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Which is greater z or 60

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Which is greater z or 60 [#permalink] New post 25 May 2018, 16:12
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\(x > y\)

Quantity A
Quantity B
z
60


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.
[Reveal] Spoiler: OA

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Re: x > y [#permalink] New post 05 Jun 2018, 23:16
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Given,
x>y hence angle opposite x will be greater than angle opposite y. This is always true for any triangle
Let the angle opposite y be a. then
since this is a isoscles triangle the three angles would be x,x,a

There is another triangle rule that angles in triangle add to 180 degrees.

A possible scenario for the three triangles above would be 70,70,40.
Let us see if we can have z less than 60 degrees.
If z was lets say 59 degree then 2z would be 118 degrees that leaves the third angle opposite to y (a) = 62 degrees
However angle a cannot be more than z.
Notice that z cannot be 60 degree as that would make this triangle an equilateral triangle however a should be less than z.
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Re: Which is greater z or 60 [#permalink] New post 05 May 2020, 10:49
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A bit of a tricky one.

Imagine you have ABC 45,45,90-->here you for sure know that the 90 angle will yield back the longest side.

imagine you have 60,60,60-->here you are more than aware that you have all the sides the same

now you know that the sides that are x are bigger than y---> leading to the conclusion that we have two angles that are larger than 60 degrees, hence answer A
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Re: Which is greater z or 60 [#permalink] New post 06 May 2020, 07:51
i dont understand. if the two sides are equal. arent their angle also equal?
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Re: Which is greater z or 60 [#permalink] New post 06 May 2020, 08:29
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Nikhil4GRE wrote:
i dont understand. if the two sides are equal. arent their angle also equal?


@bubidag is discussing a hypothetical scenario in which 2 angles are 45 degrees.
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Re: Which is greater z or 60   [#permalink] 06 May 2020, 08:29
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