If x,y and z are numbers between 1 and 10 , then 4x+6y+9z+2 is

Correct option is D

We are given the expression:

4x+6y+9z+2

where x,y and z are numbers between 1 and 10.

Step 1: Identify the Parity of Each Term

• 4x is always even (since 4 is even, multiplying by any integer keeps it even).

• 6y is always even (since 6 is even).

• 9z depends on z:

• If z is even, 9z is even.

• If z is odd, 9z is odd.

• The constant +2 is even.

Step 2: Find When the Sum is Odd or Even

• The sum 4x+6y+9z+2 is a sum of even + even + 9z + even.

• Since even + even + even = even, and even + odd = odd, the only factor that changes the parity is 9z.

• If z is even → 9z is even → Whole sum is even.

• If z is odd → 9z is odd → Whole sum is odd.

Since the expression is odd if z is odd, the correct answer is: