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

Question

\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

chetan2u · Accepted Answer

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

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

B

sudarshan22 · Answer

+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  .

Nikhil · Answer

\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  \alpha(5)

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

AnupamKT · Answer

From the question stem, if X=odd, then {x} will be least integer greater than X and
 if X=even, then {x} will be greatest integer less than X and

So, value of {-2}=-3 ; as -2 is an even no. &
 value of {5}= 6 ; as 5 is an odd no.

therefore, {-2}-{5}= -3-6=-9, Hence B is the correct answer.

ScottTargetTestPrep · Answer

Solution:

Since -2 is even, then {-2} = -3 (notice that -3 is the greatest integer less than -2). Since 5 is odd, {5} = 6 (Notice that 6 is the least integer greater than 5). Therefore, {-2} - {5} = -3 - 6 = -9.

Answer: B

Kinshook · Answer

Asked: {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 {-2} - {5} ?

{-2} = -3
{5} = 6

{-2} - {5} = -3 - 6 = -9

IMO B

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

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