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

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Joined: 07 Jun 2014
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is defined as the least integer greater than x for all odd v [#permalink]  25 Jul 2018, 17:19
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Question Stats:

80% (00:51) correct 20% (02:23) wrong based on 10 sessions
$$\alpha(x)$$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 $$\alpha(-2)-\alpha(5)$$?

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

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GRE Prep Club Legend
Joined: 07 Jun 2014
Posts: 4856
GRE 1: Q167 V156
WE: Business Development (Energy and Utilities)
Followers: 102

Kudos [?]: 1742 [0], given: 397

Re: is defined as the least integer greater than x for all odd v [#permalink]  02 Aug 2018, 06:35
Expert's post
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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Joined: 22 Jul 2018
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Kudos [?]: 10 [0], given: 5

Re: is defined as the least integer greater than x for all odd v [#permalink]  19 Oct 2018, 23:30
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
Re: is defined as the least integer greater than x for all odd v   [#permalink] 19 Oct 2018, 23:30
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