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Math Expert V
Joined: 02 Sep 2009
Posts: 59182
In triangle PQR, if PQ = x, QR = x + 2, and PR = y, which of the three  [#permalink]

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Question Stats: 87% (00:57) correct 13% (01:19) wrong based on 871 sessions

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In triangle PQR, if PQ = x, QR = x + 2, and PR = y, which of the three angles of triangle PQR has the greatest degree measure?

(1) y = x+ 3
(2) x = 2

Practice Questions
Question: 19
Page: 276
Difficulty: 600

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Originally posted by Bunuel on 13 Aug 2012, 07:16.
Last edited by Bunuel on 06 Feb 2019, 01:28, edited 1 time in total.
Renamed the topic.
Math Expert V
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Posts: 59182
Re: In triangle PQR, if PQ = x, QR = x + 2, and PR = y, which of the three  [#permalink]

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SOLUTION

In Δ PQR, if PQ = x, QR = x + 2, and PR = y, which of the three angles of Δ PQR has the greatest degree measure?

Important properties of a triangle.
The shortest side is always opposite the smallest angle.
The longest side is always opposite the largest angle.

The length of any side of a triangle must be larger than the positive difference of the other two sides, but smaller than the sum of the other two sides.

(1) y = x + 3 --> PR is the longest side, hence opposite the largest angle PQR. Sufficient.
(2) x = 2 --> PQ=2 and QR=4 --> 2<PR<6. So, we cannot determine which side is the longest QR or PR. Not sufficient.

For more on this topic check Triangles chapter of Math Book: math-triangles-87197.html
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Re: In triangle PQR, if PQ = x, QR = x + 2, and PR = y, which of the three  [#permalink]

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2
IMO A
1) Sufficient: we have comparison of all 3 sides of triangle in terms of x (x= +ve). Angle opposite to x+3 will have greatest degree measure.
2) Insufficient: We don't know value of Y.
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Re: In triangle PQR, if PQ = x, QR = x + 2, and PR = y, which of the three  [#permalink]

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Bunuel wrote:
The Official Guide for GMAT® Review, 13th Edition - Quantitative Questions Project

In triangle PQR, if PQ = x, QR = x + 2, and PR = y, which of the three angles of triangle PQR has the greatest degree measure?

(1) y = x+ 3
(2) x = 2

Practice Questions
Question: 19
Page: 276
Difficulty: 600

[/textarea]

A
1) Gives correlation between all sides, X+3 is the longest side
2) Insufficient -> x = 2, 2nd side = 4, and 3rd side 2<y<6
So y could be 3 or 5 (3rd side always greater than difference of other 2 but less than sum)
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Math Expert V
Joined: 02 Sep 2009
Posts: 59182
Re: In triangle PQR, if PQ = x, QR = x + 2, and PR = y, which of the three  [#permalink]

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1
1
SOLUTION

In Δ PQR, if PQ = x, QR = x + 2, and PR = y, which of the three angles of Δ PQR has the greatest degree measure?

Important properties of a triangle.
The shortest side is always opposite the smallest angle.
The longest side is always opposite the largest angle.

The length of any side of a triangle must be larger than the positive difference of the other two sides, but smaller than the sum of the other two sides.

(1) y = x + 3 --> PR is the longest side, hence opposite the largest angle PQR. Sufficient.
(2) x = 2 --> PQ=2 and QR=4 --> 2<PR<6. So, we cannot determine which side is the longest QR or PR. Not sufficient.

For more on this topic check Triangles chapter of Math Book: math-triangles-87197.html
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Re: In triangle PQR, if PQ = x, QR = x + 2, and PR = y, which of the three  [#permalink]

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Buneul I believe that statement (2) should be interpreted as follows: firstly, if x=2 then PQ=x=2; also, QR= x+2=4. Now the possible values of the third side lie between (4-2=)2 and (4+2=)6 that is the third side PR can take the values 3,4 or 5. For (PQ,PR,QR)=(2,3,4) largest angle is P. Next for (2,4,4) angle P=Q=greatest. Lastly, for (2,5,4) largest angle is Q. As, we are getting three different answers this statement is clearly insufficient.
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Posts: 59182
Re: In triangle PQR, if PQ = x, QR = x + 2, and PR = y, which of the three  [#permalink]

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Buneul I believe that statement (2) should be interpreted as follows: firstly, if x=2 then PQ=x=2; also, QR= x+2=4. Now the possible values of the third side lie between (4-2=)2 and (4+2=)6 that is the third side PR can take the values 3,4 or 5. For (PQ,PR,QR)=(2,3,4) largest angle is P. Next for (2,4,4) angle P=Q=greatest. Lastly, for (2,5,4) largest angle is Q. As, we are getting three different answers this statement is clearly insufficient.

From my post above:
(2) x = 2 --> PQ=2 and QR=4 --> 2<PR<6. So, we cannot determine which side is the longest QR or PR. Not sufficient.

Most of your reasoning is correct. What you did wrong is that you assumed that the length of PR must be an integer.
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Re: In triangle PQR, if PQ = x, QR = x + 2, and PR = y, which of the three  [#permalink]

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Bunuel wrote:
In triangle PQR, if PQ = x, QR = x + 2, and PR = y, which of the three angles of triangle PQR has the greatest degree measure?

(1) y = x+ 3
(2) x = 2

Practice Questions
Question: 19
Page: 276
Difficulty: 600

1) tells us the length relation among the three sides, so it's sufficient for us to know which angle has the greatest degree measure
2) tells us nothing about y and so it's insufficient..

We go with A
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Re: In triangle PQR, if PQ = x, QR = x + 2, and PR = y, which of the three  [#permalink]

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We start by sketching the triangle. We need to determine the angle with the greatest degree measure. Remember that the angle with the greatest measure is always opposite the side of greatest length.

Statement One Alone:

y = x + 3

Since we know that y = x + 3, we know that PR is the longest side of the triangle. Thus, we know that angle PQR, the angle opposite side PR, is the angle with the largest measure. Statement one is sufficient to answer the question. We can eliminate answer choices B, C, and E.

Statement Two Alone:

x = 2

Only knowing the value of x is not sufficient to answer the question because we don’t know the value of y.

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Re: In triangle PQR, if PQ = x, QR = x + 2, and PR = y, which of the three  [#permalink]

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Bunuel wrote:
In Δ PQR, if PQ = x, QR = x + 2, and PR = y, which of the three angles of Δ PQR has the greatest degree measure?

Important properties of a triangle.
The shortest side is always opposite the smallest angle.
The longest side is always opposite the largest angle.

The length of any side of a triangle must be larger than the positive difference of the other two sides, but smaller than the sum of the other two sides.

(1) y = x + 3 --> PR is the longest side, hence opposite the largest angle PQR. Sufficient.
(2) x = 2 --> PQ=2 and QR=4 --> 2<PR<6. So, we cannot determine which side is the longest QR or PR. Not sufficient.

For more on this topic check Triangles chapter of Math Book: http://gmatclub.com/forum/math-triangles-87197.html

Hope it helps.

Bunuel can you please rephrase the sentence below., cant understand it somehow The length of any side of a triangle must be larger than the positive difference of the other two sides, but smaller than the sum of the other two sides.
Math Expert V
Joined: 02 Sep 2009
Posts: 59182
Re: In triangle PQR, if PQ = x, QR = x + 2, and PR = y, which of the three  [#permalink]

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dave13 wrote:
Bunuel wrote:
In Δ PQR, if PQ = x, QR = x + 2, and PR = y, which of the three angles of Δ PQR has the greatest degree measure?

Important properties of a triangle.
The shortest side is always opposite the smallest angle.
The longest side is always opposite the largest angle.

The length of any side of a triangle must be larger than the positive difference of the other two sides, but smaller than the sum of the other two sides.

(1) y = x + 3 --> PR is the longest side, hence opposite the largest angle PQR. Sufficient.
(2) x = 2 --> PQ=2 and QR=4 --> 2<PR<6. So, we cannot determine which side is the longest QR or PR. Not sufficient.

For more on this topic check Triangles chapter of Math Book: http://gmatclub.com/forum/math-triangles-87197.html

Hope it helps.

Bunuel can you please rephrase the sentence below., cant understand it somehow The length of any side of a triangle must be larger than the positive difference of the other two sides, but smaller than the sum of the other two sides.

If the two sides of a triangle are 8 and 6, then for the third side we'd have:

(8 - 6) < (third side) < (8 + 6)
2 < (third side) < 14
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Re: In triangle PQR, if PQ = x, QR = x + 2, and PR = y, which of the three  [#permalink]

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_________________ Re: In triangle PQR, if PQ = x, QR = x + 2, and PR = y, which of the three   [#permalink] 15 Sep 2018, 11:06
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