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Mastering Important Concepts in Triangles-II : Exercise Question #1

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Mastering Important Concepts in Triangles-II : Exercise Question #1  [#permalink]

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Mastering Important Concepts Tested by GMAT in Triangles - II : Exercise Question


Q. Is ABC an equilateral triangle?

Image

1. ∠ABC = ∠ACB

2. Length of AB = Length of AC and one of the angles of the triangle is \(60^o\)



Answer Choices

A. Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.

B. Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient. 

C. BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient. 

D. EACH statement ALONE is sufficient. 

E. Statements (1) and (2) TOGETHER are NOT sufficient.




Key concepts on Triangles are explained in detail in the following posts:

1. Mastering Important Concepts Tested By GMAT in Triangle - I

2. Mastering Important Concepts Tested By GMAT in Triangle - II



Detailed solution will be posted soon.
:)

Thanks,
Saquib
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Originally posted by EgmatQuantExpert on 29 Nov 2016, 07:39.
Last edited by EgmatQuantExpert on 02 Dec 2016, 08:09, edited 3 times in total.
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Mastering Important Concepts in Triangles-II : Exercise Question #1  [#permalink]

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New post Updated on: 05 Dec 2016, 07:29
Let's look at the detailed solution of the above problem

Image

Steps 1 & 2: Understand Question and Draw Inferences

Given ABC is a triangle.
Since we don’t have any other information, let’s move on to the analysis of the statement 1.

Step 3: Analyze Statement 1 independently

Statement 1 tells us that \(∠ABC = ∠ACB\)
From this we can conclude that ABC is an isosceles triangle and we do not have sufficient information to conclude that ABC will be an equilateral triangle.

So statement 1 is not sufficient to arrive at a unique answer.

Step 4: Analyze Statement 2 independently

Statement 2 says: Length of AB = Length of AC and one of the angles of the triangle is 60o

If length AB = length AC, then we can conclude that –

\(∠ABC = ∠ACB\)

And it is also given that one of the angles is \(60^o\).

So there are two possibilities –

Case 1:
\(∠ABC = ∠ACB = 60^o\)
If this is the case, then the third angle i.e. ∠BAC will automatically become \(60^o\).

Since the sum of internal angles must be equal to \(180^o\).

Case 2:
\(∠BAC = 60^o\)

The remaining \(120^o\) angle has to be split equally between ∠ABC and ∠ACB as they equal.
This makes all angles equal to \(60^o\) each.

Thus, in both cases we find that ABC is an equilateral triangle.

Therefore, statement 2 is sufficient to arrive at a unique answer.

Hence the correct Answer is B.
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Originally posted by EgmatQuantExpert on 29 Nov 2016, 07:41.
Last edited by EgmatQuantExpert on 05 Dec 2016, 07:29, edited 3 times in total.
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Re: Mastering Important Concepts in Triangles-II : Exercise Question #1  [#permalink]

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New post 29 Nov 2016, 08:08
EgmatQuantExpert wrote:
Q. Is ABC an equilateral triangle?

1. ∠ABC = ∠ACB

2. Length of AB = Length of AC and one of the angles of the triangle is \(60^o\)


(1) ABC is an isosceles triangle. It could be an equilateral triangle or not. Insufficient.
(2) Any isosceles triangle that has one angle of 60 degree is an equilateral triangle. Sufficient.

The answer is B
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Re: Mastering Important Concepts in Triangles-II : Exercise Question #1  [#permalink]

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