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Register now and save up to $200 Available with Beat the GMAT members only code • 5 Day FREE Trial Study Smarter, Not Harder Available with Beat the GMAT members only code • 5-Day Free Trial 5-day free, full-access trial TTP Quant Available with Beat the GMAT members only code • 1 Hour Free BEAT THE GMAT EXCLUSIVE Available with Beat the GMAT members only code • Magoosh Study with Magoosh GMAT prep Available with Beat the GMAT members only code • Most awarded test prep in the world Now free for 30 days Available with Beat the GMAT members only code • Free Veritas GMAT Class Experience Lesson 1 Live Free Available with Beat the GMAT members only code ## If the lengths of the sides of a triangle are a, b, and 7 tagged by: Brent@GMATPrepNow This topic has 3 expert replies and 2 member replies gmat_winter Senior | Next Rank: 100 Posts Joined 14 Oct 2014 Posted: 34 messages Upvotes: 1 #### If the lengths of the sides of a triangle are a, b, and 7 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 Marty Murray Legendary Member Joined 03 Feb 2014 Posted: 2050 messages Followed by: 131 members Upvotes: 955 GMAT Score: 800 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 GMAT Coach m.w.murray@hotmail.com https://infinitemindprep.com/ In Person in the New York Area and Online Worldwide a.gold93 Newbie | Next Rank: 10 Posts Joined 22 Mar 2016 Posted: 1 messages 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! ### GMAT/MBA Expert DavidG@VeritasPrep Legendary Member Joined 14 Jan 2015 Posted: 2627 messages Followed by: 117 members Upvotes: 1153 GMAT Score: 770 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

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### GMAT/MBA Expert

Brent@GMATPrepNow GMAT Instructor
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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-geometry/video/860 (starting at 1:50)

Cheers,
Brent

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

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### GMAT/MBA Expert

Rich.C@EMPOWERgmat.com Elite Legendary Member
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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

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