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The circumference of the circle above is 30
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21 Jul 2025, 22:25
21 Jul 2025, 22:25
Expert Reply
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Question Stats:
66% (01:27) correct
33% (01:04) wrong based on 6 sessions
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The circumference of the circle above is 30
Quantity A |
Quantity B |
The length of chord A B |
10 |
A) Quantity A is greater.
B) Quantity B is greater.
C) The two quantities are equal.
D) The relationship cannot be determined from the information given.
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Re: The circumference of the circle above is 30
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29 Jul 2025, 12:37
29 Jul 2025, 12:37
Expert Reply
Given:
- The circumference of the circle is 30 .
- Quantity A: length of chord $A B$.
- Quantity B: 10.
Step 1: Find the radius of the circle
Circumference $\(C=2 \pi r\)$ :
$$
\(30=2 \pi r \Longrightarrow r=\frac{30}{2 \pi}=\frac{15}{\pi}\)
$$
Numerical approximation:
$$
\(r \approx \frac{15}{3.1416} \approx 4.7746\)
$$
Step 2: Calculate the diameter
$$
\(\text { Diameter }=2 r \approx 2 \times 4.7746=9.5492\)
$$
Step 3: Analyze chord $A B$
- The maximum possible chord length in a circle is the diameter.
- So, length of chord $\(A B \leq 9.55\)$ (approx).
Step 4: Compare Quantities
- Quantity A (chord $A B$ ) $\(\leq 9.55\)$
- Quantity $\(\mathrm{B}=10\)$
Since $9.55<10$,
Quantity B is greater than Quantity A.
- The circumference of the circle is 30 .
- Quantity A: length of chord $A B$.
- Quantity B: 10.
Step 1: Find the radius of the circle
Circumference $\(C=2 \pi r\)$ :
$$
\(30=2 \pi r \Longrightarrow r=\frac{30}{2 \pi}=\frac{15}{\pi}\)
$$
Numerical approximation:
$$
\(r \approx \frac{15}{3.1416} \approx 4.7746\)
$$
Step 2: Calculate the diameter
$$
\(\text { Diameter }=2 r \approx 2 \times 4.7746=9.5492\)
$$
Step 3: Analyze chord $A B$
- The maximum possible chord length in a circle is the diameter.
- So, length of chord $\(A B \leq 9.55\)$ (approx).
Step 4: Compare Quantities
- Quantity A (chord $A B$ ) $\(\leq 9.55\)$
- Quantity $\(\mathrm{B}=10\)$
Since $9.55<10$,
Quantity B is greater than Quantity A.
gmatclubot
Re: The circumference of the circle above is 30 [#permalink]
29 Jul 2025, 12:37
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