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In PQR, if PQ = x, QR = x + 2, and PR = y, which of the

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

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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
[Reveal] Spoiler: OA

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

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New post 13 Aug 2012, 07:16
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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.

Answer: A.

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

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New post 13 Aug 2012, 07:34
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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 PQR, if PQ = x, QR = x + 2, and PR = y, which of the [#permalink]

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New post 16 Aug 2012, 12:04
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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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Re: In PQR, if PQ = x, QR = x + 2, and PR = y, which of the [#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.

Answer: A.

For more on this topic check Triangles chapter of Math Book: math-triangles-87197.html
_________________

New to the Math Forum?
Please read this: Ultimate GMAT Quantitative Megathread | All You Need for Quant | PLEASE READ AND FOLLOW: 12 Rules for Posting!!!

Resources:
GMAT Math Book | Triangles | Polygons | Coordinate Geometry | Factorials | Circles | Number Theory | Remainders; 8. Overlapping Sets | PDF of Math Book; 10. Remainders | GMAT Prep Software Analysis | SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) | Tricky questions from previous years.

Collection of Questions:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.


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

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

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New post 05 Sep 2017, 18:22
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


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 Q, the angle opposite side PR, is the angle with the largest measure. Statement one is sufficient to answer the question.

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. Thus, we can’t determine which side is the longest nor which angle is the largest.

Answer: A
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Re: In PQR, if PQ = x, QR = x + 2, and PR = y, which of the   [#permalink] 05 Sep 2017, 18:22
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