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

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

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New post 22 Jun 2013, 00:26
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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
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Re: [x] denotes the greatest integer less than or equal to x.  [#permalink]

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New post 22 Jun 2013, 11:54
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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


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

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New post 22 Jun 2013, 01:22
7
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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New post 22 Jun 2013, 01:58
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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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Re: [x] denotes the greatest integer less than or equal to x.  [#permalink]

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Re: [x] denotes the greatest integer less than or equal to x.   [#permalink] 09 Apr 2019, 04:32
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