First of all, the question stem means:
for any X, we must
round down to the
nearest integer.
For example: x = 4.5 ==> [x] = 4; or x = 3.333 ==> [x] = 3
Statement 1:[3x] = 1 ==> 1/3 < x < 2/3 because:
if x < 1/3 ==> 3x < 1 ==> [3x] = 0, not 1
if x > 2/3 ==> 3x > 2 ==> [3x] greater or equal 2, not 1
So we have: 0.333 < x < 0.666 ==> 0 < x < 1 ==> [x] = 0
Statement 1 is sufficient.
Statement 2:[2x + 1] = 2 ==> 2 < 2x + 1 < 3 ==> 1/2 < x < 1
So we have: 0.5 < x < 1 ==> 0 < x < 1 ==> [x] = 0
Statement 2 is sufficient.
Hence, D is correct.
Hope it helps.
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