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505-555 (Easy)|   Algebra|      
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rockroars
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Is x = 9? 10 Nov 2010, 04:53
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C
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Difficulty:

15% (low)

Question Stats:

79% (00:29) correct 21% (00:44) wrong based on 75 sessions

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Is x = 9?

(1) x^2 = 81
(2) (x - 9)(x - 5) = 0
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C
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Is x = 9? 10 Nov 2010, 05:00
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rockroars
Q. Is x=9

1. X^2 = 81
2. (X-9) (X-5)=0

Can some one please explain?
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(1) \(x^2=81\) --> \(x=9\) or \(x=-9\). Two different answers, hence not sufficient.
(2) \((x-9)(x-5)=0\) --> \(x=9\) or \(x=5\). Two different answers, hence not sufficient.

(1)+(2) Intersection of the values from (1) and (2) is \(x=9\), so the answer to the question "is x=9" will be YES. Sufficient.

Answer: C.
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Is x = 9? 10 Nov 2010, 05:14
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But if you combine 1 and 2 wont we have 3 solutions?? They are 9, -9 and 5.

How does combining 1 and 2 eliminate the other two solutions -9 and 5?
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Is x = 9? 10 Nov 2010, 05:38
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But if you combine 1 and 2 wont we have 3 solutions?? They are 9, -9 and 5.

How does combining 1 and 2 eliminate the other two solutions -9 and 5?
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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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Is x = 9? 28 Jul 2020, 03:52
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