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M70-23

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M70-23  [#permalink]

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New post 03 Sep 2018, 05:46
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  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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Re M70-23  [#permalink]

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New post 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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Re: M70-23  [#permalink]

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New post 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?
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Re: M70-23  [#permalink]

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New post 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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Re: M70-23  [#permalink]

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New post 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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