Smita04 wrote:

[x] denotes to be the least integer no less than x. Is [2d] = 0?

(1) [d] = 0

(2) [3d] = 0

I did not jump into the equations, but tried to solve logically. Please let me know if wrong.

We need to find out if [2d] = 0?

Again its a YES or NO, question, getting Either in the statements will help us to the solutions.

(1) [d] = 0

Now according to the question [x] = integer no less than x

Hence, considering two extremes for evaluating this particular case, Lets take

[0.12] = 0 as well as [0.99] = 0 (both are valid for [d] =0)

therefore, [2d], i.e. taking the same values as above

[0.24] = 0, but [1.98] = 1

so we cant say most definitely that [2d] =0

Not Sufficient.

(2) [3d] = 0

again considering etremes here,

lets take

Minimum value => 3d = 0.12 (you can take less then this as well, i am just taking this for easy divisibility purpose, as anything less then 0.12 will also result in 0 we already know that)

and

Maximum value => 3d = 0.99

[3d] = 0 holds for both the values.

now, [2d]

minimum= [0.8] =0

maximum= [0.22] =0

hence, no matter what range we take for 3d, 2d will always be less then that.

Thus, if [3d]= 0, holds true, then [2d] =0 should hold true as well.

Hence, B

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