BREAKING: Target Test Prep releases Brand New 2026 On Demand GMAT prep course

Redeem

Geometry: In isosceles triangle ABC

This topic has expert replies
Post new topic Post Reply
Previous Topic Next Topic
Source: — Data Sufficiency |
User avatar
Legendary Member
Posts: 643
Joined: Wed Aug 14, 2013 4:27 am
Thanked: 48 times
Followed by:7 members

by vinay1983 » Thu Sep 12, 2013 9:49 pm
Yaj wrote:In isosceles triangle ABC, what is the length of AB?

(1) AC < BC/2

(2) BC = 7

[spoiler]OA: C[/spoiler]

Thank You!
Statement 2 Insufficient

Statement 1 We do not know the value of any 1 side of the triangle. Atleast One side value is needed. Insufficient

C or E

BC = 3.5

So AB is less than 3.5 so AB can either be 3.5 or be the value equal to that of AC

The point here is the inequality triangle law. the third side should be greater than difference of the remaining 2 sides and lesser than the sum of the remaining 2 sides.

So Suppose AC = 3.4, then Ab can be 3.4 or 3.5 itself, since in a scalene triangle any 2 sides are equal. So these value will follow the above mentioned rule. Hence Sufficient.

I hope I am right.

I have a question though, do we need to find the exact value of AD?Can somebody generalize this?
You can, for example never foretell what any one man will do, but you can say with precision what an average number will be up to!
Top

GMAT/MBA Expert

User avatar
Elite Legendary Member
Posts: 10392
Joined: Sun Jun 23, 2013 6:38 pm
Location: Palo Alto, CA
Thanked: 2867 times
Followed by:511 members
GMAT Score:800

by [email protected] » Thu Sep 12, 2013 10:04 pm
Hi Yaj,

This DS questions asks us for side AB of an ISOSCELES triangle?

Fact 1: AC < BC/2
There's no numeric information here, so there's no way to answer the question.
Fact 1 is INSUFFICIENT

Fact 2: BC = 7
This doesn't tell us AB, but it does tell us something about the triangle. Since it's ISOCELES....

It's either 7 7 -
Or it's 7 - - in which the two blanks are the same
Fact 2 is INSUFFICIENT

Combined, we know that...
It's an ISOSCELES triangle
BC = 7
AC < 3.5
AB = ? but either matches AC or BC

Using the Triangle Inequality Theorem, we know that AB + AC MUST BE > 7

If AB = AC, then that WOULDN'T HAPPEN.

So, AB MUST = BC

Thus AB = 7

Final AnswerC

GMAT assassins aren't born, they're made,
Rich
Contact Rich at [email protected]
Image
Top
User avatar
Master | Next Rank: 500 Posts
Posts: 234
Joined: Tue Jul 16, 2013 9:00 am
Location: West Virginia
Thanked: 9 times

by Java_85 » Fri Sep 13, 2013 9:57 am
Yaj wrote:In isosceles triangle ABC, what is the length of AB?

(1) AC < BC/2

(2) BC = 7

[spoiler]OA: C[/spoiler]

Thank You!
IMO it's E and there is no possible value for AB. Here is why:

(1) not sufficient
(2) not sufficient
(1)(2) AC=AB <3.5 and at the same time we have the constraint AB+AC<7 (Please notice it is not AB+AC<=7) --> putting this two constraint together there is no possible value for AB. --> Just E can be the answer. Please correct me if I'm wrong.
Top

GMAT/MBA Expert

User avatar
Elite Legendary Member
Posts: 10392
Joined: Sun Jun 23, 2013 6:38 pm
Location: Palo Alto, CA
Thanked: 2867 times
Followed by:511 members
GMAT Score:800

by [email protected] » Fri Sep 13, 2013 12:48 pm
Hi Java_85,

Take a look at your work again.

Have you factored in:

1) That the triangle is ISOSCELES (we're told that in the prompt)
2) Every real triangle is based on the Triangle Inequality Theorem (so any 2 sides of the triangle that are added > 3rd side).

GMAT assassins aren't born, they're made,
Rich
Contact Rich at [email protected]
Image
Top
User avatar
Master | Next Rank: 500 Posts
Posts: 234
Joined: Tue Jul 16, 2013 9:00 am
Location: West Virginia
Thanked: 9 times

by Java_85 » Fri Sep 13, 2013 5:01 pm
Thanks Rich.C, I got it now.
I was making a mistake and for no reason was assuming the two ISOSCELES are AB and AC.
Top

GMAT/MBA Expert

User avatar
GMAT Instructor
Posts: 3380
Joined: Mon Mar 03, 2008 1:20 am
Thanked: 2256 times
Followed by:1535 members
GMAT Score:800

by lunarpower » Fri Sep 13, 2013 11:27 pm
When you see statement 1, make sure you think about it for a bit. It turns out to be insufficient here, but it's still significant, because it determines exactly which sides are the congruent ones.

If the problem says this instead:
Yaj wrote:In isosceles triangle ABC, is AB = BC?

(1) AC < BC/2

(2) BC = 7

Thank You!
... then the answer is (a). Make sure you know why.
Ron has been teaching various standardized tests for 20 years.

--

Pueden hacerle preguntas a Ron en castellano
Potete chiedere domande a Ron in italiano
On peut poser des questions à Ron en français
Voit esittää kysymyksiä Ron:lle myös suomeksi

--

Quand on se sent bien dans un vêtement, tout peut arriver. Un bon vêtement, c'est un passeport pour le bonheur.

Yves Saint-Laurent

--

Learn more about ron
Top
User avatar
Newbie | Next Rank: 10 Posts
Posts: 9
Joined: Mon Jul 06, 2009 2:08 am

by shinys » Sat Sep 14, 2013 7:32 pm
Ron, should this be how we approach the question in the updated case?

Statement 1:
If AC = x, then BC is greater than 2x.
By Triangle property, third side, AB, has to be between
>2x - x = >x
and
>2x + x = >3x

Since triangle is isosceles, AB = BC because it is greater than AC.

SUFF

Statement 2:
It doesnt tell us anything about the other two sides. INSUFF
Top

GMAT/MBA Expert

User avatar
GMAT Instructor
Posts: 3380
Joined: Mon Mar 03, 2008 1:20 am
Thanked: 2256 times
Followed by:1535 members
GMAT Score:800

by lunarpower » Sun Sep 15, 2013 4:02 am
That's one way to do it.

If you haven't memorized that rule for triangles, you can also just try drawing the triangle both ways.

I.e., try drawing a triangle with sides x, x, and something that's less than half of x -- this will work just fine (you'll get a long skinny triangle, where the 2 congruent sides are the long ones).
Now try drawing a triangle with sides x, something that's less than half of x, and the same something that's less than half of x (or, equivalently, sides of y, y, and more than 2y). It won't work -- you won't be able to get the two short sides to join each other. They're too short to bridge the long side.

I'm not really capable of memorizing abstract rules like the one above, so this is how I'd go about doing it.
Ron has been teaching various standardized tests for 20 years.

--

Pueden hacerle preguntas a Ron en castellano
Potete chiedere domande a Ron in italiano
On peut poser des questions à Ron en français
Voit esittää kysymyksiä Ron:lle myös suomeksi

--

Quand on se sent bien dans un vêtement, tout peut arriver. Un bon vêtement, c'est un passeport pour le bonheur.

Yves Saint-Laurent

--

Learn more about ron
Top
Post new topic Post Reply
• Page 1 of 1