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M70-23

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Math Expert
Joined: 02 Sep 2009
Posts: 58344
M70-23  [#permalink]

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03 Sep 2018, 05:46
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Difficulty:

35% (medium)

Question Stats:

83% (02:23) correct 17% (04:33) wrong based on 6 sessions

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A circular pond is drained through a tiny hole in its middle, such that its diameter becomes smaller at a constant rate of $$x$$ meters per second. If it takes the pond $$y$$ seconds to fully drain, what was its initial circumference?

A. $$\frac{2\pi y}{x}$$
B. $$\pi xy$$
C. $$\frac{\pi xy}{2}$$
D. $$2\pi xy$$
E. $$4\pi xy$$

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Joined: 02 Sep 2009
Posts: 58344
Re M70-23  [#permalink]

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03 Sep 2018, 05:46
Official Solution:

A circular pond is drained through a tiny hole in its middle, such that its diameter becomes smaller at a constant rate of $$x$$ meters per second. If it takes the pond $$y$$ seconds to fully drain, what was its initial circumference?

A. $$\frac{2\pi y}{x}$$
B. $$\pi xy$$
C. $$\frac{\pi xy}{2}$$
D. $$2\pi xy$$
E. $$4\pi xy$$

We’ll go for ALTERNATIVE because there are variables in all the answers.

If we pick $$x = 1$$ and $$y = 2$$, it takes 2 seconds for the pool to drain, and each second represents 1 meter of the diameter, so the diameter is 2 × 1 = 2 meters long. Since the circumference is $$\pi × diameter$$, the circle’s circumference is $$\pi × 2 = 2\pi$$. Let’s check the answers: (A) $$\pi$$ − No!; (B) $$2\pi$$ − possible, but we must check the other answer choices; (C) $$\pi$$ – Nope!; (D) $$4\pi$$ – No!; (E) $$8\pi$$ – Eliminated! We are left with answer choice (B).

Answer: B
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Joined: 15 Aug 2012
Posts: 42
Schools: AGSM '19
Re: M70-23  [#permalink]

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04 Sep 2018, 16:15
1
Bunuel wrote:
Official Solution:

A circular pond is drained through a tiny hole in its middle, such that its diameter becomes smaller at a constant rate of $$x$$ meters per second. If it takes the pond $$y$$ seconds to fully drain, what was its initial circumference?

A. $$\frac{2\pi y}{x}$$
B. $$xy$$
C. $$\frac{\pi xy}{2}$$
D. $$2\pi xy$$
E. $$4\pi xy$$

We’ll go for ALTERNATIVE because there are variables in all the answers.

If we pick $$x = 1$$ and $$y = 2$$, it takes 2 seconds for the pool to drain, and each second represents 1 meter of the diameter, so the diameter is 2 × 1 = 2 meters long. Since the circumference is $$\pi × diameter$$, the circle’s circumference is $$\pi × 2 = 2\pi$$. Let’s check the answers: (A) $$\pi$$ − No!; (B) $$2\pi$$ − possible, but we must check the other answer choices; (C) $$\pi$$ – Nope!; (D) $$4\pi$$ – No!; (E) $$8\pi$$ – Eliminated! We are left with answer choice (B).

Answer: B

Hi Bunuel
If B is the right answer, shouldn't it be pi*x*y?
Math Expert
Joined: 02 Sep 2009
Posts: 58344
Re: M70-23  [#permalink]

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04 Sep 2018, 21:02
rajudantuluri wrote:
Bunuel wrote:
Official Solution:

A circular pond is drained through a tiny hole in its middle, such that its diameter becomes smaller at a constant rate of $$x$$ meters per second. If it takes the pond $$y$$ seconds to fully drain, what was its initial circumference?

A. $$\frac{2\pi y}{x}$$
B. $$xy$$
C. $$\frac{\pi xy}{2}$$
D. $$2\pi xy$$
E. $$4\pi xy$$

We’ll go for ALTERNATIVE because there are variables in all the answers.

If we pick $$x = 1$$ and $$y = 2$$, it takes 2 seconds for the pool to drain, and each second represents 1 meter of the diameter, so the diameter is 2 × 1 = 2 meters long. Since the circumference is $$\pi × diameter$$, the circle’s circumference is $$\pi × 2 = 2\pi$$. Let’s check the answers: (A) $$\pi$$ − No!; (B) $$2\pi$$ − possible, but we must check the other answer choices; (C) $$\pi$$ – Nope!; (D) $$4\pi$$ – No!; (E) $$8\pi$$ – Eliminated! We are left with answer choice (B).

Answer: B

Hi Bunuel
If B is the right answer, shouldn't it be pi*x*y?

Yes. $$\pi$$ was missing. Edited. Thank you.
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Joined: 04 Oct 2018
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Re: M70-23  [#permalink]

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31 Oct 2018, 17:47
In every second diameter reduces by X, hence radius reduces by X/2. So, in Y sec radius reduces by XY/2. This means the original radius was XY/2.
Hence circumference is 2pieXY/2 = XYpie.

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Re: M70-23   [#permalink] 31 Oct 2018, 17:47
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