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 Your Progress

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

Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.

It appears that you are browsing the GMAT Club forum unregistered!

Signing up is free, quick, and confidential.
Join other 500,000 members and get the full benefits of GMAT Club

Registration gives you:

Tests

Take 11 tests and quizzes from GMAT Club and leading GMAT prep companies such as Manhattan GMAT,
Knewton, and others. All are free for GMAT Club members.

Applicant Stats

View detailed applicant stats such as GPA, GMAT score, work experience, location, application
status, and more

Books/Downloads

Download thousands of study notes,
question collections, GMAT Club’s
Grammar and Math books.
All are free!

Thank you for using the timer!
We noticed you are actually not timing your practice. Click the START button first next time you use the timer.
There are many benefits to timing your practice, including:

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 non-negative. From (1) we have x > 10. y + z = 20 x > 10 Adding we get x + y + z > 30 ------> I think this step is correct

@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)

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) = 50-36, y=14 x+y=30 (given), hence x=16 y+z=20 (given) hence z=6 x+y+z => 16+14+6 = 36. Also, (14-6)<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.

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.

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 non-negative. From (1) we have x > 10. y + z = 20 x > 10 Adding we get x + y + z > 30 ------> I think this step is correct

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

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

Show Tags

12 Feb 2014, 06:19

1

This post received KUDOS

x+y=30 & y+z=20 so x+2y+z=50

x+y+z=50-y

If perimeter is 28 then y=50-28=22, and y+z=20 z cannot be negative. I is out. If perimeter is 36 then y=50-36 = 14. z=6, x=16. no problem here. If perimeter is 42 then y=50-42 =8. x=22, z=12. x cannot be greater than sum of y & z. III is out.

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.
_________________

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.
_________________

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"...

gmatclubot

If the sides of a triangle have lengths x, y, and z, x + y =
[#permalink]
16 May 2016, 19:45

After days of waiting, sharing the tension with other applicants in forums, coming up with different theories about invites patterns, and, overall, refreshing my inbox every five minutes to...

I was totally freaking out. Apparently, most of the HBS invites were already sent and I didn’t get one. However, there are still some to come out on...

In early 2012, when I was working as a biomedical researcher at the National Institutes of Health , I decided that I wanted to get an MBA and make the...