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MathRevolution
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If [x] is the least integer greater than or equal to x, and [x/2]=3, w 12 Jun 2017, 01:04
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If [x] is the least integer greater than or equal to x, and [x/2]=3, what is the scope of x？

A. 3<x≤4
B. 8<x≤9
C. 8<x≤10
D. 9<x≤12
E. 4<x≤6
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E
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If [x] is the least integer greater than or equal to x, and [x/2]=3, w 12 Jun 2017, 03:40
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MathRevolution
If [x] is the least integer greater than or equal to x, and [x/2]=3, what is the scope of x？

A. 3<x≤4
B. 8<x≤9
C. 8<x≤10
D. 9<x≤12
E. 4<x≤6
Show more

[x/2]=3
maximum integer value for x could be 6. [6/2] = [3] = 3
substituting x = 5, we get = [5/2] = [2.5] = 3
substituting x = 4 , we get = [4/2] =[2] = 2
So x has to be greater than 4 and less than or equal to 6.
Therefore scope of x = 4<x≤6. Answer E...
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If [x] is the least integer greater than or equal to x, and [x/2]=3, w 14 Jun 2017, 01:27
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==> For [x], you get [1.2]=2, which means rounded up. In order to get [x/2]=3, you get 2<x/2≤3 and then 4<x≤6.

Therefore, the answer is E.
Answer: E
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If [x] is the least integer greater than or equal to x, and [x/2]=3, w 20 Jun 2017, 12:18
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MathRevolution
==> For [x], you get [1.2]=2, which means rounded up....
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@MathRevoltion, would you please explain how you derived this portion a little more?
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If [x] is the least integer greater than or equal to x, and [x/2]=3, w 30 Jun 2017, 10:42
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MathRevolution
==> For [x], you get [1.2]=2, which means rounded up....
@MathRevoltion, would you please explain how you derived this portion a little more?
Show more

Hi genxer123,

Its given [x] is the least integer greater than or equal to x.

Therefore if we have 1.2; [1.2] will give least integer greater than or equal to 1.2

In this case 2 is the least integer greater than 1.2, hence [1.2] = 2

Hope its clear now. :)
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If [x] is the least integer greater than or equal to x, and [x/2]=3, w 14 Aug 2017, 18:46
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sashiim20
MathRevolution
If [x] is the least integer greater than or equal to x, and [x/2]=3, what is the scope of x？

A. 3<x≤4
B. 8<x≤9
C. 8<x≤10
D. 9<x≤12
E. 4<x≤6

[x/2]=3
maximum integer value for x could be 6. [6/2] = [3] = 3
substituting x = 5, we get = [5/2] = [2.5] = 3
substituting x = 4 , we get = [4/2] =[2] = 2
So x has to be greater than 4 and less than or equal to 6.
Therefore scope of x = 4<x≤6. Answer E...
Show more

Hello, Shashi

I am not sure I am following your approach. Could you please help me understand by giving a different explanation?
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If [x] is the least integer greater than or equal to x, and [x/2]=3, w 14 Aug 2017, 21:34
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genxer123
MathRevolution
==> For [x], you get [1.2]=2, which means rounded up....
@MathRevoltion, would you please explain how you derived this portion a little more?

Hi genxer123,

Its given [x] is the least integer greater than or equal to x.

Therefore if we have 1.2; [1.2] will give least integer greater than or equal to 1.2

In this case 2 is the least integer greater than 1.2, hence [1.2] = 2

Hope its clear now. :)
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sashiim20 , I missed your post! Belated thanks and kudos.

As I re-read, I see now that 1.2 was a random example of what [x] meant.

I understood the rule. I just couldn't figure out from where the value 1.2 came.

The sentence didn't say, "If we have a number such as 1.2," so I decided that I was missing something (namely, 1.2 in the calculations), and that I had simply guessed the right answer.

I see now that the number chosen was an example. Cheers!
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If [x] is the least integer greater than or equal to x, and [x/2]=3, w 14 Aug 2017, 23:34
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Blackbox
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MathRevolution
If [x] is the least integer greater than or equal to x, and [x/2]=3, what is the scope of x？

A. 3<x≤4
B. 8<x≤9
C. 8<x≤10
D. 9<x≤12
E. 4<x≤6

[x/2]=3
maximum integer value for x could be 6. [6/2] = [3] = 3
substituting x = 5, we get = [5/2] = [2.5] = 3
substituting x = 4 , we get = [4/2] =[2] = 2
So x has to be greater than 4 and less than or equal to 6.
Therefore scope of x = 4<x≤6. Answer E...

Hello, Shashi

I am not sure I am following your approach. Could you please help me understand by giving a different explanation?
Show more

Hi Blackbox,

Question says [x] is the least integer greater than or equal to x. And [x/2]=3

So, maximum value of x when x/2 would be equal to 3 is 6.

When x = 6, [6/2] = 3

Now when we take x = 5 , 5/2 = 2.5

Now its given [x] is least integer greater than or equal to x.

Therefore for [2.5], least integer greater than or equal to 2.5 is = 3

Therefore x can have value of 6 and 5.

Now when we take x = 4 , 4/2 = 2

Therefore for [2], least integer greater than or equal to 2 is = 2. ------ Which is not equal to 3 as given in the equation. Hence x cannot be 4.

If we take x = 7, x/2 = 3.5.

For [3.5] least integer greater than or equal to 3.5 is = 4 ------ Which is not equal to 3 as given in the equation. Hence x cannot be 7.

Therefore x has to be greater than 4 and less than or equal to 6.

Given by x = 4<x≤6. Answer (E)...

Hope its clear now... :)
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If [x] is the least integer greater than or equal to x, and [x/2]=3, w 30 Dec 2025, 08:33
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Hi can someone explain this part of the question to me?
"if [x] is the least integer greater than or equal to x"

What exactly does this mean?
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If [x] is the least integer greater than or equal to x, and [x/2]=3, w 30 Dec 2025, 08:53
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Hi

It is saying that [x] is an operation or some function, which will give the least integer greater than or equal to x, so no matter what x is, [x] will return an integer.

For example, say if x is 1.2, then [x] = [1.2] will give the least integer greater than or equal to 1.2; it will be 2, the smallest integer greater than 1.2.
If x = 2, then [x] = [2], since 2 is already an integer(note that the question says [x] gives the least integer greater than or equal to x), so the next smallest integer is 2 itself.

Hope it helps!
eaat
Hi can someone explain this part of the question to me?
"if [x] is the least integer greater than or equal to x"

What exactly does this mean?
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If [x] is the least integer greater than or equal to x, and [x/2]=3, w 30 Dec 2025, 08:55
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Hi can someone explain this part of the question to me?
"if [x] is the least integer greater than or equal to x"

What exactly does this mean?
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"[x] denotes the least integer greater than or equal to x" means that the function rounds a number UP to the nearest integer. For example, [1.5] = 2 (because 2 is the least integer greater than or equal to 1.5), [2] = 2, and [-1.5] = -1.

Check similar questions to practice here: Rounding Functions.

Hope it helps.
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