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

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

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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.

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If a·b≠0, and (x+a)(x+b)=0, is x=a?  [#permalink]

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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
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If a·b≠0, and (x+a)(x+b)=0, is x=a?  [#permalink]

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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
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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]

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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]

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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
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Location: Russian Federation
Re: If a·b≠0, and (x+a)(x+b)=0, is x=a?  [#permalink]

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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
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Re: If a·b≠0, and (x+a)(x+b)=0, is x=a?  [#permalink]

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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
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Intern  Joined: 14 May 2014
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Concentration: Finance, General Management
Re: If a·b≠0, and (x+a)(x+b)=0, is x=a?  [#permalink]

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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
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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

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Re: Pls explain this Question.  [#permalink]

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

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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.

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Re: If a·b≠0, and (x+a)(x+b)=0, is x=a?  [#permalink]

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

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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.
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Re: If a·b≠0, and (x+a)(x+b)=0, is x=a?  [#permalink]

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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?

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Re: If a·b≠0, and (x+a)(x+b)=0, is x=a?  [#permalink]

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If a=-b, (x+a)(x+b)= x sq 2- a sq2=0
So x=a, sufficient

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Re: If a·b≠0, and (x+a)(x+b)=0, is x=a?  [#permalink]

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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..
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Re: If a·b≠0, and (x+a)(x+b)=0, is x=a?  [#permalink]

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