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If $a, b, c$, are positive and odd integers, and $d$ is a non-zero int
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05 Apr 2025, 00:59
05 Apr 2025, 00:59
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Question Stats:
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85% (02:51) wrong based on 14 sessions
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If $\(a, b, c\)$, are positive and odd integers, and $\(d\)$ is a non-zero integer, then which of the following is not necessarily true?
(A) $\((a b c)^2\)$ is odd
(B) $\(a^2+b^2+c^2\)$ is even
(C) $\(\left(\frac{a^2+b^2}{2}\right) c^2\)$ is odd
(D) $\(7 a+a b+3 d\)$ is odd
(E) $\(\left(\frac{a^2+b^2}{2}\right)\)$ is odd
(A) $\((a b c)^2\)$ is odd
(B) $\(a^2+b^2+c^2\)$ is even
(C) $\(\left(\frac{a^2+b^2}{2}\right) c^2\)$ is odd
(D) $\(7 a+a b+3 d\)$ is odd
(E) $\(\left(\frac{a^2+b^2}{2}\right)\)$ is odd
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Re: If $a, b, c$, are positive and odd integers, and $d$ is a non-zero int
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09 Apr 2025, 04:00
09 Apr 2025, 04:00
Expert Reply
If we look at the answer choices, except for option $D$, all the other options can be either false or true. Option $D: 7 \mathrm{a}+a b+3 d$ is odd.
$$
\(\begin{aligned}
& \text { i.e., } 7(\text { odd })+(\text { odd })(\text { odd })+3(\text { odd or even }) \\
& =\text { odd }+ \text { odd }+(\text { odd or even }) \\
& =\text { odd or even. }
\end{aligned}\)
$$
Hence, $\(7 \mathrm{a}+a b+3 d\)$ is odd is not necessarily true.
Thus, the correct answer choice is $D$.
$$
\(\begin{aligned}
& \text { i.e., } 7(\text { odd })+(\text { odd })(\text { odd })+3(\text { odd or even }) \\
& =\text { odd }+ \text { odd }+(\text { odd or even }) \\
& =\text { odd or even. }
\end{aligned}\)
$$
Hence, $\(7 \mathrm{a}+a b+3 d\)$ is odd is not necessarily true.
Thus, the correct answer choice is $D$.
Re: If $a, b, c$, are positive and odd integers, and $d$ is a non-zero int
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07 Sep 2026, 21:52
07 Sep 2026, 21:52
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