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lokesh r: Master | Next Rank: 500 Posts; Posts: 156; Joined: Sat Sep 04, 2010 2:27 am; Location: Leeds,UK; Thanked: 1 times

by lokesh r » Tue Sep 21, 2010 2:52 am

Sorry i have not copied the image..

Question:

In Triangle ABC,

Angle ABC = X

Angle ACB = Y

Is Triangle ABC Isosceles traingle:

a. X <> Y (X is not equal to Y)

b. AB = 2 BC

OA [spoiler](C)[/spoiler]

I failed to get this question right. Request ppl to provide comprehensive answer..

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Source: Beat The GMAT — Data Sufficiency | Tue Sep 21, 2010 2:52 am

gmatmachoman: Legendary Member; Posts: 2326; Joined: Mon Jul 28, 2008 3:54 amFollowed by: 2 members; Thanked: 173 times; GMAT Score:710

by gmatmachoman » Tue Sep 21, 2010 3:33 am

ST1 & St2 are not sufficient alone.

Okay lets us try to combine 2 sts together
Plz see the attched jpg.
Rule 1: Sum of 2 sides should be greater than the third side

In case 1 {3,6,4} makes a triangle and it is NOT ISOSCELES

In case 2{ 3,3,6} doesn't make a triangle as it VIOLATES the rule. So it can't be a ISOSCELES if it wants to be a triangle.

So its very clear that any 2 sides of this triangle are NOT same. So it is not a ISOCELES triangle.

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R&D on GMAT algorithm:

https://www.beatthegmat.com/r-d-on-gmat- ... tml#305739

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lokesh r: Master | Next Rank: 500 Posts; Posts: 156; Joined: Sat Sep 04, 2010 2:27 am; Location: Leeds,UK; Thanked: 1 times

by lokesh r » Wed Sep 22, 2010 12:38 pm

@ GmatMacMohan,

as per triangle rule

x,x,2x can never make up a triangle, so can't i say triangle in discussion is not isoceles triangle and choose B as answer.

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fatalityish: Senior | Next Rank: 100 Posts; Posts: 30; Joined: Fri Sep 03, 2010 11:01 pm; Location: Dubai; Thanked: 2 times

by fatalityish » Wed Sep 22, 2010 2:11 pm

Nice question Lokesh,

I feel the answer to this should be (E)

Reasoning:-
1. Triangle Inequality Theorem:-
sum of two sides should always be greater than the third side.

2. Reverse Triangle Inequality Theorem:-
Difference of two sides of a triangle should be less than the third side.

in our case (a) and (b) are not sufficient alone to check if the triangle is isosceles.
If we take (a) and (b) together.
let

AB=x
BC=2x
then as per our theorems and given information we can conclude the following:-
AC<>x
AC>x
AC<=2x

hence
x<AC<=2x

for AC = 2x the triangle becomes isosceles but AC can have the values lesser than 2x as well.
Hence together also the information is insufficient.

Answer should be (E).

Ishaan

Practice makes does a man perfect, but a planned practice takes the man beyond perfection!!!

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lokesh r: Master | Next Rank: 500 Posts; Posts: 156; Joined: Sat Sep 04, 2010 2:27 am; Location: Leeds,UK; Thanked: 1 times

by lokesh r » Thu Sep 23, 2010 11:48 am

I assume buddys in thread know why A and B alone are not sufficient. So option A,B, and D are eliminated.

Please draw triangle ABC on sheet, for better understanding.
let us consider both and A and B.

Since B says AB=2BC.

Let us say BC=p, then AB=2p

AC could be any value b/w 2p-p<AC<2p+p(From theory of triangles)

p<AC<3p.

ABC could be isoceles only if AC=2p, not AC cannot be equal to p according to above equation.

But Statement A says angle X<> angle Y

so AC<>AB. So there is no way ABC can be isoceles traingle.

Option C.

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gmatmachoman: Legendary Member; Posts: 2326; Joined: Mon Jul 28, 2008 3:54 amFollowed by: 2 members; Thanked: 173 times; GMAT Score:710

by gmatmachoman » Thu Sep 23, 2010 9:27 pm

lokesh r wrote:@ GmatMacMohan,

as per triangle rule

x,x,2x can never make up a triangle, so can't i say triangle in discussion is not isoceles triangle and choose B as

answer.

Hey LokeshR,

ACTUALLY U HAVE used the evidence for what you are supposed to "prove"> soUNDS LIKE A CR stem?? hahaha

U have assumed that the Triangle as Isoceles and then stated X, X, 2X. But How do u know that there are X,X?? it can be like X, Y where Y> X

plz go thru my jpg for better clarity!!

R&D on GMAT algorithm:

https://www.beatthegmat.com/r-d-on-gmat- ... tml#305739

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