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# a(x) is defined as the least integer greater than x for all odd values

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Math Expert
Joined: 02 Sep 2009
Posts: 47941
a(x) is defined as the least integer greater than x for all odd values  [#permalink]

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27 Jul 2018, 01:16
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35% (medium)

Question Stats:

79% (01:17) correct 21% (01:41) wrong based on 42 sessions

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$$\alpha(x)$$ 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

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Re: a(x) is defined as the least integer greater than x for all odd values  [#permalink]

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27 Jul 2018, 02:26
Bunuel wrote:
$$\alpha(x)$$ 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

-2 is even, so @(-2)=-2-1=-3
5 is odd, so @(5)=5+1=6

Therefore @(-2)-@(5)=-3-6=-9

B
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Re: a(x) is defined as the least integer greater than x for all odd values  [#permalink]

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27 Jul 2018, 02:56
+1 for B.

α(−2) − α(5) = ?
α(−2) = Even = -2 - 1 = -3
α(5) = Odd = 5 + 1 = 6

Therefore,
α(−2) − α(5) = -3 - 6 = -9

Hence, B.
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Re: a(x) is defined as the least integer greater than x for all odd values  [#permalink]

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27 Jul 2018, 02:58
Bunuel wrote:
$$\alpha(x)$$ 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

$$\alpha(x)$$ 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

To find $$\alpha(-2)$$

Since -2 is an even integer

$$\alpha(-2)$$ is the greatest integer less than x => $$\alpha(-2)$$ = -3

$$To find [m]\alpha(5)$$[/m]

Since 5 is an odd integer

$$\alpha(5)$$ is the least integer greater than x => $$\alpha(5)$$ = 6

$$\alpha(-2)$$ - $$\alpha(5)$$ = -3 - 6 = -9

Hence option B
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Re: a(x) is defined as the least integer greater than x for all odd values &nbs [#permalink] 27 Jul 2018, 02:58
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