Answer:
a CANNOT be even ⇒ answer A
Step-by-step explanation:
* Lets revise the rules of even and odd numbers
- Even numbers any number its unit digit is (0 , 2 , 4 , 6 , 8)
- Odd numbers any number its unit digit is (1 , 3 , 5 , 7 , 9)
# even + even = even ⇒ 2 + 4 = 6
# odd + odd = even ⇒ 1 + 3 = 4
# odd + even = odd ⇒ 1 + 2 = 3
# even × even = even ⇒ 2 × 4 = 8
# odd × odd = odd
⇒ 3 × 5 = 15
# odd × even = even ⇒ 5 × 6 = 30
∵ a[b(c + d) + e] = odd
∵ odd × odd = odd
∴ a must be odd and [b(c + d) + e] must be odd
∵ odd + even = odd
∵ odd × even = even
# Case 1
∴ b(c + d) must be odd if e even
∵ b(c + d) is odd
∴ b must be odd and (c + d) must be odd
∵ c + d must be odd
∵ odd + even = odd
∴ c or d can be even
- We now now that e , c and d can be even
# case 2
∴ b(c + d) must be even if e odd
∵ b(c + d) is even
∵ even × even = even
∴ b and (c + d) both can be even
∵ c + d can be even
∴ c or d can be even or odd
- We now now that e , c , d and b can be even
∴ Only a can not be even
* a CANNOT be even
