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For all numbers x, x^#
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03 Sep 2025, 08:58
03 Sep 2025, 08:58
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Question Stats:
50% (00:52) correct
50% (02:38) wrong based on 10 sessions
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\(\begin{aligned}
&\text { For all numbers } x, x^{\#}=24-x \text {. }\\
&\frac{\text { Column A }}{\left(x^{\#}\right)^{\#}} \quad \frac{\text { Column B }}{x}
\end{aligned}\)
&\text { For all numbers } x, x^{\#}=24-x \text {. }\\
&\frac{\text { Column A }}{\left(x^{\#}\right)^{\#}} \quad \frac{\text { Column B }}{x}
\end{aligned}\)
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Re: For all numbers x, x^#
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04 Oct 2025, 12:27
04 Oct 2025, 12:27
Expert Reply
We are told:
$$
\(x^{\#}=24-x\)
$$
for all numbers $x$.
We want to compare:
Column A: $\(\left(x^{\#}\right)^{\#}\)$
Column B: $\(x\)$
Step 1: Compute $\(\left(x^{\#}\right)^{\#}\)$
First, $\(x^{\#}=24-x\)$.
Now $\(\left(x^{\#}\right)^{\#}=(24-x)^{\#}\)$.
By definition, $\((24-x)^{\#}=24-(24-x)\)$.
Step 2: Simplify
$$
\(24-(24-x)=24-24+x=x\)
$$
So $\(\left(x^{\#}\right)^{\#}=x\)$.
Step 3: Compare columns
Column A $=x$
Column B $=x$
C is the answer
$$
\(x^{\#}=24-x\)
$$
for all numbers $x$.
We want to compare:
Column A: $\(\left(x^{\#}\right)^{\#}\)$
Column B: $\(x\)$
Step 1: Compute $\(\left(x^{\#}\right)^{\#}\)$
First, $\(x^{\#}=24-x\)$.
Now $\(\left(x^{\#}\right)^{\#}=(24-x)^{\#}\)$.
By definition, $\((24-x)^{\#}=24-(24-x)\)$.
Step 2: Simplify
$$
\(24-(24-x)=24-24+x=x\)
$$
So $\(\left(x^{\#}\right)^{\#}=x\)$.
Step 3: Compare columns
Column A $=x$
Column B $=x$
C is the answer
gmatclubot
Re: For all numbers x, x^# [#permalink]
04 Oct 2025, 12:27
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