Check each of the given options by substituting any odd number for p.
E
Practice makes perfect
We are asked to determine which of the given expressions is an odd number if p is any odd number. To do this, we can check each of the given options by substituting any odd number for p. Let's try p=3.
Expression
p=3
Simplify
Even or Odd?
2p
2( 3)
6
Even
2p+2
2( 3)+2
8
Even
p/2
3/2
1.5
Neither Even nor Odd
2p-2
2( 3)-2
4
Even
p+2
3+2
5
Odd
As we can see, only p+2 is an odd number for p=3. Generally speaking, any number multiplied by 2 becomes an even number.
2* an odd number= an even number
Dividing an odd number by 2 cannot result in a whole number, as odd numbers are not divisible by 2. Adding or subtracting 2 to an even number does not change the type of a number, so the result will be also an even number and this works also for odd numbers.
2* an odd number+2= an even number+2=
an even number
2* an odd number-2= an even number-2=
an even number
an odd number+2= an odd number
Therefore, p+2 is always an odd number if p is an odd number. This corresponds with answer E.
