PS - rectangle

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karthikpandian19: Legendary Member; Posts: 1665; Joined: Thu Nov 03, 2011 7:04 pmFollowed by: 70 members; Thanked: 165 times

by karthikpandian19 » Tue Jun 12, 2012 7:16 pm

A total of 70 pounds of a certain fertilizer must be used to evenly cover a rectangular field that measures n feet by w feet. How much fertilizer, in pounds, does it take to cover each square yard of the field? (9 square feet = 1 square yard)

(A) 70nw

(B) 630nw

(C) nw/9

(D) nw/70

(E) 630/nw

Regards,
Karthik
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sam2304: Legendary Member; Posts: 1239; Joined: Tue Apr 26, 2011 6:25 amFollowed by: 26 members; Thanked: 233 times; GMAT Score:680

by sam2304 » Tue Jun 12, 2012 9:19 pm

Let the rectangular plot be 10 * 7 feet.
n = 10, m = 7
Now the plot is 70 sq ft, and we have 70 pounds of fertilizer. To cover 1 sq yard we need 9 pounds of fertilizer.

Substitute the values in option only E fits.

If you derive the formula then it goes this way.

For nw feet you need 70 pounds
for 1 sq feet you need 70/nw pounds
for 9 sq feet you need 70/nw * 9 = 630/nw. Same answer.

IMO E.

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das.ashmita: Master | Next Rank: 500 Posts; Posts: 118; Joined: Mon May 21, 2012 10:07 pmFollowed by: 4 members; Thanked: 23 times

by das.ashmita » Tue Jun 12, 2012 9:42 pm

IMO E

karthikpandian19: Legendary Member; Posts: 1665; Joined: Thu Nov 03, 2011 7:04 pmFollowed by: 70 members; Thanked: 165 times

by karthikpandian19 » Tue Jun 12, 2012 11:05 pm

@ashmita, please provide your explanation

das.ashmita wrote:IMO E

Regards,
Karthik
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karthikpandian19: Legendary Member; Posts: 1665; Joined: Thu Nov 03, 2011 7:04 pmFollowed by: 70 members; Thanked: 165 times

by karthikpandian19 » Tue Jun 12, 2012 11:10 pm

OA is E

Regards,
Karthik
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GMATGuruNY: GMAT Instructor; Posts: 15539; Joined: Tue May 25, 2010 12:04 pmFollowed by: 1906 members; Location: New York, NY; Thanked: 13060 times; GMAT Score:790

by GMATGuruNY » Wed Jun 13, 2012 5:30 am

karthikpandian19 wrote:A total of 70 pounds of a certain fertilizer must be used to evenly cover a rectangular field that measures n feet by w feet. How much fertilizer, in pounds, does it take to cover each square yard of the field? (9 square feet = 1 square yard)

(A) 70nw

(B) 630nw

(C) nw/9

(D) nw/70

(E) 630/nw

Let nw = 9 square feet.
Then the amount needed to cover nw -- 1 square yard -- is 70 pounds. This is our target.
Now we plug nw=9 into the answers to see which yields our target of 70.
Only answer choice E works:
630/nw = 630/9 = 70.

The correct answer is E.

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Abhishek009: Master | Next Rank: 500 Posts; Posts: 359; Joined: Wed Mar 11, 2009 4:37 amFollowed by: 2 members; Location: Kolkata, India; Thanked: 50 times

by Abhishek009 » Wed Jun 13, 2012 6:07 am

karthikpandian19 wrote:A total of 70 pounds of a certain fertilizer must be used to evenly cover a rectangular field that measures n feet by w feet. How much fertilizer, in pounds, does it take to cover each square yard of the field? (9 square feet = 1 square yard)

(A) 70nw

(B) 630nw

(C) nw/9

(D) nw/70

(E) 630/nw

Area of the rectangular field is -

Length * Breadth

n*w

nw sqft

Since 9 sqft = 1 yard

1 sq ft = 1/9 yards

Hence nw sqft = nw/9 yards

Now the entire 70 pound of fertilisers must be evenly distributed in the nw/9 sqft area , so fertilizer required to cover each unit area is -

nw/9/70 =>630/nw

Abhishek

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