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If a·b≠0, and (x+a)(x+b)=0, is x=a?
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21 Jul 2014, 09:32
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If a·b≠0, and (x+a)(x+b)=0, is x=a? (1) x−b=0 (2) a=−b
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Re: If a·b≠0, and (x+a)(x+b)=0, is x=a?
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21 Jul 2014, 10:43
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. Answer: A.
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If a·b≠0, and (x+a)(x+b)=0, is x=a?
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11 Aug 2014, 01:53
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...



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If a·b≠0, and (x+a)(x+b)=0, is x=a?
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11 Aug 2014, 02:27
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 orb...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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Re: If a·b≠0, and (x+a)(x+b)=0, is x=a?
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11 Aug 2014, 07:53
As the question tells that x+a =0 Replace a with b, so xb=0 and x=b.............equation 1 Now st(2) is a=b therefore a=b Replace in eq 1 x= a. Answer is D. Where am I going wrong???



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Re: If a·b≠0, and (x+a)(x+b)=0, is x=a?
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11 Aug 2014, 08:22
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.



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Re: If a·b≠0, and (x+a)(x+b)=0, is x=a?
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11 Aug 2014, 08:35
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 orb...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?



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Re: If a·b≠0, and (x+a)(x+b)=0, is x=a?
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11 Aug 2014, 09:23
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 orb...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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Re: If a·b≠0, and (x+a)(x+b)=0, is x=a?
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12 Aug 2014, 23:36
a.b≠0 means a≠0 and b≠0.Now , let's move to ptions
<1>xb=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)(xa)=0 Implies x=a or x=a Implies can not be determined whether x=a
So , A is the answer



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Pls explain this Question.
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06 Sep 2014, 03:12
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)(xa) = 0 step 2) simplify: x^2a^2 = 0, x^2 = a^2 step 3) x = a, x = a
INSUFFICIENT
Answer is A



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Re: Pls explain this Question.
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06 Sep 2014, 07:32
(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 : xb=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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Re: If a·b≠0, and (x+a)(x+b)=0, is x=a?
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06 Sep 2014, 07:52



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Re: If a·b≠0, and (x+a)(x+b)=0, is x=a?
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14 Jun 2017, 19:48
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.
Answer: A. "Since b is not 0, then x cannot be b and b simultaneously" I am unable to understand and draw an analogy here, if (x2)(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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Re: If a·b≠0, and (x+a)(x+b)=0, is x=a?
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14 Jun 2017, 21:48
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.
Answer: A. "Since b is not 0, then x cannot be b and b simultaneously" I am unable to understand and draw an analogy here, if (x2)(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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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.
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Re: If a·b≠0, and (x+a)(x+b)=0, is x=a?
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14 Jun 2017, 22:11
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?
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Re: If a·b≠0, and (x+a)(x+b)=0, is x=a?
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14 Jun 2017, 22:41
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?
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14 Jun 2017, 22:49
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..
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Re: If a·b≠0, and (x+a)(x+b)=0, is x=a?
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