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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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New post Updated on: 07 Feb 2012, 12:35
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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?

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

Originally posted by Lolaergasheva on 05 Mar 2011, 05:56.
Last edited by Bunuel on 07 Feb 2012, 12:35, edited 1 time in total.
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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 07 Feb 2012, 12:35
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1
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

Hope it helps.
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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 20 Jun 2013, 06:23
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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 03 Jul 2013, 13:37
I've got a question. What if x=0.5 ? In that case, sum of PQ and QR would be 3 whereas PR would be 3.5 Wouldn't this invalidate (a) making (c) the right answer ? Or am I overreaching by questioning the validity of the triangle when it is stated that PQR is a triangle ?
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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 03 Jul 2013, 13:46
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gmatnoob23 wrote:
I've got a question. What if x=0.5 ? In that case, sum of PQ and QR would be 3 whereas PR would be 3.5 Wouldn't this invalidate (a) making (c) the right answer ? Or am I overreaching by questioning the validity of the triangle when it is stated that PQR is a triangle ?


The length of any side of a triangle must be larger than the positive difference of the other two sides:

PR - QR < PQ
(x+3) - (x+2) < x
1 < x

Therefore x cannot be 0.5.

Hope it's clear.
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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 03 Jul 2013, 14:13
Thanks. That cleared it up.
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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 18 Nov 2013, 21:22
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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Re: In PQR, if PQ = x, QR = x + 2, and PR = y, which of the  [#permalink]

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New post 19 Nov 2013, 02:08
madn800 wrote:
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 PQR, if PQ = x, QR = x + 2, and PR = y, which of the  [#permalink]

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New post 11 Sep 2015, 02:12
statement 1 : y=X+3 gives us following points
x,x+2,x+3 are the sides

Statement 2 " nothing conclusive


hence 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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New post 25 Aug 2016, 15:52
2
We start by sketching the triangle.

Image

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.

The answer is 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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New post 25 Apr 2018, 12:53
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.

Answer: A.

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.
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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 25 Apr 2018, 21:32
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.

Answer: A.

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

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New post 26 Apr 2018, 07:19
dave13 wrote:
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.


This simple means if a,b,c are three sides of a triangle then as per the rule
a-b<c<a+b we can write is for any side so
b-c<a<b+c and
c-a<b<c+a

this rule will follow. and yes as we are talking about the length -ve sign to neglect because lenght can not be negative..

so for example if two sides of a triangle are 3 and 9 then third side can only be between 9-3 < third side < 9+3 = 6< Third side< 12

Hope it helps..
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Re: In PQR, if PQ = x, QR = x + 2, and PR = y, which of the &nbs [#permalink] 26 Apr 2018, 07:19
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