If ab ≠ 0, and (x + a)(x + b) = 0, is x = a ? (1) x − b = 0 (2) a = -b

Question

If ab ≠ 0, and (x + a)(x + b) = 0, is x = a ?

(1) x − b = 0

(2) a = −b

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GMATinsight · Answer

Given: x = -a or -b

Question: Is x = a?

Statement 1 : x − b = 0 
i.e. x = b
i.e. x ≠ -b i.e. x = -a

SUFFICIENT

Statement 2 : a = −b

i.e. if x = -a, then x = b NO
i.e. if x = -b, then x = a YES

i..e. Both conditions are possible hence

NOT SUFFICIENT

Answer: Option A

GCMEMBER · Answer

If ab ≠ 0, and (x + a)(x + b) = 0, is x = a ?

(1) x − b = 0
x = b
(x + a)(x + b) = 0
(x + a)(b + b) = 0
(x + a) = 0
x = -a
Sufficient

2) a = −b
(x + a)(x + b) = 0
(x + a)(x - a) = 0
x = a or -a
Not sufficient

Option A

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TarunKumar1234 · Answer

If ab ≠ 0, and (x + a)(x + b) = 0, is x = a ? Stat1: x − b = 0, then, (x +a)*2b = 0 or, x = -a. Sufficient. Stat2: a = −b, we don't know any relationship with x. Not Sufficient. So, I think A.

HoneyLemon · Answer

imo  A  
If ab ≠ 0, and (x + a)(x + b) = 0, is x = a ?

(1) x − b = 0

=> x=b . So X = -a . Hence is x = a ? => Ans is No .
 St 1 is  Sufficient  .
 
(2) a = −b
Hence 
(x + a)(x -a) = 0
=> x^2 = a^2 
=> x = +- a , is x = a ? .. The ans is both Yes and No . 
 St 2 is  NOt Sufficient  .

Hence Ans is  A

EgmatQuantExpert · Answer

Solution

Given  
  ab ≠ 0
 (x + a)(x + b) = 0

To find  
We need to determine
 • whether x = a

Approach and Working out

• Question Statement Analysis
 o ab ≠ 0
  a ≠ 0
 b ≠ 0 
o (x + a)(x + b) = 0
  x + a = 0 or x + b = 0
 x = -a or x = -b --------(1)

• Statement 1
 o x – b = 0 
  x = b --------(2)  
 • So, x ≠ -b. -------(3)
 o Since, if x= -b as well, then from (2), b = -b, which means b = 0. (Impossible)  
 • From (1) and (3), x = -a.
 o Again, this means that x ≠ a, since a ≠ 0.
o So, we get a sure NO.
o Statement 1 is sufficient alone.

• Statement 2
 o a = -b --------(3)
  From question statement, we have x = -a or x = -b.

• Case 1: If x = -a, then from (3), we get x = b.
 o Now, if x = -a, it cannot be equal to a as well.
  Since -a ≠ a (since a ≠ 0) 
o So, we get NO from this case.

• Case 2: If x = -b, then from (3), we get x = a.
 o So, we get YES from this case.
o Statement 2 is insufficient alone.

Thus, option A is the correct answer.
  Correct Answer: Option A

bumpbot · Answer

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If ab ≠ 0, and (x + a)(x + b) = 0, is x = a ? (1) x − b = 0 (2) a = -b

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