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If AB=BD, then what is the value of x/y?
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05 Jan 2023, 00:05
05 Jan 2023, 00:05
Expert Reply
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Question Stats:
100% (01:42) correct
0% (00:00) wrong based on 2 sessions
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GRE If AB=BD, then what is the value of xy.jpg [ 22.99 KiB | Viewed 905 times ]
If AB=BD, then what is the value of x/y?
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20/140
Re: If AB=BD, then what is the value of x/y?
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30 Jan 2023, 11:17
30 Jan 2023, 11:17
Expert Reply
OE
According to the problem, AB = BD. Therefore, triangle ABD is an isosceles triangle, and angle BAD is equal to x. Additionally, since you know angle AD E = 90 and angle DAE = 30, you can determine that angle AED = 180 - 90 - 30 = 60 (since these three angles form the triangle ADE). You can update the diagram as follows:
screenshot.1188.jpg [ 37.26 KiB | Viewed 878 times ]
The angles of the large triangle, ACE, must sum to 180. Therefore, 70 + 60 + 30 + x = 180, so x = 20. Since y, x, and x must sum to 180 (they form the angles of triangle ABD), y = 180 - 2x, so y = 140. Thus, the correct ratio is 20/140
According to the problem, AB = BD. Therefore, triangle ABD is an isosceles triangle, and angle BAD is equal to x. Additionally, since you know angle AD E = 90 and angle DAE = 30, you can determine that angle AED = 180 - 90 - 30 = 60 (since these three angles form the triangle ADE). You can update the diagram as follows:
Attachment:
screenshot.1188.jpg [ 37.26 KiB | Viewed 878 times ]
The angles of the large triangle, ACE, must sum to 180. Therefore, 70 + 60 + 30 + x = 180, so x = 20. Since y, x, and x must sum to 180 (they form the angles of triangle ABD), y = 180 - 2x, so y = 140. Thus, the correct ratio is 20/140
gmatclubot
Re: If AB=BD, then what is the value of x/y? [#permalink]
30 Jan 2023, 11:17
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