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Angle BAD = y, Angle BAC = z, Angle ABC = x, and Angle ACB

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Arun1992
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Angle BAD = y, Angle BAC = z, Angle ABC = x, and Angle ACB [#permalink] New post   Updated on: 03 Dec 2018, 15:32
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∠BAD = y°, ∠BAC = z°, ∠ABC = x°, and ∠ACB = w°


Quantity A
Quantity B
x + w
y + z


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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Official Answer
D

Originally posted by Arun1992 on 03 Dec 2018, 04:39.
Last edited by GreenlightTestPrep on 03 Dec 2018, 15:32, edited 10 times in total.
Edited by Carcass
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Carcass
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Re: Given Angle BAD = y, Angle BAC = Z [#permalink] New post   03 Dec 2018, 11:22
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No, mainly because we do have all the questions explained here https://gre.myprepclub.com/forum/official- ... html#p3207

And I didn't see this question before.

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GreenlightTestPrep
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Re: Given Angle BAD = y, Angle BAC = Z [#permalink] New post   03 Dec 2018, 11:29
Carcass wrote:
No, mainly because we do have all the questions explained here https://gre.myprepclub.com/forum/official- ... html#p3207

And I didn't see this question before.

Regards


That too :-)

It's a great question either way!
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Carcass
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Re: Given Angle BAD = y, Angle BAC = Z [#permalink] New post   03 Dec 2018, 11:43
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Sir,

please give us some explanation to this question, if you can. Meanwhile, I will edit the main post.

Thank you so much.

Regards
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Re: Angle BAD = y, Angle BAC = z, Angle ABC = x, and Angle ACB [#permalink] New post   03 Dec 2018, 12:43
The answer is A right? Sum of two angles in a triangle is greater than the third angle
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GreenlightTestPrep
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Re: Angle BAD = y, Angle BAC = z, Angle ABC = x, and Angle ACB [#permalink] New post   03 Dec 2018, 15:32
2
Arun1992 wrote:
Image
∠BAD = y°, ∠BAC = z°, ∠ABC = x°, and ∠ACB = w°


Quantity A
Quantity B
x + w
y + z


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


Let's test some possible values (angles)

Case i:
Image
In the above case, y = 70, z = 110, x = 40 and w = 30
So, we get:
QUANTITY A: x + w = 40 + 30 = 70
QUANTITY B: y + z = 70 + 110 = 180
In this case, Quantity B is greater


Case ii:
Image
In the above case, y = 40, z = 50, x = 70 and w = 60
So, we get:
QUANTITY A: x + w = 70 + 60 = 130
QUANTITY B: y + z = 40 + 50 = 90
In this case, Quantity A is greater

Answer: D

Cheers,
Brent
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GreenlightTestPrep
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Re: Angle BAD = y, Angle BAC = z, Angle ABC = x, and Angle ACB [#permalink] New post   03 Dec 2018, 15:34
kruttikaaggarwal wrote:
The answer is A right? Sum of two angles in a triangle is greater than the third angle


Great idea but, unfortunately, that's not a rule.
I believe you're taking the rule regarding side LENGTHS in a triangle and extending it to work with ANGLES (which doesn't work).

Cheers,
Brent
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GreenlightTestPrep
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Re: Given Angle BAD = y, Angle BAC = Z [#permalink] New post   03 Dec 2018, 15:35
1
Carcass wrote:
Sir,

please give us some explanation to this question, if you can. Meanwhile, I will edit the main post.

Thank you so much.

Regards


Done!
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Arun1992
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Re: Angle BAD = y, Angle BAC = z, Angle ABC = x, and Angle ACB [#permalink] New post   03 Dec 2018, 22:24
GreenlightTestPrep wrote:
Arun1992 wrote:
∠BAD = y°, ∠BAC = z°, ∠ABC = x°, and ∠ACB = w°


Quantity A
Quantity B
x + w
y + z


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


Let's test some possible values (angles)

In the above case, y = 70, z = 110, x = 40 and w = 30
So, we get:
QUANTITY A: x + w = 40 + 30 = 70
QUANTITY B: y + z = 70 + 110 = 180
In this case, Quantity B is greater


In the above case, y = 40, z = 50, x = 70 and w = 60
So, we get:
QUANTITY A: x + w = 70 + 60 = 130
QUANTITY B: y + z = 40 + 50 = 90
In this case, Quantity A is greater

Answer: D

Cheers,
Brent



Hi @GreenlightTestPrep

Thanks a lot for ur explanation.
But can u tell me how did u pick the correct angles to check. Is there any logic behind it ?
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HappyMathtutor
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Re: Angle BAD = y, Angle BAC = z, Angle ABC = x, and Angle ACB [#permalink] New post   17 Dec 2018, 20:25
Expert Reply
Just think about this, since we don't have ANY number associated with any of the angles, it's a total crapshoot.
for all we know, it could be a scalene triangle, where x and w are 10 degrees each while y and z total to 160, or the complete opposite.
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Re: Angle BAD = y, Angle BAC = z, Angle ABC = x, and Angle ACB [#permalink] New post   11 Jan 2019, 16:43
I just think in diagram
case1 (Not quantity): angle A= 179.999999
case2 (Not quantity): angle B= 179.999999

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Re: Angle BAD = y, Angle BAC = z, Angle ABC = x, and Angle ACB [#permalink] New post   01 Aug 2022, 07:05
1
Case 1 - maximize x and y
Let x =89.9° and y=89.9°
Quantity B is now very small.

Case 2 - maximize y and z
y =179.9°
Now Quantity A is very small

So, D
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Re: Angle BAD = y, Angle BAC = z, Angle ABC = x, and Angle ACB [#permalink] New post   05 Oct 2023, 18:19
1
Let the third angles in both the triangles be a and b.
a+b=180
z+w+a=180
y+x+b=180

b=180-x-y
a=180-z-w

a+b = 180-x-y+180-z-w
180=360-(x+y+z+w)
Simplifying,
x+y+z+w=180

Hence, x+y=180-(z+w) or vice versa. Hence D
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Re: Angle BAD = y, Angle BAC = z, Angle ABC = x, and Angle ACB [#permalink] New post   26 Oct 2024, 10:03
Carcass, and Arun1992, where can I find problems of the same type?
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Angle BAD = y, Angle BAC = z, Angle ABC = x, and Angle ACB [#permalink] New post   26 Oct 2024, 10:21
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tkorzhan wrote:
Carcass, and Arun1992, where can I find problems of the same type?



here GRE PREMIUM Quant Question Banks - Topic-Wise 2700 Questions under geometry https://gre.myprepclub.com/forum/gre-pr ... ml#p116140

or via tags https://gre.myprepclub.com/forum/search ... earch_tags
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Re: Angle BAD = y, Angle BAC = z, Angle ABC = x, and Angle ACB [#permalink] New post   26 Oct 2024, 10:22
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Re: Angle BAD = y, Angle BAC = z, Angle ABC = x, and Angle ACB [#permalink]
26 Oct 2024, 10:22
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