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Retired Moderator Joined: 07 Jun 2014
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is defined as the least integer greater than x for all odd v [#permalink]
Expert's post 00:00

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.
Updated Retired Moderator Joined: 07 Jun 2014
Posts: 4803
GRE 1: Q167 V156 WE: Business Development (Energy and Utilities)
Followers: 171

Kudos [?]: 2921  , given: 394

Re: is defined as the least integer greater than x for all odd v [#permalink]
1
KUDOS
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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Re: is defined as the least integer greater than x for all odd v [#permalink]
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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]
Expert's post
Update the question.

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GRE Prep Club Members of the Month: Each member of the month will get three months free access of GRE Prep Club tests. Re: is defined as the least integer greater than x for all odd v   [#permalink] 08 Jan 2020, 15:17
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