Trignometry problem

Expert replies

camitava: Legendary Member; Posts: 645; Joined: Wed Sep 05, 2007 4:37 amFollowed by: 5 members; Location: India; Thanked: 34 times

by camitava » Fri Sep 14, 2007 4:41 am

Again a trignometric problem ...

18. The figure above represents a rectangular parking lot that is 30 meters by 40 meters and an attached semicircular driveway that has an outer radius of 20 meters and an inner radius of 10 meters. If the shaded region is not included, what is the area, in square meters, of the lot and driveway?
(A) 1,350π
(B) 1,200 + 400π
(C) 1,200 + 300π
(D) 1,200 + 200π
(E) 1,200 + 150π

To me, C is coming as the correct choice. But in the answer, it is saying that the OC is E. How and why, friends?

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Correct me If I am wrong

Regards,

Amitava

Source: Beat The GMAT — Problem Solving | Fri Sep 14, 2007 4:41 am

mschling52: Master | Next Rank: 500 Posts; Posts: 105; Joined: Mon Sep 18, 2006 12:34 pm; Location: OH; Thanked: 7 times; GMAT Score:780

by mschling52 » Fri Sep 14, 2007 5:01 am

I agree with C.

Area of rectangle = 1200
Area of semicircle = 400(pi)
Area of shaded = 100(pi)

Total w/o shaded = 1200+400(pi)-100(pi) = 1200+300(pi)

tanyajoseph: Master | Next Rank: 500 Posts; Posts: 103; Joined: Wed May 30, 2007 6:17 amFollowed by: 1 member

by tanyajoseph » Fri Sep 14, 2007 5:23 am

Area of rect = 1200
Area of Outer CIRCLE - 400pi
Area of Inner CIRCLE - 100pi

So area of semicircle excluding inner circle should be either (400pi-100pi)/2
or 400pi/2 - 100pi/2 which would both give 150 pi.
So answer would be 1200 + 150 pi --->E

Key: The catch is to calculate the area of semicircle and not the area of circle

kajcha: Master | Next Rank: 500 Posts; Posts: 321; Joined: Tue Aug 28, 2007 5:42 am; Thanked: 1 times

by kajcha » Fri Sep 14, 2007 5:31 am

Should be E

camitava: Legendary Member; Posts: 645; Joined: Wed Sep 05, 2007 4:37 amFollowed by: 5 members; Location: India; Thanked: 34 times

by camitava » Sat Sep 15, 2007 12:07 am

Ohhhhh! Now got it. Thanks a lot friends. Look another example of overlook and carelessness. While solving the problem, I really forgot that we are dealing with semi-circles not a circle! Look how careless I am.

Correct me If I am wrong

Regards,

Amitava

niks_01.27: Senior | Next Rank: 100 Posts; Posts: 45; Joined: Wed Jun 20, 2007 12:40 pm; Location: Cleveland, OH

by niks_01.27 » Sun Sep 16, 2007 3:21 pm

I always write on the scratch paper things like "semi-circle" here, that helps. You can also try it out.

regards
niks...

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