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Joined: 10 Apr 2015
Posts: 6218
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A project requires a rectangular sheet of cardboard satisfyi
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30 Jan 2019, 09:28
30 Jan 2019, 09:28
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A project requires a rectangular sheet of cardboard satisfying the following requirement: When the sheet is cut into identical rectangular halves, each of the resulting rectangles has the same ratio of length to width as the original sheet. Which of the following sheets comes closest to satisfying the requirement?
(A) A sheet measuring 7 inches by 10 inches
(B) A sheet measuring 8 inches by 14 inches
(C) A sheet measuring 10 inches by 13 inches
(D) A sheet measuring 3 feet by 5 feet
(E) A sheet measuring 5 feet by 8 feet
(A) A sheet measuring 7 inches by 10 inches
(B) A sheet measuring 8 inches by 14 inches
(C) A sheet measuring 10 inches by 13 inches
(D) A sheet measuring 3 feet by 5 feet
(E) A sheet measuring 5 feet by 8 feet
Re: A project requires a rectangular sheet of cardboard satisfyi
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30 Jan 2019, 20:31
30 Jan 2019, 20:31
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GreenlightTestPrep wrote:
A project requires a rectangular sheet of cardboard satisfying the following requirement: When the sheet is cut into identical rectangular halves, each of the resulting rectangles has the same ratio of length to width as the original sheet. Which of the following sheets comes closest to satisfying the requirement?
(A) A sheet measuring 7 inches by 10 inches
(B) A sheet measuring 8 inches by 14 inches
(C) A sheet measuring 10 inches by 13 inches
(D) A sheet measuring 3 feet by 5 feet
(E) A sheet measuring 5 feet by 8 feet
(A) A sheet measuring 7 inches by 10 inches
(B) A sheet measuring 8 inches by 14 inches
(C) A sheet measuring 10 inches by 13 inches
(D) A sheet measuring 3 feet by 5 feet
(E) A sheet measuring 5 feet by 8 feet
So, when you half a rectangle, one side will get halved and other will remain the same.
Thus the ratio of B:L should be same as L/2:B or L:2B..
This means B:L=L:2B or \(L^2=2B^2\)..
Let us check the options with this.
(A) A sheet measuring 7 inches by 10 inches
B=7 and L=10, so \(L^2=2B^2...10^2=2*7^2....100=98\)..YES almost equal
(B) A sheet measuring 8 inches by 14 inches
B=8 and L=14, so \(L^2=2B^2...14^2=2*8^2....196=128\)..NO
(C) A sheet measuring 10 inches by 13 inches
B=10 and L=13, so \(L^2=2B^2...13^2=2*10^2....169=200\)..NO
(D) A sheet measuring 3 feet by 5 feet
B=3 and L=5, so \(L^2=2B^2...5^2=2*3^2....25=18\)..NO
(E) A sheet measuring 5 feet by 8 feet
B=5 and L=8, so \(L^2=2B^2...8^2=2*5^2....64=50\)..NO
A
General Discussion
Retired Moderator
Joined: 10 Apr 2015
Posts: 6218
Given Kudos: 136
Re: A project requires a rectangular sheet of cardboard satisfyi
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31 Jan 2019, 10:46
31 Jan 2019, 10:46
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GreenlightTestPrep wrote:
A project requires a rectangular sheet of cardboard satisfying the following requirement: When the sheet is cut into identical rectangular halves, each of the resulting rectangles has the same ratio of length to width as the original sheet. Which of the following sheets comes closest to satisfying the requirement?
(A) A sheet measuring 7 inches by 10 inches
(B) A sheet measuring 8 inches by 14 inches
(C) A sheet measuring 10 inches by 13 inches
(D) A sheet measuring 3 feet by 5 feet
(E) A sheet measuring 5 feet by 8 feet
(A) A sheet measuring 7 inches by 10 inches
(B) A sheet measuring 8 inches by 14 inches
(C) A sheet measuring 10 inches by 13 inches
(D) A sheet measuring 3 feet by 5 feet
(E) A sheet measuring 5 feet by 8 feet
Here's an algebraic solution:
Let x be length of the LONG side of the original rectangle
Let y be length of the SHORT side of the original rectangle
Then cut the rectangle into two pieces
We want the resulting rectangles to have the same ratio of length to width as the original sheet.
In other words, we want x/y = y/(x/2)
Cross multiply to get: x²/2 = y²
Multiply both sides by 2 to get: x² = 2y²
Divide both sides by y² to get: x²/y² = 2
Take square root of both sides to get: x/y = √2
IMPORTANT: For the GRE, it's often useful to know the following APPROXIMATIONS: √2 ≈ 1.4, √3 ≈ 1.7, √5 ≈ 2.2
So, we know that x/y ≈ 1.4
In other words, the ratio (LONG side)/(SHORT side) ≈ 1.4
Now check the answer choices:
(A) 10/7 = 1 3/7 ≈ 1.4 LOOKS GOOD!
(B) 14/8 = 1 6/8 = 1.75 ELIMINATE
(C) 13/10 = 1.3 ELIMINATE
(D) 5/3 = 1 2/3 ≈ 1.66 ELIMINATE
(E) 8/5 = 1.6 ELIMINATE
Answer: A
Cheers,
Brent
