A cow is tethered to the corner of a rectangular shed. If the length

Question

https://gmatclub.com/forum/download/file.php?id=21039 A cow is tethered to the corner of a rectangular shed. If the length of the rope is 5, and the shed has length 4 and width 3, what is the maximum area that is accessible to the cow? (The cow cannot enter the shed). A. 12 \pi B. 15 \pi C. 16 \pi D. 18 \pi E. 20 \pi cowandrope_figure.PNG

Bunuel · Accepted Answer

https://gmatclub.com/forum/download/file.php?id=21039 A cow is tethered to the corner of a rectangular shed. If the length of the rope is 5, and the shed has length 4 and width 3, what is the maximum area that is accessible to the cow? (The cow cannot enter the shed). A. 12 \pi B. 15 \pi C. 16 \pi D. 18 \pi E. 20 \pi Look at the diagram below: https://gmatclub.com/forum/download/file.php?id=21040 The area equals to 3/4th of the red circle + 1/4th of the green circle + 1/4th of the blue circle \frac{3}{4}\pi{5^2}+\frac{1}{4}\pi{2^2}+\frac{1}{4}\pi{1^2}=20\pi . Answer: E. cow.PNG

nhattruong1302 · Answer

E
Be quick: the area that the cow can access to would definitely more than 25*pie*3/4 > 18*pie
=> 20*pie is correct

PareshGmat · Answer

What a nice explanation this is.... This question was not so easy as to what I thought... Kudos to you Bunuel

Patronus · Answer

Hi  Bunuel  ,

Why can't I take the "Area of red circle" and subtract the "Area of rectangular shed" from it?
This also satisfies the condition that the cow cannot be inside the rectangular shed, in my opinion.

Please explain.

ENGRTOMBA2018 · Answer

You can subtract the area of the rectangle (= 12 unit^2 ) from the area of the circle (= 25* \pi ) to get approx.  21 \pi  (assuming  \pi = 3 ). To be sure you can see that the area would be greater than 3/4* area of the circle (even if you dont do the actual calculatoons for 1/4 blue circle and 1/4 of the green circles) and 3/4 * area of the circle = (approx.)  18.75* \pi . So your answer should be between  18.75\pi  and  21\pi . Only option E satisfies these conditions.

manlog · Answer

It's not written anywhere that the rope is in the same plane as the shed, so we can't assume that. Thus there is a region behind the shed which is not accounted for. The correct answer should be 25pi - 12 without any approximation (since the stem doesn't ask for an approximate solution).

Bunuel · Answer

Official Guide: All figures lie in a plane unless otherwise indicated.

So, no need to over-complicate things.

manlog · Answer

Bunuel , agree. thanks for the quote!

bumpbot · Answer

Automated notice from GMAT Club BumpBot: 

A member just gave Kudos to this thread, showing it’s still useful. I’ve bumped it to the top so more people can benefit. Feel free to add your own questions or solutions.

 This post was generated automatically.

A cow is tethered to the corner of a rectangular shed. If the length

Prep Toolkit

Top 5 GMAT Debrief Videos

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards

GMAT Problem Solving (PS) Questions

A cow is tethered to the corner of a rectangular shed. If the length

Prep Toolkit

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards