$$Statement\ 1\ =>\ x^2+x+2>8$$
$$\ x^2+x+2-8>0$$
$$\ x^2+x-6>0$$
$$\ x^2+3x-2x-6>0$$
$$x\left(x+3\right)-2\left(x+3\right)>0$$
$$\left(x-2\right)\left(x+3\right)>0$$
$$x-2>0\ or\ x+3>0$$
$$x>2\ or\ x>-3$$
There are 2 solutions gotten from this statement if x > 2
Definitely x > 1 but if x > -3 then x < 1. Since target question cannot be answered with certainty, statement 1 is NOT SUFFICIENT
Statement 2 => 8 (x - 4) > 4 (x - 2 )
8x - 32 > 4x - 8
8x - 4x > -8 + 32
4x/4 > 24/4
x > 6
There is only one solution to x and it specifically states that x > 6, definitely, x > 1
Statement 2 alone is SUFFICIENT,
Answer = B
Is \(x>1?\)
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Source: Beat The GMAT — Data Sufficiency |
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deloitte247
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