT 1: 690 Q49 V33
GPA: 3.3
Re: If a·b≠0, and (x+a)(x+b)=0, is x=a?  [#permalink]

### Show Tags

14 Jun 2017, 20:48
Bunuel wrote:
If a·b≠0, and (x+a)(x+b)=0, is x=a?

a·b≠0 implies that none of them is 0.

$$(x+a)(x+b)=0$$ --> $$x=-a$$ or $$x=-b$$.

(1) x−b=0 --> $$x=b$$. Since b is not 0, then x cannot be b and -b simultaneously (x=b and x=-b would mean that b=-b --> b=0), hence $$x\neq{-b}$$. So, $$x=-a$$. The question asks whether $$x=a$$: again since a is not 0, then x cannot be a and -a simultaneously, hence $$x\neq{a}$$. We have a NO answer to the question. Sufficient.

(2) a=−b --> $$x=-a$$ or $$x=-b=a$$. So, x may or may not equal to a. Not sufficient.

"Since b is not 0, then x cannot be b and -b simultaneously"

I am unable to understand and draw an analogy here, if (x-2)(x+2) = 0 is possible with 2 and -2 as its roots, then how can we say that if x=b and x=-b would mean b = 0?
Math Expert
Joined: 02 Sep 2009
Posts: 56267
Re: If a·b≠0, and (x+a)(x+b)=0, is x=a?  [#permalink]

### Show Tags

14 Jun 2017, 22:48
stressed wrote:
Bunuel wrote:
If a·b≠0, and (x+a)(x+b)=0, is x=a?

a·b≠0 implies that none of them is 0.

$$(x+a)(x+b)=0$$ --> $$x=-a$$ or $$x=-b$$.

(1) x−b=0 --> $$x=b$$. Since b is not 0, then x cannot be b and -b simultaneously (x=b and x=-b would mean that b=-b --> b=0), hence $$x\neq{-b}$$. So, $$x=-a$$. The question asks whether $$x=a$$: again since a is not 0, then x cannot be a and -a simultaneously, hence $$x\neq{a}$$. We have a NO answer to the question. Sufficient.

(2) a=−b --> $$x=-a$$ or $$x=-b=a$$. So, x may or may not equal to a. Not sufficient.

"Since b is not 0, then x cannot be b and -b simultaneously"

I am unable to understand and draw an analogy here, if (x-2)(x+2) = 0 is possible with 2 and -2 as its roots, then how can we say that if x=b and x=-b would mean b = 0?

From the stem we have that $$x=-b$$ or $$x=-a$$.

(1) says that $$x=b$$. So, b = -b or b = -a (from above).

b = -b implies that b = 0, which cannot be true because we are also given that b ≠ 0. Thus, b = -a.

So we have that x = b = -a. The question asks whether x = a, therefore the question becomes whether -a = a. This would imply that a = 0 but we know that a ≠ 0, thus -a ≠ a and x ≠ a.

Hope it's clear.
_________________
Director
Joined: 13 Mar 2017
Posts: 731
Location: India
Concentration: General Management, Entrepreneurship
GPA: 3.8
WE: Engineering (Energy and Utilities)
Re: If a·b≠0, and (x+a)(x+b)=0, is x=a?  [#permalink]

### Show Tags

14 Jun 2017, 23:11
abhisheksharma85 wrote:
If a·b≠0, and (x+a)(x+b)=0, is x=a?

(1) x−b=0

(2) a=−b

a.b =/= 0
-> a=/=0, b=/=0

(x+a)(x+b) = 0
-> x= -a or x=-b ..........(i)
Statement 1: x= b , so x=/= -b (as b=/=0)
-> x=-a so it is sufficient for ques x=a?

Statement 2: a=-b
From (i), x = -a or x = a... So it is not sufficient for ques x=a?

_________________
CAT 2017 (98.95) & 2018 (98.91) : 99th percentiler
UPSC Aspirants : Get my app UPSC Important News Reader from Play store.

MBA Social Network : WebMaggu

Appreciate by Clicking +1 Kudos ( Lets be more generous friends.)

What I believe is : "Nothing is Impossible, Even Impossible says I'm Possible" : "Stay Hungry, Stay Foolish".
Intern
Joined: 13 May 2017
Posts: 8
Re: If a·b≠0, and (x+a)(x+b)=0, is x=a?  [#permalink]

### Show Tags

14 Jun 2017, 23:41
If a=-b, (x+a)(x+b)= x sq 2- a sq2=0
So x=a, sufficient

Sent from my iPhone using GMAT Club Forum
Director
Joined: 13 Mar 2017
Posts: 731
Location: India
Concentration: General Management, Entrepreneurship
GPA: 3.8
WE: Engineering (Energy and Utilities)
Re: If a·b≠0, and (x+a)(x+b)=0, is x=a?  [#permalink]

### Show Tags

14 Jun 2017, 23:49
lalitmach22 wrote:
If a=-b, (x+a)(x+b)= x sq 2- a sq2=0
So x=a, sufficient

Sent from my iPhone using GMAT Club Forum

x^2 - a^2 = 0
-> x^2 = a^2
-> x= +/-a not only a .. Hope u got it..
_________________
CAT 2017 (98.95) & 2018 (98.91) : 99th percentiler
UPSC Aspirants : Get my app UPSC Important News Reader from Play store.

MBA Social Network : WebMaggu

Appreciate by Clicking +1 Kudos ( Lets be more generous friends.)

What I believe is : "Nothing is Impossible, Even Impossible says I'm Possible" : "Stay Hungry, Stay Foolish".
Non-Human User
Joined: 09 Sep 2013
Posts: 11668
Re: If a·b≠0, and (x+a)(x+b)=0, is x=a?  [#permalink]

### Show Tags

16 Aug 2018, 15:50
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.
_________________
Re: If a·b≠0, and (x+a)(x+b)=0, is x=a?   [#permalink] 16 Aug 2018, 15:50
Display posts from previous: Sort by

# If a·b≠0, and (x+a)(x+b)=0, is x=a?

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

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