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:

Re: If AB=3, what is the shortest side of triangle ABC? (1) AC= [#permalink]

Show Tags

18 Aug 2013, 11:21

1

This post received KUDOS

blueseas wrote:

If AB=3, what is the shortest side of triangle ABC?

(1) AC=5

(2) The perimeter of ΔABC is 13.

From F.S 1, we get a valid triangle for AC=5 and BC=4, and the smallest side is AB. Again, for BC=2.1, we get another valid triangle and this time, the smallest side is BC. As we get 2 different answers, Insufficient.

From F.S 2, we know that AC+BC = 13-3 = 10. Now, we know that the difference of 2 sides must be less than the third side of a valid triangle.

Thus, as have |AC-BC|<3. Replacing the value of AC, we get \(|10-BC-BC|<3 \to -3<10-2BC<3 \to 3.5<BC<6.5\). Similarly, we will get the same range for AC. Thus, as both of them are greater than 3.5, the least value WILL BE for the side AB=3. Sufficient.

Re: If AB=3, what is the shortest side of triangle ABC? (1) AC= [#permalink]

Show Tags

22 Apr 2014, 04:32

mau5 wrote:

blueseas wrote:

If AB=3, what is the shortest side of triangle ABC?

(1) AC=5

(2) The perimeter of ΔABC is 13.

From F.S 1, we get a valid triangle for AC=5 and BC=4, and the smallest side is AB. Again, for BC=2.1, we get another valid triangle and this time, the smallest side is BC. As we get 2 different answers, Insufficient.

From F.S 2, we know that AC+BC = 13-3 = 10. Now, we know that the difference of 2 sides must be less than the third side of a valid triangle.

Thus, as have |AC-BC|<3. Replacing the value of AC, we get \(|10-BC-BC|<3 \to -3<10-2BC<3 \to 3.5<BC<6.5\). Similarly, we will get the same range for AC. Thus, as both of them are greater than 3.5, the least value WILL BE for the side AB=3. Sufficient.

B.

Dear mau5, could you please elaborate on why |AC-BC|<3?

Re: If AB=3, what is the shortest side of triangle ABC? (1) AC= [#permalink]

Show Tags

22 Apr 2014, 05:02

1

This post received KUDOS

jlgdr wrote:

Dear mau5, could you please elaborate on why |AC-BC|<3?

Thanks! Cheers J

This is due to the triangle inequality and comes directly from mau5's previous statement:

Quote:

From F.S 2, we know that AC+BC = 13-3 = 10. Now, we know that the difference of 2 sides must be less than the third side of a valid triangle.

I'll explain the sufficiency of (2) a bit differently to see if it helps.

Suppose AB isn't the shortest side, and there is a shorter side BC. So let BC = 3. Then AC must be 7 (since perimeter is 13). A 3-3-7 isn't a valid triangle due to the triangle inequality (try to draw a triangle with sides 3, 3, and 7!).
_________________

Re: If AB=3, what is the shortest side of triangle ABC? [#permalink]

Show Tags

10 May 2014, 10:48

Stat.(1): you can only plug in BC, which, according to the Third Side Rule must be smaller than 8 (the sum of AB and AC) and greater than 2 (their difference). Plug in BC=2.5 and BC becomes the smallest side; plug in BC=7 and AB is the smallest side. Hence, Stat.(1)->IS->BCE.

Stat.(2) tells you BC+AC=10. Plug in BC=5 AC=5 and AB becomes the smallest side. But can you plug in less than 3 (less than AB)? If you plug in BC=3, AC must be 7 and the Third Side Rule is broken (AB+BC<AC). Any BC smaller than 3 would also fail. So AB must be the smallest side. Hence, Stat.(2)->S->B.

Re: If AB=3, what is the shortest side of triangle ABC? [#permalink]

Show Tags

03 Jun 2014, 22:46

AB = 3 and BC+CA=10...considering the general rules that sum of 2 sides is greater than the 3rd side and difference between 2 sides is less than the third side...what I get are the 2 combinations for BC and CA ... those are 5+5 and 4+6...so we can have triangles 5,5,3 and 3,4,6...

hence, if I am not missing something, answer to this question would be C (I need both the statements to answer it).

If AB=3, what is the shortest side of triangle ABC?

(1) AC=5

(2) The perimeter of ΔABC is 13.

AB = 3 and BC+CA=10...considering the general rules that sum of 2 sides is greater than the 3rd side and difference between 2 sides is less than the third side...what I get are the 2 combinations for BC and CA ... those are 5+5 and 4+6...so we can have triangles 5,5,3 and 3,4,6...

hence, if I am not missing something, answer to this question would be C (I need both the statements to answer it).

The question asks what is the shortest side of triangle ABC? In both your examples the shortest side is 3. Isn't it? Also, notice that we are NOT told that the lenghts of the sides are integers, so there could be many more combinations than you wrote.

The point is that from (2) it follows that no side can be less than or equal AB=3, because if any of the sides is, then the third side must be more than or equal to 7, which would be more than the sum of the other two sides (3 and less than or equal 3).

Re: If AB=3, what is the shortest side of triangle ABC? [#permalink]

Show Tags

04 Jun 2014, 10:13

Bunuel wrote:

execnitinsharma wrote:

If AB=3, what is the shortest side of triangle ABC?

(1) AC=5

(2) The perimeter of ΔABC is 13.

AB = 3 and BC+CA=10...considering the general rules that sum of 2 sides is greater than the 3rd side and difference between 2 sides is less than the third side...what I get are the 2 combinations for BC and CA ... those are 5+5 and 4+6...so we can have triangles 5,5,3 and 3,4,6...

hence, if I am not missing something, answer to this question would be C (I need both the statements to answer it).

The question asks what is the shortest side of triangle ABC? In both your examples the shortest side is 3. Isn't it? Also, notice that we are NOT told that the lenghts of the sides are integers, so there could be many more combinations than you wrote.

The point is that from (2) it follows that no side can be less than or equal AB=3, because if any of the sides is, then the third side must be more than or equal to 7, which would be more than the sum of the other two sides (3 and less than or equal 3).

Does this make sense?

Gosh...what was I thinking You are absolutely correct. Thanks!!

Re: If AB=3, what is the shortest side of triangle ABC? [#permalink]

Show Tags

29 May 2016, 14:31

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.
_________________

Campus visits play a crucial role in the MBA application process. It’s one thing to be passionate about one school but another to actually visit the campus, talk...

Its been long time coming. I have always been passionate about poetry. It’s my way of expressing my feelings and emotions. And i feel a person can convey...

Marty Cagan is founding partner of the Silicon Valley Product Group, a consulting firm that helps companies with their product strategy. Prior to that he held product roles at...

Written by Scottish historian Niall Ferguson , the book is subtitled “A Financial History of the World”. There is also a long documentary of the same name that the...