Isoceles Triangle

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harsh.champ: Legendary Member; Posts: 1132; Joined: Mon Jul 20, 2009 3:38 amFollowed by: 6 members; Location: India; Thanked: 64 times; GMAT Score:760

by harsh.champ » Wed Feb 17, 2010 5:37 am

Is ABC an isosceles triangle?

1.Exactly two of the angles <A and <B have the same measure.
2.<B and <C do not have the same measure.

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ajith: Legendary Member; Posts: 1275; Joined: Thu Sep 21, 2006 11:13 pmFollowed by: 2 members; Location: Arabian Sea; Thanked: 125 times

by ajith » Wed Feb 17, 2010 6:31 am

harsh.champ wrote:Is ABC an isosceles triangle?

1.Exactly two of the angles <A and <B have the same measure.
2.<B and <C do not have the same measure.

1. Sufficient
2) Not sufficient - Third angle could be anything

A

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shashank.ism: Legendary Member; Posts: 1022; Joined: Mon Jul 20, 2009 11:49 pmFollowed by: 2 members; Location: Gandhinagar; Thanked: 41 times

by shashank.ism » Sun Feb 21, 2010 7:27 pm

harsh.champ wrote:Is ABC an isosceles triangle?

1.Exactly two of the angles <A and <B have the same measure.
2.<B and <C do not have the same measure.

St.1) if <A and <B are equal surely it represents an isoceles trangle.. sufficient.
St.2) <B and <C do not have the same measure. It doesn't say if there are any two equal angles ...so insufficient.
Ans A

Def: isoceles triangle : In an isosceles triangle, two sides are equal in length.[2] An isosceles triangle also has two angles of the same measure; namely, the angles opposite to the two sides of the same length; this fact is the content of the Isosceles triangle theorem.

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lunarpower: GMAT Instructor; Posts: 3380; Joined: Mon Mar 03, 2008 1:20 amFollowed by: 1535 members; Thanked: 2256 times; GMAT Score:800

by lunarpower » Tue Feb 23, 2010 6:44 am

you guys pretty much have this one covered.

BY THE WAY:
this is irrelevant to this particular problem, but you should also know that an equilateral triangle also qualifies as "isosceles". (this is so for the same reason that squares are still rectangles.)

so let's pretend that statement (1) says
(1) <A and <B have the same measure

unlike the current #1, this allows the possibility that the triangle is equilateral - but that wouldn't matter, since equilateral triangles are still isosceles.

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rahul.s: Master | Next Rank: 500 Posts; Posts: 324; Joined: Thu Dec 24, 2009 6:29 amFollowed by: 1 member; Thanked: 17 times

by rahul.s » Tue Feb 23, 2010 6:50 am

lunarpower wrote:you guys pretty much have this one covered.

BY THE WAY:
this is irrelevant to this particular problem, but you should also know that an equilateral triangle also qualifies as "isosceles". (this is so for the same reason that squares are still rectangles.)

so let's pretend that statement (1) says
(1) <A and <B have the same measure

unlike the current #1, this allows the possibility that the triangle is equilateral - but that wouldn't matter, since equilateral triangles are still isosceles.

so, if the questions was: "is triangle ABC equilateral?," would your statement (1) be sufficient?

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lunarpower: GMAT Instructor; Posts: 3380; Joined: Mon Mar 03, 2008 1:20 amFollowed by: 1535 members; Thanked: 2256 times; GMAT Score:800

by lunarpower » Tue Feb 23, 2010 7:09 am

rahul.s wrote:so, if the questions was: "is triangle ABC equilateral?," would your statement (1) be sufficient?

no, since you only have two angles. to guarantee equilateral, you would need all three.

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Ian Stewart: GMAT Instructor; Posts: 2623; Joined: Mon Jun 02, 2008 3:17 amFollowed by: 355 members; Location: Montreal; Thanked: 1090 times; GMAT Score:780

by Ian Stewart » Tue Feb 23, 2010 10:26 am

lunarpower wrote:
BY THE WAY:
this is irrelevant to this particular problem, but you should also know that an equilateral triangle also qualifies as "isosceles". (this is so for the same reason that squares are still rectangles.)

There is actually no consensus in mathematics here - some take 'isosceles' to mean exactly two equal sides, and some take it to mean at least two equal sides. My understanding is that the original meaning was *exactly two equal sides*, but that in recent years the meaning has evolved to include equilateral triangles. All this is irrelevant for the GMAT of course!

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lunarpower: GMAT Instructor; Posts: 3380; Joined: Mon Mar 03, 2008 1:20 amFollowed by: 1535 members; Thanked: 2256 times; GMAT Score:800

by lunarpower » Tue Feb 23, 2010 10:41 pm

Ian Stewart wrote:
lunarpower wrote:
BY THE WAY:
this is irrelevant to this particular problem, but you should also know that an equilateral triangle also qualifies as "isosceles". (this is so for the same reason that squares are still rectangles.)
There is actually no consensus in mathematics here - some take 'isosceles' to mean exactly two equal sides, and some take it to mean at least two equal sides. My understanding is that the original meaning was *exactly two equal sides*, but that in recent years the meaning has evolved to include equilateral triangles. All this is irrelevant for the GMAT of course!

will respond by PM, since this is going to get way, way off topic

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