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(a+6)(a-6)=0
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08 Sep 2025, 00:27
08 Sep 2025, 00:27
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Question Stats:
61% (00:47) correct
38% (00:50) wrong based on 21 sessions
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\(\begin{aligned}
& (a+6)(a-6)=0 \\
& (b+6)(b-6)=0
\end{aligned}\)
& (a+6)(a-6)=0 \\
& (b+6)(b-6)=0
\end{aligned}\)
Quantity A |
Quantity B |
\(a+6\) |
\(b+6\) |
- Part of the project: PrepClub Daily GRE Quant Questions: Arithmetic, Algebra, Geometry & DA
- Also replying to the unanswered questions
Re: (a+6)(a-6)=0
[#permalink]
06 Oct 2025, 15:18
06 Oct 2025, 15:18
Expert Reply
Given the equations:
$$
\(\begin{aligned}
& (a+6)(a-6)=0 \Longrightarrow a=-6 \text { or } a=6 \\
& (b+6)(b-6)=0 \Longrightarrow b=-6 \text { or } b=6
\end{aligned}\)
$$
We need to compare:
Quantity A: $a+6$
Quantity B: $b+6$
Possible values for each quantity:
- If $a=-6$, then $a+6=0$
- If $a=6$, then $a+6=12$
Similarly for $b$ :
- If $b=-6$, then $b+6=0$
- If $b=6$, then $b+6=12$
Possible comparisons:
- If $a=-6$ and $b=6$, Quantity $\(\mathrm{A}=0\)$ and Quantity $\(\mathrm{B}=12 \rightarrow\)$ Quantity B is greater
- If $a=6$ and $b=-6$, Quantity $\(\mathrm{A}=12\)$ and Quantity $\(\mathrm{B}=0 \rightarrow\)$ Quantity A is greater
- If $a=b$, quantities are equal.
Conclusion:
The relationship cannot be determined from the information given. Each quantity can be equal or can be greater than the other depending on values of $a$ and $b$.
$$
\(\begin{aligned}
& (a+6)(a-6)=0 \Longrightarrow a=-6 \text { or } a=6 \\
& (b+6)(b-6)=0 \Longrightarrow b=-6 \text { or } b=6
\end{aligned}\)
$$
We need to compare:
Quantity A: $a+6$
Quantity B: $b+6$
Possible values for each quantity:
- If $a=-6$, then $a+6=0$
- If $a=6$, then $a+6=12$
Similarly for $b$ :
- If $b=-6$, then $b+6=0$
- If $b=6$, then $b+6=12$
Possible comparisons:
- If $a=-6$ and $b=6$, Quantity $\(\mathrm{A}=0\)$ and Quantity $\(\mathrm{B}=12 \rightarrow\)$ Quantity B is greater
- If $a=6$ and $b=-6$, Quantity $\(\mathrm{A}=12\)$ and Quantity $\(\mathrm{B}=0 \rightarrow\)$ Quantity A is greater
- If $a=b$, quantities are equal.
Conclusion:
The relationship cannot be determined from the information given. Each quantity can be equal or can be greater than the other depending on values of $a$ and $b$.
gmatclubot
Re: (a+6)(a-6)=0 [#permalink]
06 Oct 2025, 15:18
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