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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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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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Collection of Questions:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.


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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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Joined: 02 Sep 2009
Posts: 49258
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.
_________________

New to the Math Forum?
Please read this: Ultimate GMAT Quantitative Megathread | All You Need for Quant | PLEASE READ AND FOLLOW: 12 Rules for Posting!!!

Resources:
GMAT Math Book | Triangles | Polygons | Coordinate Geometry | Factorials | Circles | Number Theory | Remainders; 8. Overlapping Sets | PDF of Math Book; 10. Remainders | GMAT Prep Software Analysis | SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) | Tricky questions from previous years.

Collection of Questions:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.


What are GMAT Club Tests?
Extra-hard Quant Tests with Brilliant Analytics

Re: M70-23 &nbs [#permalink] 04 Sep 2018, 21:02
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