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26 Nov 2014, 07:43
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E
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Tough and Tricky questions: Geometry.
A Persian rug set on a dining room floor measures a inches by b inches, which includes the actual rug design and a solid colored border c inches. Which algebraic expression below represents the area of the solid colored border in square inches?
A) ab − 4c
B) a + b − [(a − c) + (b − c)]
C) 2a + 2b − [2(a − 2c) + 2(b − 2c)]
D) ab − (a − c)(b − c)
E) ab − (a − 2c)(b − 2c)
Kudos for a correct solution.
Source: Chili Hot GMAT
hopeful101candidate
Joined: 12 Aug 2014
Last visit: 15 May 2018
Posts: 144
Given Kudos: 29
Location: United States (AZ)
Concentration: Finance, Strategy
Schools: Cnsrtm-Johnson '20 (A) Cnsrtm-Darden '20 (A) Cnsrtm-Goizueta '20 (A) Cnsrtm-McCombs '20 (A)
GMAT 1: 700 Q47 V39
Schools: Cnsrtm-Johnson '20 (A) Cnsrtm-Darden '20 (A) Cnsrtm-Goizueta '20 (A) Cnsrtm-McCombs '20 (A)
GMAT 1: 700 Q47 V39
Posts: 144
26 Nov 2014, 08:26
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See attached image.
Think of the length and widths of the carpet with the border as a and b. Then the length and width of the carpet without the border would be a - 2c and b - 2c. The formula for calculating the area of just the border would then be:
ab - (a-2c)(b-2c)
Answer is E.
Think of the length and widths of the carpet with the border as a and b. Then the length and width of the carpet without the border would be a - 2c and b - 2c. The formula for calculating the area of just the border would then be:
ab - (a-2c)(b-2c)
Answer is E.
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intheend14
GMAT 1: 740 Q49 V41
Posts: 125
26 Nov 2014, 11:47
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Total area including everything is just a*b
The area of the rug without the border is simply (a-2c)*(b-2c)--subtract 2c from each dimension as we have a uniform border on both sides, so we factor in a 2c
The area of just the border is the difference between the two values: ab-(a-2c)(b-2c)
Choice E
The area of the rug without the border is simply (a-2c)*(b-2c)--subtract 2c from each dimension as we have a uniform border on both sides, so we factor in a 2c
The area of just the border is the difference between the two values: ab-(a-2c)(b-2c)
Choice E
