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P, Q and R are 3 points in a plane. The length of the line segment P
[#permalink]
08 Aug 2025, 09:42
08 Aug 2025, 09:42
Expert Reply
00:00
Question Stats:
66% (00:57) correct
33% (00:17) wrong based on 9 sessions
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P, Q and R are 3 points in a plane. The length of the line segment PQ is 15 and that of line segment QR is 10.
Quantity A |
Quantity B |
Distance between points P and R. |
20 |
Re: P, Q and R are 3 points in a plane. The length of the line segment P
[#permalink]
20 Aug 2025, 11:03
20 Aug 2025, 11:03
Expert Reply
Given points $P, Q, R$ in a plane with:
- $P Q=15$
- $Q R=10$
We want to compare:
- Quantity A: distance PR
- Quantity B: 20
By the triangle inequality, the distance between two points $P$ and $R$ satisfies:
$$
\(|P Q-Q R| \leq P R \leq P Q+Q R\)
$$
Substitute the values:
$$
\(\begin{gathered}
|15-10| \leq P R \leq 15+10 \\
5 \leq P R \leq 25
\end{gathered}\)
$$
Thus, $P R$ could be less than, equal to, or greater than 20 depending on the configuration of points $P, Q$, and $R$.
Conclusion:
The relationship between Quantity A and Quantity B cannot be determined from the given information.
- $P Q=15$
- $Q R=10$
We want to compare:
- Quantity A: distance PR
- Quantity B: 20
By the triangle inequality, the distance between two points $P$ and $R$ satisfies:
$$
\(|P Q-Q R| \leq P R \leq P Q+Q R\)
$$
Substitute the values:
$$
\(\begin{gathered}
|15-10| \leq P R \leq 15+10 \\
5 \leq P R \leq 25
\end{gathered}\)
$$
Thus, $P R$ could be less than, equal to, or greater than 20 depending on the configuration of points $P, Q$, and $R$.
Conclusion:
The relationship between Quantity A and Quantity B cannot be determined from the given information.
gmatclubot
Re: P, Q and R are 3 points in a plane. The length of the line segment P [#permalink]
20 Aug 2025, 11:03
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