If the lengths of the sides of a triangle are a, b, and 7

Expert replies

gmat_winter: Senior | Next Rank: 100 Posts; Posts: 34; Joined: Tue Oct 14, 2014 8:23 am; Thanked: 1 times

by gmat_winter » Wed Mar 25, 2015 8:32 am

If the lengths of the sides of a triangle are a, b, and 7, which of the following could be the value of a - b?

1)4
11)7
111)12

I only
II only
I and II only
II and III only
I, II, and III

OAA

Like this post

Source: Beat The GMAT — Problem Solving | Wed Mar 25, 2015 8:32 am

DavidG@VeritasPrep: Legendary Member; Posts: 2663; Joined: Wed Jan 14, 2015 8:25 amFollowed by: 128 members; Location: Boston, MA; Thanked: 1153 times; GMAT Score:770

by DavidG@VeritasPrep » Wed Mar 25, 2015 8:37 am

This question is testing the Third Side Rule of triangles: the third side of a triangle must always be less than the sum of the other two sides, and greater than the difference.

In this case, 7 must less than the sum of the other two sides, and 7 < a + b

And 7 must be greater than the difference of the other two sides, so 7 > a - b; This is the same as a - b < 7. We're concerned about a - b, so this is the relevant fact here.

If a - b < 7, then only 4 will work as a value of a - b

Answer is A

Veritas Prep | GMAT Instructor

Veritas Prep Reviews
Save $100 off any live Veritas Prep GMAT Course

Like this post

GMAT/MBA Expert

Brent@GMATPrepNow: GMAT Instructor; Posts: 16207; Joined: Mon Dec 08, 2008 6:26 pmFollowed by: 1268 members; Location: Vancouver, BC; Thanked: 5254 times; GMAT Score:770

by Brent@GMATPrepNow » Wed Mar 25, 2015 8:43 am

gmat_winter wrote:If the lengths of the sides of a triangle are a, b, and 7, which of the following could be the value of a - b?

1)4
11)7
111)12

I only
II only
I and II only
II and III only
I, II, and III

OAA

IMPORTANT RULE: If two sides of a triangle have lengths A and B, then . . .
difference between sides A and B < third side < sum of sides A and B

Plugging in we get: a - b < 7 < a + b
So, a - b < 7
Answer: A

RELATED RESOURCE:
We explain HOW and WHY the rule (above) works in the following video: https://www.gmatprepnow.com/module/gmat ... /video/860 (starting at 1:50)

Cheers,
Brent

Last edited by Brent@GMATPrepNow on Wed Mar 23, 2016 7:13 am, edited 1 time in total.

Brent Hanneson - Creator of GMATPrepNow.com

Like this post

GMAT/MBA Expert

[email protected]: Elite Legendary Member; Posts: 10392; Joined: Sun Jun 23, 2013 6:38 pmFollowed by: 511 members; Location: Palo Alto, CA; Thanked: 2867 times; GMAT Score:800

by [email protected] » Wed Mar 25, 2015 5:52 pm

Hi gmat_winter,

This question is based on the Triangle Inequality Theorem, as the other posters have noted. Since the three Roman Numerals are all numbers, and the question asks what COULD be the value of A-B, you can take more of a 'hands-on' approach and TEST VALUES (instead of trying to handle this with the broad rules that the Theorem is base don.

We know that one of the three sides is a 7

I. COULD the difference in the other two sides be 4?

If the sides were 11 and 7, then we'd have an isosceles triangle with sides of 7, 7 and 11. The difference COULD be 4.
Roman Numeral I is possible.

II. COULD the difference in the other two sides be 7?

If the sides were 8 and 1, then we would not have a triangle - we'd have a line "on top" of another line (since 1+7 = 8).
If the sides were 9 and 2, then we'd have the same situation.
If the sides were 10 and 3, then we'd have the same situation.
Etc.
Roman Numeral II is NOT possible

III. COULD the difference in the other two sides be 12?

If the sides were 13 and 1, then the "1" and the "7" could not meet (they're too far away from one another).
If the sides were 14 and 2, then we'd have the same situation.
If the sides were 15 and 3, then we'd have the same situation.
Etc.
Roman Numeral III is NOT possible.

Only Roman Numeral 1 is possible.

Final Answer: A

GMAT assassins aren't born, they're made,
Rich

Contact Rich at [email protected]

Like this post

a.gold93: Newbie | Next Rank: 10 Posts; Posts: 1; Joined: Tue Mar 22, 2016 6:07 pm

by a.gold93 » Tue Mar 22, 2016 6:10 pm

Hi,

I'm kind of stunned by this question. I though that the rule was that the sum of any 2 sides as to be greater than the 3rd side. If you put a-b = 4, then lets say a=5, b=1, and c=7 (given). 5+1 < 7. 5 and 1 being the 2 sides, 7 being the 3rd side

I'm likely confusing 2 different topics, I would appreciate if somebody can clarify what I'm missing or doing wrong.

Thanks! Much appreciated!

Like this post

MartyMurray: Legendary Member; Posts: 2135; Joined: Mon Feb 03, 2014 9:26 amFollowed by: 140 members; Location: https://martymurraycoaching.com/; Thanked: 955 times; GMAT Score:800

by MartyMurray » Tue Mar 22, 2016 6:35 pm

a.gold93 wrote:Hi,

I'm kind of stunned by this question. I though that the rule was that the sum of any 2 sides as to be greater than the 3rd side. If you put a-b = 4, then lets say a=5, b=1, and c=7 (given). 5+1 < 7. 5 and 1 being the 2 sides, 7 being the 3rd side

I'm likely confusing 2 different topics, I would appreciate if somebody can clarify what I'm missing or doing wrong.

Thanks! Much appreciated!

What you are doing wrong is extending the question in a way that does not make sense.

The question is asking which of the DIFFERENCES between a and b are possible.

4 is possible. For instance you could have a triangle such that one side has length 4, one has length 8 and the third has length 7.

However you can't extend the idea "a difference of 4 is possible" to make it "any two numbers that differ by 4 work as lengths of the two sides."

Marty Murray
Perfect Scoring Tutor With Over a Decade of Experience
MartyMurrayCoaching.com
Contact me at [email protected] for a free consultation.

Like this post

GMAT/MBA Expert

Scott@TargetTestPrep: GMAT Instructor; Posts: 8144; Joined: Sat Apr 25, 2015 10:56 amFollowed by: 29 members; Location: Los Angeles, CA; Thanked: 43 times

Re: If the lengths of the sides of a triangle are a, b, and 7

by Scott@TargetTestPrep » Tue Jan 19, 2021 9:22 am

gmat_winter wrote: ↑
Wed Mar 25, 2015 8:32 am
If the lengths of the sides of a triangle are a, b, and 7, which of the following could be the value of a - b?

1)4
11)7
111)12

I only
II only
I and II only
II and III only
I, II, and III

OAA

Solution:

The triangle inequality theorem tells us that the difference between the lengths of any two sides of a triangle must be greater than the length of the third side. Thus, we have a - b < 7. Therefore, the only number in the given Roman numeral choices that could be the value of a - b is 4.

Answer: A

Scott Woodbury-Stewart
Founder and CEO
[email protected]

See why Target Test Prep is rated 5 out of 5 stars on BEAT the GMAT. Read our reviews

Like this post

Post new topic Post Reply

• Page 1 of 1

GMAT Course Reviews

560 reviews

1168 reviews

431 reviews

359 reviews

147 reviews

5/5

5 Star (560 Reviews)

"Target Test Prep is the closest to the official version of the GMAT exam, about 99% accuracy in terms of the quality and quantity of information. The course has excellently created singular sets of focused lessons and tests for every possible topic that one could come across in the official GMAT exam."

"The TTP course maximizes the efficiency of the time you spend studying. It will take time and effort but I could almost guarantee that if you complete the course exactly as it is laid out you will get an amazing score. They also have a very responsive team willing to help with any questions you might have."

"TTP has two things that I think no other test prep company offers: A teaching approach that reinforces understanding and an attitude that will give you the mental preparedness needed to succeed on the test. TTP gives you a deep understanding of the concept you need to know while teaching you how to think."

Write a Review