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# If denotes to be the least integer no less than x, is

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Manager
Joined: 10 Oct 2005
Posts: 61

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If denotes to be the least integer no less than x, is  [#permalink]

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27 Oct 2005, 16:10
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If [x] denotes to be the least integer no less than x, is [x] zero?
1) [2x]=0
2) [3x]=0

OA is D... pls explain!

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VP
Joined: 22 Aug 2005
Posts: 1111

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Location: CA

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27 Oct 2005, 16:30
Guess the trick here is to understand working of the question stem.
all its saying is:
[x] = x

rest is obvious:

(1) 2x = 0 or x = 0
(2) 3x = 0, x = 0

D.

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Manager
Joined: 17 Sep 2005
Posts: 72

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Location: California

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27 Oct 2005, 16:44
Is it U for Unclear

I didn't like this Q for it's ambiquity.

Q: [x]=0 ?
Given: [x] is an int, [x] >= x I interpreted no less than as >= and not as =
Ambiguity: Is [2x] = 2*[x] ??

I would love to see the OE.

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Intern
Joined: 22 Mar 2005
Posts: 39

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28 Oct 2005, 10:52
Quote:
Guess the trick here is to understand working of the question stem.
all its saying is:
[x] = x

rest is obvious:

(1) 2x = 0 or x = 0
(2) 3x = 0, x = 0

D.

x doesn't have to be an integer in this problem (you still get the same answer though). [x] means find the closest integer not less than x so:

[-0.5] = 0
[0.5] = 1

Now for criteria #1:
Try x = -0.25
[2*-.25] = [-0.5] = 0, b/c 0 is the smallest integer not less than -0.5. Now try x = -0.5
[2*-0.5] = [-1] = -1, b/c -1 is the smallest integer not less than -1. This is no good so x must be greater than -0.5 and less than or equal to 0

Now for criteria #2:
Same story, x must be greater than -0.3333 and less than or equal to 0

So in each case you can say that [x] = 0, in criteria #1 try [-0.49], it equals 0. Now for criteria #2 try [-0.32], it also equals 0 as 0 is the smallest integer not less than x.

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28 Oct 2005, 10:52
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