If m and n are positive integers and mn, then how many even integers

Question

If m and n are positive integers and m > n, then how many even integers are there between 2m and 2n, excluding 2m and 2n?

A. m - n
B. m - n - 1
C. m - n + 1
D. 2m - 2n - 1
E. 2m - 2n + 1

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ManifestDreamMBA · Answer

Given
m and n are positive integers
m > n

Q - Number of even integers are there between 2m and 2n,  excluding  2m and 2n?

(2m-2n)/2 - 1
m-n-1

SwapnilBangera · Answer

Even integers are spaced by 2. Therefore, the even integers between 
2n and 2m are:

2n+2, 2n+4, 2n+6, ..., 2m−2

This sequence of even integers forms an arithmetic progression where:

First term (a) = 2n+2,
Last term (l) = 2m−2,
Common difference (d) = 2.

The number of terms in the sequence can be calculated using the formula for the number of terms in an arithmetic progression:

k=((l−a)/d)+1

Substituting the values:

k =(((2m−2)−(2n+2))/2)+1
k=((2m−2−2n−2)/2)+1
k=((2m−2n−4)/2)+1
k=m−n−1

Option B

Sketchitesh · Answer

m>n,

Even integers between 2m and 2n ?

Case 1. (2,1) => (4,2) even integers 0 
Only B and D matches 
Case 2: (3,1) => (6,2) 1 even integer, 4. 
Only B matches.

B is the answer

Missinga · Answer

n<m
Even integers between 2m and 2n 
Let, m= 3 and n= 1 
Between 6 & 2, there is one even integer (4) 
m-n-1= 3-1-1= 1

Let, m= 5 and n= 1
Between 10 & 2, there are three even integers (4,6,8) 
m-n-1= 5-1-1= 3

Answer: B

GMATinsight · Answer

let, m = 3 and n = 2
2m = 6 and 2n = 4
even integers between 2m and 2n =  0

A. m - n = 3-2 = 1
B. m - n - 1 = 3-2-1   = 0  
C. m - n + 1. =3-2+1 = 2
D. 2m - 2n - 1 = 6 - 4 - 1 = 1
E. 2m - 2n + 1 = 6 - 4 + 1 = 3

Answer: Option B

Dereno · Answer

Given: m and n are positive integers m,n >0

m > n

We get, m>n>0

How many even numbers are between 2m and 2n ?

let’s take m= 2, n=1

2m =4 and 2n =2 . Even numbers between 4 and 2 is zero.

A. m - n = 2-1 =1. Eliminated

B. m - n - 1 = 2-1-1 = 0
 
C. m - n + 1 = 2-1+1 = 2. Eliminated

D. 2m - 2n - 1 = 4-2-1= 1 Eliminated

E. 2m - 2n + 1 = 4-2+1 =3 Eliminated

Option B

If m and n are positive integers and m>n, then how many even integers

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