Hi here are my two cents for this questions.
If this question were to be marked based on options here is how i would go about solving it .
Well,
Option A, C can be ruled out for following reason.
\(\frac{odd}{Even}\) is never Integer and we are looking for how many even integers would there be between v and m excluding m ,
and Option E gives number of integers between v and m, excluding either m or v
Which leaves us with choice B and D
Now choice B and D both gives us integers value but look at choice D . It actually gives us number of integers between v and m excluding both .
So our answer is Choice B
Lets do this algebraically.
if v is odd, then v+1 will be even . and if m is even
So we have number of integers between m and v+1 excluding one of the ends is = \(\frac{m-v-1}{2}\)
So we do have a formula for such type of questions
If we are counting in steps of x , from \(n_1\) to \(n_z\) including both end points we get \(\frac{n_z - n_1}{x}\) +1
If we are counting in steps of x , from \(n_1\) to \(n_z\) including only one end points we get \(\frac{n_z - n_1}{x}\)
If we are counting in steps of x , from \(n_1\) to \(n_z\) excluding both end points we get \(\frac{n_z - n_1}{x}\) -1
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Probus
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