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What is the value of x^2 − 5x?

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by VJesus12 » Thu Dec 21, 2017 11:45 am
What is the value of x^2 − 5x?

(1) x(x − 4) = x − 4

(2) x(x − 12) = −16 − 4x

The OA is the option D.

How can I use the statement (2) to get an answer here? Experts, can you help me here, please?
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Source: — Data Sufficiency |
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by elias.latour.apex » Thu Dec 28, 2017 4:43 pm
Normally a quadratic equation yields two possible answers, but not always. The exception is when the equation is a perfect square.

Statement 2 states:

x(x - 12) = -16 - 4x

Which becomes:

x^2 - 12x + 4x + 16 = 0
x^2 - 8x + 16 = 0
(x-4)(x-4)=0

So x must equal 4.

The problem, really, is statement 1.
X could equal 1, in which case 1(1-3) = (1-3) --> -2 = -2
OR
X could equal 4, in which case 4(4-4)=(4-4) --> 0 = 0

so you might be tempted to think that statement 1 is not sufficient because it yields two possible values for x.

However, 1^2 - 5(1) = -4 AND
4^2 - 5(4) = 16-20 = -4
Elias Latour
Verbal Specialist @ ApexGMAT
blog.apexgmat.com
+1 (646) 736-7622
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