If a,b,c,d, and e are whole numbers and a(b(c+d)+e) is odd, then which of the following cannot be even?
a) a
b) b
c) c
d) d
To determine which of the variables (a, b, c, d) cannot be even, we need to understand the properties of odd and even numbers.
Odd numbers: Odd numbers are integers that cannot be divided evenly by 2. They have a remainder of 1 when divided by 2.
Even numbers: Even numbers are integers that can be divided evenly by 2. They have no remainder when divided by 2.
Given the expression a(b(c+d)+e) is odd, we need to investigate how each variable affects the final result.
Let's break it down step by step:
1. c + d: The sum of two even numbers or two odd numbers is always even. So the sum (c + d) is even, regardless of the values of c and d.
2. b multiplied by (c + d): When an even number (b) is multiplied by an even number (c + d), the result is always even. Multiplying two odd numbers also results in an even number. So regardless of the values of b, c, and d, the product (b(c + d)) is even.
3. (b(c + d)) + e: Adding an even number (b(c + d)) and a whole number (e) can result in either an even or an odd number.
4. a multiplied by ((b(c + d)) + e): Finally, an even number (b(c + d)) + e multiplied by any number (a) is always even. Multiplying any number (a) with an even number results in an even number.
Since the final result a(b(c + d)) + e is odd, we can conclude that the only variable that cannot be even is:
c) c
This is because, regardless of the values of a, b, and d, the sum (c + d) is always even. Therefore, for the expression to be odd, c must be odd.