Is x = 9?

On the GMAT, two data sufficiency statements always provide TRUE information and these statements never contradict each other.

From (1) we have that \(x=9\) OR \(x=-9\);
From (2) we have that \(x=9\) OR \(x=5\).

In order BOTH statements to be true x must be 9 only. In other words -5 can not be the value of \(x\) as \(x=-5\) doesn't satisfy \(x^2=81\), the same for -9, it can not be the value of \(x\) as \(x=-9\) doesn't satisfy \((x-9)(x-5)=0\).

In DS questions when you have some values for an unknown from (1) and (2) then when you consider (1)+(2) you will have that given unknown can take only intersection of these values (common values, common range).

For example: Is -1<x<1?

(1) x>0, not sufficient.
(2) x<1/2, not sufficient.

(1)+(2) Intersection of the ranges from (1) and (2) is 0<x<1/2, so the answer is YES. Sufficient.

Answer: C.

Alternately you can solve the original question as follows: from (1) \(x^2=81\) and from (2) \((x-9)(x-5)=x^2-14x+45=0\) --> \(x^2-14x+45=81-14x+45=0\) --> \(14x=126\) --> \(x=9\).

Hope it's clear.

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