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

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Director
Joined: 08 Jul 2004
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In PQR, if PQ = x + 2, and PR = y, which of the three [#permalink]

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26 Aug 2004, 09:13
00:00

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5% (low)

Question Stats:

84% (00:31) correct 16% (00:52) wrong based on 225 sessions

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

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

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OPEN DISCUSSION OF THIS QUESTION IS HERE: https://gmatclub.com/forum/in-pqr-if-pq ... 37224.html
Director
Joined: 05 May 2004
Posts: 573
Location: San Jose, CA
Re: In PQR, if PQ = x + 2, and PR = y, which of the three [#permalink]

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26 Aug 2004, 14:59
E
We dont know anything about RQ
1. RQ can be anything between >1 and <2x+3 The largest angle is always oppostite to the largest side ... insufficient as we cant say for sure which side is largest
2. insufficient
Together ... insufficient same reason as above!
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Location: Singapore
Re: In PQR, if PQ = x + 2, and PR = y, which of the three [#permalink]

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27 Aug 2004, 00:41
E for me too! No information given for the third side.
Director
Joined: 23 May 2008
Posts: 744
Re: In PQR, if PQ = x + 2, and PR = y, which of the three [#permalink]

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12 May 2009, 22:10
typhoidX wrote:
typhoidX wrote:
meesawoosa wrote:
from mba.com Gmat Free Prep Test Software GMAT Practice Test 1

Figure: A right triangle with points S (the right angle), P and Q. from point P, another line extends ending between Q and S. The endpoint of this line is point R.

Basically, the figure has two right triangles - Triangle PSQ and Triangle PRS with Triangle PRS inside Triangle PSQ.

In the figure shown, the measure of angle PRS is how many degrees greater than the measure of angle PQR?

(1) The measure of angle QPR is 30 degrees.
(2) The measure of angles PQR and PRQ combined are 150 degrees.

Any help?

Hopefully I drew the triangle right... anyway,

(1) From this we know the angle of SPQ (60), but we don't know where point R falls along line SQ, so (1) isn't enough.
(2) From this we know RPQ is 30, I don't think we can be sure of anything else...
(Combined) We can find QPR & we can find out PRS, this is enough.

I would probably go with answer (C), but I still have a nagging feeling that we could find out from (2) alone, so I'm not entirely sure.

Okay... now I've figured it out (well, my mom figured it out)... the CORRECT answer is (B), you can indeed find out the answer from (2)alone.

We can solve this algebraically:
Let PQR=A;
Let PRQ=B;
Let PRS=C;

A+B = 150 degrees (from statement 2);
C+B = 180 degrees

We'll subtract the first equation from the second equation, this would eliminate B on the left side of the equal sign, and leave us with 30 degrees on the right side. This leaves us with:
A-C = 30 degrees.
We don't know the precise values of A & C, but we don't need to know, we've algebraically proven that the difference is 30 degrees (correction, my mom has proven that the difference is 30).

great solution, but doesnt statement 1 and 2 give us the same information, wouldnt the answer be D?
Intern
Joined: 12 Apr 2009
Posts: 24
Re: In PQR, if PQ = x + 2, and PR = y, which of the three [#permalink]

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12 May 2009, 23:02
great explanation - thank you. and yes, the answer is D, since both statements give us the same info.
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Joined: 20 Dec 2010
Posts: 1903
Re: In PQR, if PQ = x + 2, and PR = y, which of the three [#permalink]

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05 Mar 2011, 06:09
1
KUDOS
PQ=x
QR=x+2
PR=y

Question: is y>x+2

(1)
y=x+3
x+3>x+2
The angle opposite to the longest side of the triangle is greatest.
$$\angle PQR$$ is the greatest.

Sufficient.

(2)
x=2;
x+2=4;
2<y<6

If y is about 2; the angle opposite y will be smaller than angle opposite x+2.
If y is about 6; the angle opposite y will be the greatest.
Not Sufficient.

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

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05 Mar 2011, 08:26
fluke wrote:
PQ=x
QR=x+2
PR=y

Question: is y>x+2

(1)
y=x+3
x+3>x+2
The angle opposite to the longest side of the triangle is greatest.
$$\angle PQR$$ is the greatest.

Sufficient.

(2)
x=2;
x+2=4;
2<y<6

If y is about 2; the angle opposite y will be smaller than angle opposite x+2.
If y is about 6; the angle opposite y will be the greatest.
Not Sufficient.

Ans: "A"

You are great as always. But I didn't understand why you suppose y>x+2 ?
Math Forum Moderator
Joined: 20 Dec 2010
Posts: 1903
Re: In PQR, if PQ = x + 2, and PR = y, which of the three [#permalink]

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05 Mar 2011, 08:59
1
KUDOS
Lolaergasheva wrote:
fluke wrote:
PQ=x
QR=x+2
PR=y

Question: is y>x+2

(1)
y=x+3
x+3>x+2
The angle opposite to the longest side of the triangle is greatest.
$$\angle PQR$$ is the greatest.

Sufficient.

(2)
x=2;
x+2=4;
2<y<6

If y is about 2; the angle opposite y will be smaller than angle opposite x+2.
If y is about 6; the angle opposite y will be the greatest.
Not Sufficient.

Ans: "A"

You are great as always. But I didn't understand why you suppose y>x+2 ?

No, I didn't suppose so. I just rephrased what's asked in the question. The question asks
which angle is the greatest among the three angles.

What sides are there;
x,x+2,y
What angles are opposite these sides;
opposite x -> $$\angle QRP$$
opposite x+2 -> $$\angle QPR$$
opposite y -> $$\angle PQR$$

x+2 will always be greater than x. So; angle opposite to side x+2 will be greater than the
angle oppsite to x.

$$\angle QPR$$ will always be greater than $$\angle QRP$$. We need to know about
$$\angle PQR$$.

The only question then stands, "Is y> x+2 or y<x+2"

If y> x+2; then y becomes the longest side and the angle opposite to it will become the greatest angle.

If y< x+2; then x+2 becomes the longest side and the angle opposite to it will become the greatest angle.

That's all!!

1) This statements tells us that y=x+3

For any value of x;
y will be the longest side and the angle oppsite y will be the greatest.

2) This statement tells us that;
x=2
x+2=4

y is any value between 2 and 6(if one side of the triangle is 2 and other side 4; the third side will be between the difference
and sum of the other two sides)
means
(4-2) < y < (4+2)
2<y<6

y can be 3 which is less than x+2. x+2 becomes longest.
y can be 5 which is greater than x+2. y becomes longest.
So; we don't definitely know whether y>x+2.
Not sufficient.
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Re: In PQR, if PQ = x + 2, and PR = y, which of the three [#permalink]

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06 Mar 2011, 20:00
The answer is A, reasoning is same as given by fluke.
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Re: In PQR, if PQ = x + 2, and PR = y, which of the three [#permalink]

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07 Jul 2011, 06:42
great solution, thanks for sharing.
Intern
Joined: 06 Jul 2011
Posts: 25
Re: In PQR, if PQ = x + 2, and PR = y, which of the three [#permalink]

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09 Nov 2011, 07:40
I fail to see how (1) provides the same information as (2). Could anyone explain?

From what someone said ("(1) From this we know the angle of SPQ (60), but we don't know where point R falls along line SQ, so (1) isn't enough."), I don't see that one either. How should we know anything about SPQ just by statement 1?
Intern
Joined: 21 Dec 2016
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Re: In PQR, if PQ = x + 2, and PR = y, which of the three [#permalink]

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30 Aug 2017, 15:37
Answer should be A. In option 2, we need to find out value of 'y' to get to the answer

Sent from my Nexus 5 using GMAT Club Forum mobile app
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Joined: 02 Jul 2017
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GMAT 1: 730 Q50 V38
Re: In PQR, if PQ = x + 2, and PR = y, which of the three [#permalink]

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31 Aug 2017, 10:20
Given : Triangle PQR : PQ = x, QR = x + 2, and PR = y
We have to find greatest angle

Rule: The angle opposite to largest side is greatest also angle opposite to smallest side is smallest.

1) y=x+3,
Now we know all the sides in terms of x. Now side PR becomes largest with value x+3 as compared to other 2 sides .
So angle Q is greatest Angle.

Sufficient

2) x= 2. By this we know value of two sides, but we dont know the value of y ie the third side.

So Not Sufficient.

Intern
Joined: 26 Jul 2017
Posts: 7
Re: In PQR, if PQ = x + 2, and PR = y, which of the three [#permalink]

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31 Aug 2017, 11:04
What about the possibility of using both statements? x=2 in y=x+3 or y=5. So pq=2, qr=4 and PR= 5. now we can find out the greatest angle will be opposite PR.
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Joined: 02 Sep 2009
Posts: 45225
Re: In PQR, if PQ = x + 2, and PR = y, which of the three [#permalink]

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31 Aug 2017, 21:25
kartiksfc wrote:
What about the possibility of using both statements? x=2 in y=x+3 or y=5. So pq=2, qr=4 and PR= 5. now we can find out the greatest angle will be opposite PR.

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

OPEN DISCUSSION OF THIS QUESTION IS HERE: https://gmatclub.com/forum/in-pqr-if-pq ... 37224.html
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Re: In PQR, if PQ = x + 2, and PR = y, which of the three   [#permalink] 31 Aug 2017, 21:25
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