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15 Nov 2021, 02:30
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D
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Difficulty:
5%
(low)
Question Stats:
90% (01:25) correct
10%
(01:32)
wrong
based on 77
sessions
History
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Square G has sides of length 4 inches. Is the area of Square H exactly one half the area of Square G?
(1) The length of the diagonal of Square H equals the length of one side of Square G.
(2) The perimeter of Square H is twice the length of the diagonal of Square G
(1) The length of the diagonal of Square H equals the length of one side of Square G.
(2) The perimeter of Square H is twice the length of the diagonal of Square G
15 Nov 2021, 05:20
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Statement (1) The length of the diagonal of Square H equals the length of one side of Square G.
We can calculate side of square H - Sufficient
Statement (2) The perimeter of Square H is twice the length of the diagonal of Square G
We can calculate side of square H - Sufficient
(D) is correct
We can calculate side of square H - Sufficient
Statement (2) The perimeter of Square H is twice the length of the diagonal of Square G
We can calculate side of square H - Sufficient
(D) is correct
15 Nov 2021, 09:05
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Bunuel
Given: Square G has sides of length 4 inches.
Area of square G = (side)² = 4² = 16
Target question: Is the area of Square H exactly one half the area of Square G?
This is a good candidate for rephrasing the target question.
Area of square G = 16
So, the target question is asking how's the weather the area of Square H = 8 (which is half of 16)
If the area of Square H were 8, then each side of the square would have length √8
REPHRASED target question: Does each side of Square H have length √8?
Aside: the video below has tips on rephrasing the target question
Statement 1: The length of the diagonal of Square H equals the length of one side of Square G.
In other words, the diagonal of Square H has length 4, which means we have the following:
When we apply the Pythagorean theorem we get, x² + x² = 4²
Simplify: 2x² = 16
Divide both sides by 2 to get: x² = 8
Solve: x = √8
So, the answer to the REPHRASED target question is YES, each side of Square H has length √8
Statement 1 is SUFFICIENT
Statement 2: The perimeter of Square H is twice the length of the diagonal of Square G
Here's Square G:
When we apply the Pythagorean theorem we get, 4² + 4² = d²
Simplify: 16 + 16 = d²
Simplify: 32 = d²
Solve: d = √32 = 2√8 (notice that I didn't completely simplify √32 to get 4√2. You'll see why shortly)
This means the perimeter of Square H = 2(2√8) = 4√8
So, each side of Square H has length √8
The answer to the REPHRASED target question is YES, each side of Square H has length √8
Statement 2 is SUFFICIENT
Answer: D
VIDEO ON REPHRASING THE TARGET QUESTION:
