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22 Feb 2022, 06:30
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D
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
65%
(hard)
Question Stats:
54% (02:14) correct
46%
(01:35)
wrong
based on 83
sessions
History
Date
Time
Result
Not Attempted Yet
If AC = BC and CD = DE then, in terms of x, the value of y is
Note: Figure not drawn to scale
A. x
B. 180 - 2x
C. 90 - 2x
D. 4x - 180
E. 45 + x/4
Are You Up For the Challenge: 700 Level Questions
GMAT_PS_Magoosh_359.png [ 1.96 KiB | Viewed 5205 times ]
Note: Figure not drawn to scale
A. x
B. 180 - 2x
C. 90 - 2x
D. 4x - 180
E. 45 + x/4
Are You Up For the Challenge: 700 Level Questions
Attachment:
GMAT_PS_Magoosh_359.png [ 1.96 KiB | Viewed 5205 times ]
22 Feb 2022, 11:18
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Bunuel
When we add the given information to the diagram we get:
In an isosceles triangle, the angles opposite the equal sides are always equal.
This means ∠A = x°
Also, since the angles in a triangle must add to 180°, we know that ∠ACB = 180 - 2x
The angles in the other triangle are a little trickier, so, let's label them k to get the following diagram:
Since the angles in a triangle must add to 180°, we can write: k + k + y = 180
Simplify: 2k + y = 180
Subtract y from both sides: 2k = 180 - y
Divide both sides by 2 to get: : k = (180 - y)/2
So, we can add this information to our diagram:
Finally, since opposite angles are equal, we can write the following equation: 180 - 2x = k = (180 - y)/2 [we need to solve this equation for y]
Multiply both sides of the equation by 2 to get: 360 - 4x = 180 - y
Subtract 180 from both sides of the equation to get: 180 - 4x = -y
Multiply both sides of the equation by -1 to get: -180 + 4x = y, which can be rearranged as follows: y = 4x - 180
Answer: D
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03 Apr 2024, 02:11
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