Question
Given that 𝑎 and 𝑏 are integers and 𝑎 + 𝑎 2𝑏 3 is odd, which one of the following statements is correct?
Options :
𝑎 and 𝑏 are both odd
𝑎 and 𝑏 are both even
𝑎 is even and 𝑏 is odd
𝑎 is odd and 𝑏 is even
Answer :
𝑎 is odd and 𝑏 is even
Solution :
a + a2b3 is odd
Taking a common a
(1+ab3) is odd
Odd number is obtained after multiplication if both numbers multiplied are odd.
Hence, a is odd and 1+ab3 is also odd.
1+ab3 is odd, so ab3 will be even. (odd-1= even quantity)
Because a is odd so for ab3 to be even b must be even.
So, a is odd and b is even.
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