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x+y or 90
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21 Jun 2023, 03:27
21 Jun 2023, 03:27
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Quantity A |
Quantity B |
x+y |
90 |
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.
Post A Detailed Correct Solution For The Above Questions And Get Kudos.
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Re: x+y or 90
[#permalink]
22 Jun 2023, 04:20
22 Jun 2023, 04:20
1
3 mins to solve.. but we got there!
Lets consider p=1
If p=1, the sides are: 7,7,10
This triangle is valid per inequality (17>7, 14>10) so we don't have to worry about an invalid case.
In this case, x and y are the same angle. Their sum will therefore be 180-z (z is the third angle).
If this were a right isos triangle, the hypotenuse would be: \(7\sqrt{2}\), which is roughly 9.8. Since our actual hypotenuse is greater than 9.8, this implies that the angle z must be greater than 90. This, in turn, implies that x+y<90.
So for this case, we have QA<QB
Lets consider p=0
If p=0, the sides are: 6,8,10
-> valid triangle once again (14>10, 18>6, 16>8)
Notice that this is a 3:4:5 triangle -> this implies that the angle z is 90. Which in turn implies that x and y must sum to 90 in this case. Therefore, for this case, x+y=90 -> QA=QB.
As we have two valid cases, the answer is D.
Lets consider p=1
If p=1, the sides are: 7,7,10
This triangle is valid per inequality (17>7, 14>10) so we don't have to worry about an invalid case.
In this case, x and y are the same angle. Their sum will therefore be 180-z (z is the third angle).
If this were a right isos triangle, the hypotenuse would be: \(7\sqrt{2}\), which is roughly 9.8. Since our actual hypotenuse is greater than 9.8, this implies that the angle z must be greater than 90. This, in turn, implies that x+y<90.
So for this case, we have QA<QB
Lets consider p=0
If p=0, the sides are: 6,8,10
-> valid triangle once again (14>10, 18>6, 16>8)
Notice that this is a 3:4:5 triangle -> this implies that the angle z is 90. Which in turn implies that x and y must sum to 90 in this case. Therefore, for this case, x+y=90 -> QA=QB.
As we have two valid cases, the answer is D.
Re: x+y or 90
[#permalink]
26 Oct 2024, 20:37
26 Oct 2024, 20:37
Hello from the GRE Prep Club BumpBot!
Thanks to another GRE Prep Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).
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Thanks to another GRE Prep Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).
Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
