Author 
Message 
TAGS:

Hide Tags

Director
Status: Impossible is not a fact. It's an opinion. It's a dare. Impossible is nothing.
Affiliations: University of Chicago Booth School of Business
Joined: 03 Feb 2011
Posts: 900

If the sides of a triangle have lengths x, y, and z, x + y = [#permalink]
Show Tags
04 May 2011, 19:35
2
This post received KUDOS
16
This post was BOOKMARKED
Question Stats:
62% (03:04) correct
38% (02:01) wrong based on 291 sessions
HideShow timer Statistics
If the sides of a triangle have lengths x, y, and z, x + y = 30, and y + z = 20, then which of the following could be the perimeter of the triangle? I. 28 II. 36 III. 42 A I only B II only C I and II only D I and III only E I, II, and III OA is B.
I don't have the solution but this is how I think it is done. Pls verify the reasoning.
The question is basically asking us to determine the limits on x.
x + y = 30  (1) y + z = 20  (2) x  z = 10. This means y > 10 [Axiom : The third side is greater than the difference of the two sides.]
x + y = 30 y > 10 From this we get x < 20. y + z = 20 x < 20 Adding we get x + y + z < 40 > I think this step is correct
From (2) we have y < 20. Since side z is nonnegative. From (1) we have x > 10. y + z = 20 x > 10 Adding we get x + y + z > 30 > I think this step is correct
Hence 30 < x + y + z < 40. Hence B
Official Answer and Stats are available only to registered users. Register/ Login.



SVP
Joined: 16 Nov 2010
Posts: 1663
Location: United States (IN)
Concentration: Strategy, Technology

Re: Triangle [#permalink]
Show Tags
04 May 2011, 19:52
4
This post received KUDOS
1
This post was BOOKMARKED
(I) is out as x+y = 30 > 28 (perimeter can't be < sum of two sides) And all answers excepy B contain I as option So Answer  B
_________________
Formula of Life > Achievement/Potential = k * Happiness (where k is a constant)
GMAT Club Premium Membership  big benefits and savings



Director
Status: Impossible is not a fact. It's an opinion. It's a dare. Impossible is nothing.
Affiliations: University of Chicago Booth School of Business
Joined: 03 Feb 2011
Posts: 900

Re: Triangle [#permalink]
Show Tags
04 May 2011, 19:56
Brilliant !!! I was assuming there will be a solution like this. Thanks so much There is one more thing  can you also verify the explanation in the spoiler ? Cheers subhashghosh wrote: (I) is out as x+y = 30 > 28 (perimeter can't be < sum of two sides)
And all answers excepy B contain I as option
So Answer  B



VP
Status: There is always something new !!
Affiliations: PMI,QAI Global,eXampleCG
Joined: 08 May 2009
Posts: 1326

Re: Triangle [#permalink]
Show Tags
04 May 2011, 20:07
This took me more than 2 min's though Using POE since x+y = 30, means 1 can be nullified altogether. But a better approach will take a STAB at this, I am focusing on Z (min) and Z (max) values. x+y = 30, y+z = 20 means xz = 10 Z(min) = 1, means X = 11 and Y = 19 thus Perimeter (Z min) = 31 Z(max) = 9, since Y >10, means Y = 11 and X = 19 thus Perimeter (Zmax) = 37. Thus B fits in. Likewise, one can try for either X(min) or Y (min) and max values too. Keeping the limits X<20,Z<30 and Y>10.
_________________
Visit  http://www.sustainablesphere.com/ Promote Green Business,Sustainable Living and Green Earth !!



SVP
Joined: 16 Nov 2010
Posts: 1663
Location: United States (IN)
Concentration: Strategy, Technology

Re: Triangle [#permalink]
Show Tags
05 May 2011, 04:48
@gmat1220, I think you're right. I also deduced x + y + z < 40 initially (by using the length of 3rd side < sum of two sides), and then I spotted the odd man out in the answer choices.
_________________
Formula of Life > Achievement/Potential = k * Happiness (where k is a constant)
GMAT Club Premium Membership  big benefits and savings



Senior Manager
Joined: 03 Mar 2010
Posts: 440

Re: Triangle [#permalink]
Show Tags
05 May 2011, 04:49
2
This post received KUDOS
gmat1220 wrote: If the sides of a triangle have lengths x, y, and z, x + y = 30, and y + z = 20, then which of the following could be the perimeter of the triangle? I. 28 II. 36 III. 42
A I only B II only C I and II only D I and III only E I, II, and III perimeter is x+y+z = ? Apply POE 1) Clearly, x+y=30 then how can x+y+z = 28?. OUT 2) x+y+z=36 x+2y+z=50 Subtracting, x+2y+z(x+y+z) = 5036, y=14 x+y=30 (given), hence x=16 y+z=20 (given) hence z=6 x+y+z => 16+14+6 = 36. Also, (146)<16<(14+6). Same can be tested for other sides as well. 3) x+y+z=42 x+2y+z=50 Subtracting, y=8 x+y=30 (given), hence x=22 y+z=20 (given) hence z=12 x+y+z => 22+8+12=42 BUT X(22) IS NOT LESS THAN SUM OF OTHER TWO SIDES (8+12=20).It doesn't satisfy triangle inequality theorem. Hence, OUT. OA. B
_________________
My dad once said to me: Son, nothing succeeds like success.



Intern
Status: ThinkTank
Joined: 07 Mar 2009
Posts: 28

Re: Triangle [#permalink]
Show Tags
05 May 2011, 09:18
1
This post received KUDOS
1
This post was BOOKMARKED
The POE approach above works fast. The algebraic approach is: First, establish the equation we are looking or x + y + z = ? and name it A if we add both given equations we can get x + y + z + y = 50. Isolate A and you get A + y = 50 Now we know from triangle inequality theorem that x  z < y < x +z. We can get x  z by substracting both equation we are given and use the other for x + z. So we get 10 < y < 20 so: so A = 50  GT (10) so A = LT (40) and A = 50  LT (20) so A = GT (30) 30 < A < 40 Only II (36) meets this criteria. I think you can solve under 2mn with this or even better by recognizing the trick subhashghosh explained. Hope this is helpful.
_________________
http://www.hannibalprep.com



Manager
Joined: 07 May 2013
Posts: 109

Re: If the sides of a triangle have lengths x, y, and z, x + y = [#permalink]
Show Tags
29 Nov 2013, 21:29
20101040N 1911939Y 1812838Y 1713737Y 1614636Y xyzper.triangle? 1515535Y 1416434Y 1317333N



Math Expert
Joined: 02 Sep 2009
Posts: 39673

Re: If the sides of a triangle have lengths x, y, and z, x + y = [#permalink]
Show Tags
30 Nov 2013, 03:58
gmat1220 wrote: PS : What do you think we must guess. Or is there a more intuitive approach which guarantees the result in less than 2 mins? If the sides of a triangle have lengths x, y, and z, x + y = 30, and y + z = 20, then which of the following could be the perimeter of the triangle? I. 28 II. 36 III. 42 A I only B II only C I and II only D I and III only E I, II, and III OA is B.
I don't have the solution but this is how I think it is done. Pls verify the reasoning.
The question is basically asking us to determine the limits on x.
x + y = 30  (1) y + z = 20  (2) x  z = 10. This means y > 10 [Axiom : The third side is greater than the difference of the two sides.]
x + y = 30 y > 10 From this we get x < 20. y + z = 20 x < 20 Adding we get x + y + z < 40 > I think this step is correct
From (2) we have y < 20. Since side z is nonnegative. From (1) we have x > 10. y + z = 20 x > 10 Adding we get x + y + z > 30 > I think this step is correct
Hence 30 < x + y + z < 40. Hence B Similar questions to practice: iftwosidesofatrianglehavelengths2and5whichofth163409.htmlsamistrainingforthemarathonhedrove12milesfromhis158375.htmlinpqrifpqxqrx2andprywhichofthe110404.htmlif3and8arethelengthsoftwosidesofatriangular21008.htmlifkisanintegerand2k7forhowmanydifferent135543.htmlwhatistheperimeterofisoscelestrianglemnp134505.htmlistheperimeteroftriangleabcgreaterthan87112.html12easypiecesornot126366.htmlinpqrifpqxqrx2andprywhichofthe110404.htmldevilsdozen129312.htmlyouhave6sticksoflengths1020304050and133667.htmlintriangleabcifabxbcyandacxywhichof135495.htmlwhatistheperimeterofisoscelestriangleabc34552.htmlintriangleabcifabxbcyandacxywhichof135495.htmlFor more check Triangles chapter of Math Book: mathtriangles87197.htmlHope this helps.
_________________
New to the Math Forum? Please read this: 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.
What are GMAT Club Tests? Extrahard Quant Tests with Brilliant Analytics



Senior Manager
Joined: 13 May 2013
Posts: 469

Re: If the sides of a triangle have lengths x, y, and z, x + y = [#permalink]
Show Tags
12 Dec 2013, 11:03
PS : What do you think we must guess. Or is there a more intuitive approach which guarantees the result in less than 2 mins?
If the sides of a triangle have lengths x, y, and z, x + y = 30, and y + z = 20, then which of the following could be the perimeter of the triangle?
As others have pointed out, we can rule out I.) because it indicates that all three sides add up to 28 when the question says that just two sides add up to 30.
x + y = 30 y + z = 20
x + z + 2y = 50 We can solve by ruling out answer choices, so let's say that we assume x + y + z = 36
x + z + 2y = 50 x + y + z = 36 __________________(  ) y = 14
x + y = 30 x + (14) = 30 x = 16
x + y = 30 (16) + y = 30 y = 14
We don't even need to test III.) because it is always lumped in with I.) which we know is not possible.
B.)
I. 28 II. 36 III. 42
A I only B II only C I and II only D I and III only E I, II, and III



Manager
Joined: 25 Oct 2013
Posts: 169

Re: If the sides of a triangle have lengths x, y, and z, x + y = [#permalink]
Show Tags
12 Feb 2014, 06:19
2
This post received KUDOS
x+y=30 & y+z=20 so x+2y+z=50 x+y+z=50y If perimeter is 28 then y=5028=22, and y+z=20 z cannot be negative. I is out. If perimeter is 36 then y=5036 = 14. z=6, x=16. no problem here. If perimeter is 42 then y=5042 =8. x=22, z=12. x cannot be greater than sum of y & z. III is out. B is answer.
_________________
Click on Kudos if you liked the post!
Practice makes Perfect.



GMAT Club Legend
Joined: 09 Sep 2013
Posts: 15978

Re: If the sides of a triangle have lengths x, y, and z, x + y = [#permalink]
Show Tags
15 Mar 2015, 16:08
Hello from the GMAT Club BumpBot! Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up  doing my job. I think you may find it valuable (esp those replies with Kudos). Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
_________________
GMAT Books  GMAT Club Tests  Best Prices on GMAT Courses  GMAT Mobile App  Math Resources  Verbal Resources



GMAT Club Legend
Joined: 09 Sep 2013
Posts: 15978

Re: If the sides of a triangle have lengths x, y, and z, x + y = [#permalink]
Show Tags
13 May 2016, 09:26
Hello from the GMAT Club BumpBot! Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up  doing my job. I think you may find it valuable (esp those replies with Kudos). Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
_________________
GMAT Books  GMAT Club Tests  Best Prices on GMAT Courses  GMAT Mobile App  Math Resources  Verbal Resources



CEO
Joined: 17 Jul 2014
Posts: 2524
Location: United States (IL)
Concentration: Finance, Economics
GPA: 3.92
WE: General Management (Transportation)

If the sides of a triangle have lengths x, y, and z, x + y = [#permalink]
Show Tags
16 May 2016, 19:45
gmat1220 wrote: If the sides of a triangle have lengths x, y, and z, x + y = 30, and y + z = 20, then which of the following could be the perimeter of the triangle?
I. 28 II. 36 III. 42 A I only B II only C I and II only D I and III only E I, II, and III
my approach... x+y=30, +z will be >30. so I is out right away. A, C, D, and E are eliminated. less than 30 seconds needed to figure it out. answer choices should be given more "confusing"...



Intern
Joined: 17 Oct 2014
Posts: 5

Re: If the sides of a triangle have lengths x, y, and z, x + y = [#permalink]
Show Tags
01 Dec 2016, 06:04
Q.Integer x represents the product of all integers between 1 and 25, inclusive. The smallest prime factor of (x + 1) must be _____.
can somebody help me how to solve this question



Math Expert
Joined: 02 Sep 2009
Posts: 39673

Re: If the sides of a triangle have lengths x, y, and z, x + y = [#permalink]
Show Tags
01 Dec 2016, 06:25



Manager
Joined: 02 Nov 2013
Posts: 97
Location: India

Re: If the sides of a triangle have lengths x, y, and z, x + y = [#permalink]
Show Tags
01 Dec 2016, 08:17
Remember the theory of the triangle, Side of the triangle will be greater than difference of the remaining two sides and less than sum of the two remaining sides. Let say in this case, XY<Z<X+Y. Looking at the answers easily we can eliminate one answer i.e. 28 which is anyway not following the first equation x + y = 30. The rest of the two options 36 is the correct answer.
My choice is B.



Manager
Joined: 20 Apr 2014
Posts: 120

Re: If the sides of a triangle have lengths x, y, and z, x + y = [#permalink]
Show Tags
02 Dec 2016, 01:01
1
This post was BOOKMARKED
I guess the fastest and clearest approach here is to use the given choices 28  36  42. P of triangle = x+y+z 1 ) x+y+z=28 we are given that x+y=30 so first option is false since answer can not be negative
2 ) x+y+z=36 we are given that x+y=30 so 30+z=36 z=6 y= 14 x = 16 the third side must be less than sum of other two sides and more than the difference of the other two sides of the triangle. it could be P of the triangle like that: z<x+y z>xy and the same for x and y
3 ) x+y+z=42 if we try the same property above, we will find that it couldn't be P of the triangle. So answer is D if it helps, please press kudos for me.




Re: If the sides of a triangle have lengths x, y, and z, x + y =
[#permalink]
02 Dec 2016, 01:01








Similar topics 
Author 
Replies 
Last post 
Similar Topics:


17


Right triangle ABC has sides with length x, y and z. If triangle ABC

GMATPrepNow 
5 
19 Jun 2017, 11:25 

61


A certain right triangle has sides of length x, y, and z, wh

Bunuel 
7 
02 May 2017, 22:42 

18


Two sides of a triangle have lengths x and y and meet at a r

xhimi 
13 
27 Feb 2017, 22:27 

93


A certain right triangle has sides of length x, y, and z

tonebeeze 
18 
25 May 2017, 11:23 

39


A certain right triangle has sides of length x, y, and z

vibhaj 
15 
10 Mar 2011, 21:03 



