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# [x] denotes the greatest integer less than or equal to x.

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Joined: 29 Nov 2012
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[x] denotes the greatest integer less than or equal to x. [#permalink]

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21 Jun 2013, 23:26
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[x] denotes the greatest integer less than or equal to x. What is the value of [x]?

(1) [3x] = 1
(2) [2x+1] = 2
[Reveal] Spoiler: OA

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Re: [x] denotes the greatest integer less than or equal to x. wh [#permalink]

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22 Jun 2013, 00:22
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First of all, the question stem means: for any X, we must round down to the nearest integer.
For example: x = 4.5 ==> [x] = 4; or x = 3.333 ==> [x] = 3

Statement 1:
[3x] = 1 ==> 1/3 < x < 2/3 because:
if x < 1/3 ==> 3x < 1 ==> [3x] = 0, not 1
if x > 2/3 ==> 3x > 2 ==> [3x] greater or equal 2, not 1
So we have: 0.333 < x < 0.666 ==> 0 < x < 1 ==> [x] = 0
Statement 1 is sufficient.

Statement 2:
[2x + 1] = 2 ==> 2 < 2x + 1 < 3 ==> 1/2 < x < 1
So we have: 0.5 < x < 1 ==> 0 < x < 1 ==> [x] = 0
Statement 2 is sufficient.

Hence, D is correct.

Hope it helps.
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Re: [x] denotes the greatest integer less than or equal to x. wh [#permalink]

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22 Jun 2013, 00:58
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fozzzy wrote:
$$[x]$$ denotes the greatest integer less than or equal to x. what is the value of $$[x]$$?

1) $$[3x] = 1$$
2) $$[2x+1] = 2$$

What the question stem means is that for any given x, move to the left of x on the number line, till you reach the first integer. If x is an integer, then [x] = x.

From F. S 1, we know that $$[3x] = 1$$. Thus, 1<3x<2 -->$$\frac{1}{3}$$<x<$$\frac{2}{3}$$ . Thus, [x] = 0. Sufficient.

From F. S 2, we know that $$[2x+1] = 2$$. Thus, 2<2x+1<3 --> 1<2x<2 --> 0.5<x<1 . Thus, [x] = 0. Sufficient.

D.
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Re: [x] denotes the greatest integer less than or equal to x. [#permalink]

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22 Jun 2013, 10:54
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Re: [x] denotes the greatest integer less than or equal to x. [#permalink]

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24 Jun 2014, 02:45
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fozzzy wrote:
[x] denotes the greatest integer less than or equal to x. What is the value of [x]?

(1) [3x] = 1
(2) [2x+1] = 2

Check other rounding functions questions in Special Questions Directory

Rounding Functions
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Re: [x] denotes the greatest integer less than or equal to x. [#permalink]

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22 Jan 2018, 11:12
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Re: [x] denotes the greatest integer less than or equal to x.   [#permalink] 22 Jan 2018, 11:12
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# [x] denotes the greatest integer less than or equal to x.

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