GMAT Question of the Day - Daily to your Mailbox; hard ones only

 It is currently 17 Nov 2018, 08:01

### GMAT Club Daily Prep

#### Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized
for You

we will pick new questions that match your level based on your Timer History

Track

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History

## Events & Promotions

###### Events & Promotions in November
PrevNext
SuMoTuWeThFrSa
28293031123
45678910
11121314151617
18192021222324
2526272829301
Open Detailed Calendar
• ### FREE Quant Workshop by e-GMAT!

November 18, 2018

November 18, 2018

07:00 AM PST

09:00 AM PST

Get personalized insights on how to achieve your Target Quant Score. November 18th, 7 AM PST
• ### How to QUICKLY Solve GMAT Questions - GMAT Club Chat

November 20, 2018

November 20, 2018

09:00 AM PST

10:00 AM PST

The reward for signing up with the registration form and attending the chat is: 6 free examPAL quizzes to practice your new skills after the chat.

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

Author Message
TAGS:

### Hide Tags

Manager
Joined: 04 Feb 2011
Posts: 53
Location: US
In PQR, if PQ = x, QR = x + 2, and PR = y, which of the  [#permalink]

### Show Tags

Updated on: 07 Feb 2012, 11:35
2
8
00:00

Difficulty:

5% (low)

Question Stats:

88% (00:52) correct 12% (01:09) wrong based on 604 sessions

### HideShow timer Statistics

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, 04:56.
Last edited by Bunuel on 07 Feb 2012, 11:35, edited 1 time in total.
Math Expert
Joined: 02 Sep 2009
Posts: 50623
Re: In PQR, if PQ = x, QR = x + 2, and PR = y, which of the  [#permalink]

### Show Tags

07 Feb 2012, 11:35
1
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.

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

Hope it helps.
_________________
Math Expert
Joined: 02 Sep 2009
Posts: 50623
Re: In PQR, if PQ = x, QR = x + 2, and PR = y, which of the  [#permalink]

### Show Tags

20 Jun 2013, 05:23
Bumping for review and further discussion*. Get a kudos point for an alternative solution!

*New project from GMAT Club!!! Check HERE

_________________
Intern
Joined: 07 Sep 2012
Posts: 4
Re: In PQR, if PQ = x, QR = x + 2, and PR = y, which of the  [#permalink]

### Show Tags

03 Jul 2013, 12:37
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 ?
Math Expert
Joined: 02 Sep 2009
Posts: 50623
Re: In PQR, if PQ = x, QR = x + 2, and PR = y, which of the  [#permalink]

### Show Tags

03 Jul 2013, 12:46
1
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.
_________________
Intern
Joined: 07 Sep 2012
Posts: 4
Re: In PQR, if PQ = x, QR = x + 2, and PR = y, which of the  [#permalink]

### Show Tags

03 Jul 2013, 13:13
Thanks. That cleared it up.
Manager
Joined: 07 May 2013
Posts: 97
Re: In PQR, if PQ = x, QR = x + 2, and PR = y, which of the  [#permalink]

### Show Tags

18 Nov 2013, 20:22
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.
Math Expert
Joined: 02 Sep 2009
Posts: 50623
Re: In PQR, if PQ = x, QR = x + 2, and PR = y, which of the  [#permalink]

### Show Tags

19 Nov 2013, 01:08
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.
_________________
Intern
Joined: 10 Sep 2015
Posts: 15
Re: In PQR, if PQ = x, QR = x + 2, and PR = y, which of the  [#permalink]

### Show Tags

11 Sep 2015, 01:12
statement 1 : y=X+3 gives us following points
x,x+2,x+3 are the sides

Statement 2 " nothing conclusive

hence A
Target Test Prep Representative
Affiliations: Target Test Prep
Joined: 04 Mar 2011
Posts: 2830
Re: In PQR, if PQ = x, QR = x + 2, and PR = y, which of the  [#permalink]

### Show Tags

25 Aug 2016, 14:52
2
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.

_________________

Jeffery Miller

GMAT Quant Self-Study Course
500+ lessons 3000+ practice problems 800+ HD solutions

VP
Joined: 09 Mar 2016
Posts: 1080
Re: In PQR, if PQ = x, QR = x + 2, and PR = y, which of the  [#permalink]

### Show Tags

25 Apr 2018, 11:53
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.

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
Joined: 02 Sep 2009
Posts: 50623
Re: In PQR, if PQ = x, QR = x + 2, and PR = y, which of the  [#permalink]

### Show Tags

25 Apr 2018, 20:32
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.

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
_________________
Senior Manager
Joined: 21 Jan 2015
Posts: 346
Location: India
Concentration: Strategy, Marketing
GMAT 1: 620 Q48 V28
GMAT 2: 690 Q49 V35
WE: Sales (Consumer Products)
Re: In PQR, if PQ = x, QR = x + 2, and PR = y, which of the  [#permalink]

### Show Tags

26 Apr 2018, 06:19
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..
_________________

--------------------------------------------------------------------
The Mind is Everything, What we Think we Become.
Kudos will encourage many others, like me.
Thanks

Re: In PQR, if PQ = x, QR = x + 2, and PR = y, which of the &nbs [#permalink] 26 Apr 2018, 06:19
Display posts from previous: Sort by