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is greater x or y
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11 Jun 2023, 23:21
11 Jun 2023, 23:21
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Question Stats:
53% (02:15) correct
46% (01:33) wrong based on 15 sessions
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Quantity A |
Quantity B |
x |
y |
A Quantity A is greater.
B Quantity B is greater.
C The two quantities are equal.
D The relationship cannot be determined from the information given.
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Re: is greater x or y
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14 Jun 2023, 04:00
14 Jun 2023, 04:00
Expert Reply
OE
The question states that AB = BC, which means that triangle ABC is isosceles, and that triangle ABC is the combining of two right triangles, each with a hypotenuse of 10 and legs of 5 and 10/2 = 5. So, triangle ABD is an isosceles right triangle with interior angles of 45-45-90, which means that angle BAC is equal to 45° and x = 45. Triangle EFG is isosceles, which means that triangle EFG is the combining of two right triangles, each with a hypotenuse of 12 and one leg equal to 6. So, triangle EFH is a 30-60-90 triangle, and the leg opposite the 30° angle is equal to one half the hypotenuse, which means that angle FEH is 30° and y = 30. The correct answer is (A).
The question states that AB = BC, which means that triangle ABC is isosceles, and that triangle ABC is the combining of two right triangles, each with a hypotenuse of 10 and legs of 5 and 10/2 = 5. So, triangle ABD is an isosceles right triangle with interior angles of 45-45-90, which means that angle BAC is equal to 45° and x = 45. Triangle EFG is isosceles, which means that triangle EFG is the combining of two right triangles, each with a hypotenuse of 12 and one leg equal to 6. So, triangle EFH is a 30-60-90 triangle, and the leg opposite the 30° angle is equal to one half the hypotenuse, which means that angle FEH is 30° and y = 30. The correct answer is (A).
gmatclubot
Re: is greater x or y [#permalink]
14 Jun 2023, 04:00
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