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is defined as the least integer greater than x for all odd v

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is defined as the least integer greater than x for all odd v [#permalink] New post 25 Jul 2018, 17:19
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Question Stats:

80% (00:55) correct 19% (01:31) wrong based on 31 sessions
\(\boxed{x}\)is defined as the least integer greater than x for all odd values of x, and the greatest integer less than x for all even values of x. What is the value of \(\boxed{-2}-\boxed{5}\)?

(A) –12
(B) –9
(C) –8
(D) –7
(E) 3
[Reveal] Spoiler: OA

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Last edited by Carcass on 08 Jan 2020, 15:17, edited 1 time in total.
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Retired Moderator
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Joined: 07 Jun 2014
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GRE 1: Q167 V156
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Kudos [?]: 2921 [1] , given: 394

Re: is defined as the least integer greater than x for all odd v [#permalink] New post 02 Aug 2018, 06:35
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Explanation

If \(x\) is odd, \(\alpha (x)\) equals the least integer greater than x (e.g., if x = 3, then the “least integer greater than 3” is equal to 4)

If \(x\) is even, \(\alpha (x)\) equals the greatest integer less than x (e.g., if x = 6, the “greatest integer less than x” is equal to 5.

Since –2 is even, \(\alpha (-2)\) the greatest integer less than –2, or –3.

Since \(5\) is odd, \(\alpha(5)=\) the least integer greater than 5, or 6.

Thus, \(\alpha(-2)-\alpha(5) = -3 - 6 = -9\).
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Re: is defined as the least integer greater than x for all odd v [#permalink] New post 19 Oct 2018, 23:30
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when x is odd then f(x)= x+1, f(5)= 5+1=6
when x is even then f(x)= x-1= -2-1= -3
-3-6=-9
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Re: is defined as the least integer greater than x for all odd v [#permalink] New post 08 Jan 2020, 15:17
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Update the question.

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Re: is defined as the least integer greater than x for all odd v   [#permalink] 08 Jan 2020, 15:17
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