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Is x = 1?

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by VJesus12 » Thu Jun 14, 2018 1:44 am

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Is x = 1? $$(1)\ \ x=x^{3^0}\ .$$ $$(2)\ \ x^2-2x+1=0$$ The OA is the option B.

Why is not sufficient the first statement? May someone gives me some help?
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Source: — Data Sufficiency |

by GMATGuruNY » Thu Jun 14, 2018 3:14 am
VJesus12 wrote:Is x = 1? $$(1)\ \ x=x^{3^0}\ .$$ $$(2)\ \ x^2-2x+1=0$$

Why is not sufficient the first statement? May someone gives me some help?
Statement 1:
Substituting 3� = 1 into the given equation, we get:
x = x¹.
Case 1: x=0
In this case, the answer to the question stem is NO.
Case 2: x=1
In this case, the answer to the question stem is YES.
Since the answer is NO in Case 1 but YES in Case 2, INSUFFICIENT.

Statement 2:
x² - 2x + 1 = 0
(x-1)(x-1) = 0
x = 1.
Thus, the answer to the question stem is YES.
SUFFICIENT.

The correct answer is B.
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