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# If [x] is the least integer greater than or equal to x, and [x/2]=3, w

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Math Revolution GMAT Instructor
Joined: 16 Aug 2015
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If [x] is the least integer greater than or equal to x, and [x/2]=3, w  [#permalink]

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12 Jun 2017, 01:04
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5% (low)

Question Stats:

87% (01:20) correct 13% (01:38) wrong based on 119 sessions

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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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If [x] is the least integer greater than or equal to x, and [x/2]=3, w  [#permalink]

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12 Jun 2017, 03:40
1
1
MathRevolution wrote:
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...
Math Revolution GMAT Instructor
Joined: 16 Aug 2015
Posts: 7230
GMAT 1: 760 Q51 V42
GPA: 3.82
Re: If [x] is the least integer greater than or equal to x, and [x/2]=3, w  [#permalink]

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14 Jun 2017, 01:27
==> 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.

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If [x] is the least integer greater than or equal to x, and [x/2]=3, w  [#permalink]

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20 Jun 2017, 12:18
MathRevolution wrote:
==> For [x], you get [1.2]=2, which means rounded up....

@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  [#permalink]

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30 Jun 2017, 10:42
1
genxer123 wrote:
MathRevolution wrote:
==> 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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Re: If [x] is the least integer greater than or equal to x, and [x/2]=3, w  [#permalink]

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14 Aug 2017, 18:46
sashiim20 wrote:
MathRevolution wrote:
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

Senior SC Moderator
Joined: 22 May 2016
Posts: 2642
If [x] is the least integer greater than or equal to x, and [x/2]=3, w  [#permalink]

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14 Aug 2017, 21:34
sashiim20 wrote:
genxer123 wrote:
MathRevolution wrote:
==> 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.

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  [#permalink]

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14 Aug 2017, 23:34
Blackbox wrote:
sashiim20 wrote:
MathRevolution wrote:
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

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...
If [x] is the least integer greater than or equal to x, and [x/2]=3, w   [#permalink] 14 Aug 2017, 23:34
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