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Priyaranjan
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Statement 1: |x + 1| = 2|x - 1|Priyaranjan wrote:Q. Is |x|< 1?
I) |x + 1| = 2|x - 1|
II) |x - 3| > 0
Case 1: signs unchanged
x+1 = 2(x-1)
x+1 = 2x-2
3=x
x=3.
In this case, |x|>1, so the answer to the question stem is NO.
Case 2: signs changed in one absolute value
-x-1 = 2(x-1)
-x-1 = 2x-2
1=3x
1/3=x
x=1/3.
In this case, |x|<1, so the answer to the question stem is YES.
Since the answer is NO in Case 1 but YES in Case 2, INSUFFICIENT.
Statement 2: |x-3| > 0
Case 1: signs unchanged
x-3 > 0
x>3.
In this case, |x|>1, so the answer to the question stem is NO.
Case 2: signs changed in the absolute value
-x+3 > 0
3>x
x<3.
If x=0, then |x|<1, so the answer to the question stem is YES.
Since the answer is NO in Case 1 but can be YES in Case 2, INSUFFICIENT.
Statements combined:
Statement 2 requires that x<3 or x>3.
Of the two values that satisfy statement 1 (x=3 and x=1/3), only x=1/3 also satisfies statement 2.
Thus:
x=1/3, with the result that |x|<1.
SUFFICIENT.
The correct answer is C.
