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# In the triangle above is RP > PQ ?

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Math Expert
Joined: 02 Sep 2009
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In the triangle above is RP > PQ ?  [#permalink]

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28 May 2017, 01:50
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Difficulty:

25% (medium)

Question Stats:

82% (01:37) correct 18% (01:44) wrong based on 106 sessions

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In the triangle above is RP > PQ ?

(1) y = 180 – x
(2) y = z = 60

Attachment:

2017-05-28_1248.png [ 6.98 KiB | Viewed 1073 times ]

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Re: In the triangle above is RP > PQ ?  [#permalink]

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28 May 2017, 02:22
From the triangle
y+z+180-x = 180
y+z = x

1. y = 180 – x
Substituting in the equation, y+z = x
180 + z = 2x
If angle x is obtuse(specifically equal than 120), there is a possibility of this equation holding true.
But there can be a lot of combinations for angle z and y for which this equation will hold good.
Therefore, we cannot clearly predict which side will be longer.
Hence, insufficient.

2. y = z = 60
When this happens, the triangle will become an equilateral triangle where all sides are equal.
This alone is sufficient.(Option B)
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Re: In the triangle above is RP > PQ ?  [#permalink]

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23 Jan 2018, 01:27
I have a doubt here:

cant it be for the first statement : (1) y = 180 – x is given => x+y= 180 linear pair => the traingle is isosceles with pq = pr => RP< PQ ?

and hence D as ans?

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Re: In the triangle above is RP > PQ ?  [#permalink]

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23 Jan 2018, 01:51
pkh99 wrote:
I have a doubt here:

cant it be for the first statement : (1) y = 180 – x is given => x+y= 180 linear pair => the traingle is isosceles with pq = pr => RP< PQ ?

and hence D as ans?

It's not clear how you concluded that the triangle is isosceles. Also, the highlighted part is contradictory.

In the triangle above is RP > PQ ?

In a triangle larger side is opposite larger angle, so the question basically asks whether z > y. Also, according to the Exterior angle theorem (the measure of an exterior angle of a triangle is equal to the sum of the measures of the remote interior angles), x = y + z.

(1) y = 180 – x.

x = 180 - y;
Substitute in x = y + z:
180 - y = y + z;
2y + z = 180.

If y = z = 60, then the answer to the question is NO but if z = 100 and y = 40, then the answer to the question is YES. Not sufficient.

(2) y = z = 60. Directly gives a NO answer to the question. Sufficient.

Hope it's clear.
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Re: In the triangle above is RP > PQ ?  [#permalink]

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23 Jan 2018, 01:52
pkh99 wrote:
I have a doubt here:

cant it be for the first statement : (1) y = 180 – x is given => x+y= 180 linear pair => the traingle is isosceles with pq = pr => RP< PQ ?

and hence D as ans?

For other subjects:
ALL YOU NEED FOR QUANT ! ! !

Hope it helps.
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Re: In the triangle above is RP > PQ ?  [#permalink]

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24 Jan 2018, 03:44
I concluded the following:

1) If y=180-x the, the according to the Exterior angle Theorem x=angle at Point P -> triangle is isosceles. This means that PQ=QR however it does not provide any information about RP (could be longer or shorter) NOT SUFFICIENT

2) Clearly sufficient if x=y=60 => equilateral triangle, which means all sides have the same length SUFFICIENT
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Re: In the triangle above is RP > PQ ?  [#permalink]

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24 Jan 2018, 06:52
Bunuel wrote:

In the triangle above is RP > PQ ?

(1) y = 180 – x
(2) y = z = 60

Attachment:
2017-05-28_1248.png

From the figure x = y+z

From Statement 1: 2x = 180 + z,. Hence, angle RPQ = 90 - (x/2), which means angle RPQ < 90. However, we dont know anything about other angles. So, Insufficient.
From Statement B: Its clear that its an equilateral triangle. So, Sufficient.
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Re: In the triangle above is RP > PQ ?   [#permalink] 24 Jan 2018, 06:52
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