If [x] denotes is the least integer greater than or equal to x, what

Question

If   denotes is the least integer greater than or equal to x, what i the value of  =?

(1)   =1
(2)   = 1

umangshah · Answer

To find: Value of  
Given:  = Least integer >= x

Statement 1:  =1, meaning value of x is between 0.01 to 1. So by adding 1 to x we get value of x+1 between 1.01 to 2. Thus  =2. Sufficient.
Statement 2:  =1, meaning value of x is between 0.01 to 0.5. So by adding 1 to x we get value of x+1 between 1.01 to 1.5. Thus  =2. Sufficient.

Option D is correct.

sunshineeee · Answer

Hi, can u elaborate how can it translate to 0.01 to 1??

1:  =1, meaning value of x is between 0.01 to 1

miag · Answer

Hi, You’re right to question 0.01 to 1. That range is incorrect. = 1 => We only know that 0

crimson_noise · Answer

Statement (1):   = 1
If the smallest integer ≥ x is 1, then:
0 < x <= 1
Adding 1 to all parts:
1 < x+1 <= 2
Since x+1 is in the range 1 to 2, the smallest integer ≥ (x+1) is 2.
So   = 2
SUFFICIENT

Statement (2):   = 1
If the smallest integer ≥ 2x is 1, then:
0 < 2x <= 1
Dividing by 2:
0 < x <= 0.5
Adding 1:
1 < x+1 <= 1.5
Since x+1 is in the range 1 to 1.5, the smallest integer ≥ (x+1) is 2.
So   = 2
SUFFICIENT

Both statements independently give   = 2

If [x] denotes is the least integer greater than or equal to x, what

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GMAT Data Sufficiency (DS) Questions

If [x] denotes is the least integer greater than or equal to x, what

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