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Data Sufficiency (DS) | Is 2 < x < 4?

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vitorpteixeira wrote:

Is 2 < x < 4?
(1) x^2 – 5x + 6 < 0
(2) 3x^2 – 9x < 0




Hi..
we can substitue values to see if answers match or find the values of x in eachcase..

\((1) x^2 – 5x + 6 < 0\)..
\(x^2-5x+6<0....(x-3)(x-2)<0\)
so two cases..
A)\(x-3<0\) and\(x-2>0\)
that is x<3 and x>2...
2<x<3..
matches with the range B)\(x-3>0\) and\(x-2<0\) ..
x>3 and x<2...
NOT possible
so ONLY range is 2<x<3 ans is YES

sufficient

(2) 3x^2 – 9x < 0
\( 3x(x-3)<0\)
...

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