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# If [x] denotes the least integer greater than or equal to x

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If [x] denotes the least integer greater than or equal to x [#permalink]  27 Jul 2020, 09:03
Expert's post
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Question Stats:

49% (01:03) correct 49% (01:03) wrong based on 14 sessions
If [x] denotes the least integer greater than or equal to x and [x/2] = 0, which of the following could be the value of x?

A. -2
B. -3/2
C. 1/2
D. 1
E. 2
[Reveal] Spoiler: OA

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Founder
Joined: 18 Apr 2015
Posts: 12642
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Kudos [?]: 3178 [0], given: 11677

Re: If [x] denotes the least integer greater than or equal to x [#permalink]  27 Jul 2020, 09:04
Expert's post
Post A Detailed Correct Solution For The Above Questions And Get A Kudos.
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Re: If [x] denotes the least integer greater than or equal to x [#permalink]  27 Jul 2020, 10:30
Checking each option for [x/2] = 0 as per the given rule..

A) -2 => [-2/2] = -1 NOT equals to 0. Out.
B) -3/2 => [-3/4] = 0 Looks good.
c) 1/2 => [1/4] = 1 NOT equals to 0. Out.
D) 1 => [1/2] = 1 NOT equals to 0. Out.
E) 2 => [2/2] = 1 NOT equals to 0. Out.

Ans B
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Re: If [x] denotes the least integer greater than or equal to x [#permalink]  27 Jul 2020, 11:31
We want [x/2] = 0. That happens when x = 0, or when -1 < (x/2) < 0, as [x/2] is then zero, or -2 < x < 0. The only option where this is satisfied is B.
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Re: If [x] denotes the least integer greater than or equal to x [#permalink]  27 Jul 2020, 12:27
Expert's post
Carcass wrote:
If [x] denotes the least integer greater than or equal to x and [x/2] = 0, which of the following could be the value of x?

A. -2
B. -3/2
C. 1/2
D. 1
E. 2

First, let's take a moment to get a good idea of what this strange notation means.
A few examples:
[5.1] = 6
[3] = 3
[8.9] = 9
[-1.4] = -1
[-13.6] = -13

So, if [x/2] = 0, then we know that -1 < x/2 ≤ 0
Multiply all sides of the inequality by 2 to get: -2 < x ≤ 0

Only -3/2 falls inside that range.

Cheers,
Brent
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Re: If [x] denotes the least integer greater than or equal to x   [#permalink] 27 Jul 2020, 12:27
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