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Bunuel
What is the value of x?

(1) (|x| + 9)(x - 9) = 0
(2) (|x| - 9)(x + 9) = 0


IMO A

stmt 1: the first parenthesis will always be a positive number >0, so we want to focus on the second parenthesis.
solve for x-9= 0 you get x=9 suff.


stmt 2: because the absolute value is in the parenthesis containing the subtraction, x could either be 9 or -9. Insuff.
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Quote:
What is the value of x?

(1) (|x| + 9)(x - 9) = 0
(2) (|x| - 9)(x + 9) = 0

My attempt::
(1) (|x| + 9)(x - 9) = 0
This equation gives only one solution x=9.
as |x|+9 cannot be 0. (x-9) will be equal to 0.
=> x=9.
Sufficient.

(2) (|x| - 9)(x + 9) = 0
here either (|x|-9) can be 0 or (x+9) can be 0.
=> Either |x| = 9 => x = 9 or -9. OR x = -9.
Hence, Insufficient.

So Answer is A.
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Bunuel
What is the value of x?

(1) (|x| + 9)(x - 9) = 0
(2) (|x| - 9)(x + 9) = 0

statement 1 gives us two bracket : (|x|+9) and (x-9)
(|x|+9) has 9, which is positive and |x|, which is non negative. So (|x|+9) will always be positive.
Thus x-9 =0...........so x=9..
Sufficient

statement 2 gives us two bracket : (|x|-9) and (x+9)
Now, (|x|-9)=0, when |x|=9.
So x can be 9 or -9.
Insufficient


ans A
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hello guys,

Can someone explain this problem, i do not understand anything on the bracket difference. I do understand that |X| cannot be equal to -9 as an absolute value is always positie. Can someone explain this point ?

Thank you
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blanchif
hello guys,

Can someone explain this problem, i do not understand anything on the bracket difference. I do understand that |X| cannot be equal to -9 as an absolute value is always positie. Can someone explain this point ?

Thank you

I have added some more details in the earlier post. Please go through and if you still have any query, please revert.
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