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GRE Math Challenge #140-y or 4x
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Updated on: 24 Jul 2020, 16:13
Updated on: 24 Jul 2020, 16:13
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A
B
C
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Question Stats:
77% (00:50) correct
22% (01:15) wrong based on 169 sessions
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Quantity A |
Quantity B |
y |
4x |
A)The quantity in Column A is greater.
B)The quantity in Column B is greater.
C)The two quantities are equal.
D)The relationship cannot be determined from the information given.
Kudos for the right answer and explanation
Show: ::
Attachment:
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Retired Moderator
Joined: 10 Apr 2015
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Given Kudos: 136
Re: GRE Math Challenge #140
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16 May 2015, 14:18
16 May 2015, 14:18
2
sandy wrote:
Quantity A: y
Quantity B: 4x
First find the value of x.
The lower triangle has 3 angles: x, 2x, 90
So, we know that x + 2x + 90 = 180
Simplify: 3x + 90 = 180
Simplify: 3x = 90
Solve: x = 30
This means the angle opposite x is also 30 degrees.
So, we know 2 of the 3 angles in the top triangle. They are 30 and 90 degrees.
30 + 90 = 120, so the 3rd angle in the top triangle = 60 degrees.
Since angles on a line add to 180 degrees, we know that y = 120 degrees
We get:
Quantity A: y = 120
Quantity B: 4x = (4)(30) = 120
Answer:
Show: ::
C
Cheers,
Brent
Re: GRE Math Challenge #140-y or 4x
[#permalink]
24 Aug 2020, 18:24
24 Aug 2020, 18:24
1
Here is one simple approach to the problem comparing y and 4x:
1. Recognize that the angle vertically opposite from x must also be x degrees.
2. Recognize that y is the exterior angle of the top triangle, meaning it equals the sum of the two further interior angles of the top triangle. Put differently, y = x + 90
3. Using matching operations, simplify y ? 4x --> x+90 ? 4x --> 90 ? 3x --> x ? 30 degrees
4. Compare x ? 30 by turning your attention to the lower triangle. There, we know that 90 + 2x + x = 180 degrees --> x = 30. The relationship b/w x and 30 is equal, so our answer is C.
I hope this helps!
1. Recognize that the angle vertically opposite from x must also be x degrees.
2. Recognize that y is the exterior angle of the top triangle, meaning it equals the sum of the two further interior angles of the top triangle. Put differently, y = x + 90
3. Using matching operations, simplify y ? 4x --> x+90 ? 4x --> 90 ? 3x --> x ? 30 degrees
4. Compare x ? 30 by turning your attention to the lower triangle. There, we know that 90 + 2x + x = 180 degrees --> x = 30. The relationship b/w x and 30 is equal, so our answer is C.
I hope this helps!
