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500<x<1,000
[#permalink]
05 Sep 2025, 02:36
05 Sep 2025, 02:36
Expert Reply
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Question Stats:
62% (01:03) correct
37% (00:30) wrong based on 8 sessions
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\(\begin{aligned}
&500<x<1,000\\
&\begin{array}{ll}
\text { Column A } & \text { Column B } \\
1,000-x & x-500
\end{array}
\end{aligned}\)
&500<x<1,000\\
&\begin{array}{ll}
\text { Column A } & \text { Column B } \\
1,000-x & x-500
\end{array}
\end{aligned}\)
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Re: 500<x<1,000
[#permalink]
04 Oct 2025, 12:20
04 Oct 2025, 12:20
Expert Reply
Given the conditions:
$$
\(500<x<1000\)
$$
Compare Column A and Column B:
- Column A: $\(1000-x\)$
- Column B: $\(x-500\)$
Since $x$ is between 500 and 1000:
- $1000-x$ is positive, decreasing as $x$ increases
- $x-500$ is positive, increasing as $x$ increases
Let's check the sum:
$$
\((1000-x)+(x-500)=1000-x+x-500=500\)
$$
The sum of both columns is always 500 .
When $x$ is closer to 500 :
- Column A $\(=1000-500=500\)$ (max value)
- Column B = 500-500=0 (min value)
So Column A > Column B.
When $x$ is closer to 1000 :
- Column A = 1000 - $1000=0$ (min value)
- Column B = $1000-500=500$ (max value)
So Column B > Column A.
Therefore, depending on $x$, Column A may be greater than Column B or vice versa.
$$
\(500<x<1000\)
$$
Compare Column A and Column B:
- Column A: $\(1000-x\)$
- Column B: $\(x-500\)$
Since $x$ is between 500 and 1000:
- $1000-x$ is positive, decreasing as $x$ increases
- $x-500$ is positive, increasing as $x$ increases
Let's check the sum:
$$
\((1000-x)+(x-500)=1000-x+x-500=500\)
$$
The sum of both columns is always 500 .
When $x$ is closer to 500 :
- Column A $\(=1000-500=500\)$ (max value)
- Column B = 500-500=0 (min value)
So Column A > Column B.
When $x$ is closer to 1000 :
- Column A = 1000 - $1000=0$ (min value)
- Column B = $1000-500=500$ (max value)
So Column B > Column A.
Therefore, depending on $x$, Column A may be greater than Column B or vice versa.
gmatclubot
Re: 500<x<1,000 [#permalink]
04 Oct 2025, 12:20
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