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[X] represents remainder of number 3x/2
Now, question asks which of the following is equal to 1.
Now, 3[x] + 1 represents remainder of number: 3(3x)/2 + 1 {replacing value of [x]}
=>i.e. remainder of 9x/2 + 1
9x/2 will have remainder either 1 or 0
Thus, 9x/2 + 1 will have only 1 as remainder.
Why?
when 9x/2 has remainder 0 => 9x/2 + 1 has remainder 1
9x/2 has remainder 1=> 9x/2 + 1 has remainder 0

For choice A, number is 0.
choice B, number is 0 or 1.
choice C, number is 1 or 3.
- Vicks

answer is c I guess... Although depending on what x is, b could be valid too...

case a:
[2x] is the remainder of 3(2x)/2. The fraction resolves itself quite nicely to 3x, so there is no remainder. [2x]=0.

case b:
[3x] is the remainder of 3(3x)/2. This fraction may or may not have a remainder, depending on what x is. If x=2, then [3x]+1 = 1. If x=7, then [3x]+1=1+1=2

case c:
looking at (a) above, [2x]=0, so [2x]+1=1.

definitely c, and maybe b depending on the value of x...

oops, just read the answers but don't understand... did you fix your typo in the question prat?