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A,B,, and C are consecutive odd integers such
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04 Jan 2026, 13:41
04 Jan 2026, 13:41
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A,B,, and C are consecutive odd integers such that $\(\mathrm{A}<\mathrm{B}<\mathrm{C}\)$. If $\(\mathrm{A}+\mathrm{B}+\mathrm{C}=81\)$, then $\(\mathrm{A}+\mathrm{C}=\)$
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Re: A,B,, and C are consecutive odd integers such
[#permalink]
09 Jan 2026, 05:00
09 Jan 2026, 05:00
Expert Reply
Let the integers be represented in terms of the middle integer, $B$. Since $\(\mathrm{A}, \mathrm{B}\)$, and \(C\) are consecutive odd integers:
- $A=B-2$
- $B=B$
- $C=B+2$
2. Use the Given Sum
We are given that the sum of the three integers is 81 :
$$
\(A+B+C=81\)
$$
Substitute the definitions from Step 1 into the equation:
$$
\((B-2)+B+(B+2)=81\)
$$
3. Solve for B
Simplify the equation:
$$
\(\begin{gathered}
(B+B+B)+(-2+2)=81 \\
3 B=81 \\
B=\frac{81}{3} \\
B=27
\end{gathered}\)
$$
4. Find $A$ and $C$
Now that we know $B=27$, we can find $A$ and $C$ :
- $A=B-2=27-2=25$
- $C=B+2=27+2=29$
Check the sum: $25+27+29=81$. (Correct)
5. Calculate the Required Sum
The problem asks for the value of $A+C$ :
$$
\(\begin{gathered}
A+C=25+29 \\
A+C=54
\end{gathered}\)
$$
Answer
The value of $A+C$ is $\(\mathbf{5 4}\)$.
- $A=B-2$
- $B=B$
- $C=B+2$
2. Use the Given Sum
We are given that the sum of the three integers is 81 :
$$
\(A+B+C=81\)
$$
Substitute the definitions from Step 1 into the equation:
$$
\((B-2)+B+(B+2)=81\)
$$
3. Solve for B
Simplify the equation:
$$
\(\begin{gathered}
(B+B+B)+(-2+2)=81 \\
3 B=81 \\
B=\frac{81}{3} \\
B=27
\end{gathered}\)
$$
4. Find $A$ and $C$
Now that we know $B=27$, we can find $A$ and $C$ :
- $A=B-2=27-2=25$
- $C=B+2=27+2=29$
Check the sum: $25+27+29=81$. (Correct)
5. Calculate the Required Sum
The problem asks for the value of $A+C$ :
$$
\(\begin{gathered}
A+C=25+29 \\
A+C=54
\end{gathered}\)
$$
Answer
The value of $A+C$ is $\(\mathbf{5 4}\)$.
gmatclubot
Re: A,B,, and C are consecutive odd integers such [#permalink]
09 Jan 2026, 05:00
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