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A Persian rug set on a dining room floor measures a inches by b inches

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A Persian rug set on a dining room floor measures a inches by b inches [#permalink]

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New post 26 Nov 2014, 06:43
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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)

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[Reveal] Spoiler: OA

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Re: A Persian rug set on a dining room floor measures a inches by b inches [#permalink]

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New post 26 Nov 2014, 07:26
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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.
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image.png [ 3.91 KiB | Viewed 1502 times ]

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Re: A Persian rug set on a dining room floor measures a inches by b inches [#permalink]

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New post 26 Nov 2014, 10:47
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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

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Re: A Persian rug set on a dining room floor measures a inches by b inches [#permalink]

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New post 26 Nov 2014, 22:06
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Answer = E) ab − (a − 2c)(b − 2c)

Refer diagram below:
Attachment:
rug.png
rug.png [ 2.37 KiB | Viewed 1459 times ]


We require to find area of the shaded region

Total area = ab

Area of non-shaded region = (a-2c)(b-2c)

Area of shaded region = ab − (a − 2c)(b − 2c)
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Re: A Persian rug set on a dining room floor measures a inches by b inches [#permalink]

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New post 27 Nov 2014, 06:34
Bunuel wrote:

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


You all got it right. The answer is E.
_________________

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

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Re: A Persian rug set on a dining room floor measures a inches by b inches [#permalink]

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Re: A Persian rug set on a dining room floor measures a inches by b inches   [#permalink] 21 Oct 2017, 10:31
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