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M03-08

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Bunuel
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M03-08 [#permalink] New post   16 Sep 2014, 00:19
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81% (00:44) correct 19% (00:56) wrong based on 860 sessions
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Is triangle \(ABC\) equilateral?


(1) \(AB = 1\)

(2) \(BC + AC = 2\)
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E
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Bunuel
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Re M03-08 [#permalink] New post   16 Sep 2014, 00:19
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The triangle is equilateral when all of its sides have the same length.

Statement (1) by itself is insufficient. We don't know anything about the length of the other sides.

Statement (2) by itself is insufficient. Knowing that \(BC + AC = 2\), doesn't give us enough information to be sure that the triangle is equilateral. Suppose \(BC=1.1\) and \(AC=0.9\).

Statements (1) and (2) combined are insufficient. Combining the two statements doesn't ensure that BC and AC equal exactly 1 each.


Answer: E
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girishiyer
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Re: M03-08 [#permalink] New post   14 Dec 2017, 04:13
Hi,

I got C.

Since we know :[A-B] <C<A+B

We can easily say its not an equilateral triangle

pls brunei can you specify
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Bunuel
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Re: M03-08 [#permalink] New post   14 Dec 2017, 05:24
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girishiyer wrote:
Hi,

I got C.

Since we know :[A-B] <C<A+B

We can easily say its not an equilateral triangle

pls brunei can you specify


How?

Case 1: all sides are of lengths 1.
Case 2: sides are: 0.9, 1, 1.1.
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girishiyer
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Re: M03-08 [#permalink] New post   29 Dec 2017, 08:35
thanks bunuel for clarifying
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Re: M03-08 [#permalink] New post   04 Mar 2020, 08:57
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Bunuel wrote:
Is triangle \(ABC\) equilateral?


(1) \(AB = 1\)

(2) \(BC + AC = 2\)


For first few seconds, I was thinking where is the image. lol

Coming to the question, we can see that either the answer is C or E and that basically means one thing : Prove with one case that it is incorrect and you're good to go.

Combined :

AB=1 Assume BC and AC can only be nice sweet integers 1 and 1 the answer is Yes. It is an Eq Triangle.
But if AB=1 BC=0.5 AC=1.5. well it is not possible because AB+BC is not greater than AC and that means it is not a triangle in the first place.
But we can go further than that.
AB=1 BC=0.8 AC=1.2. It is a triangle but not equilateral.

We have enough information to declare E as the winner :)
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Re: M03-08 [#permalink] New post   24 Nov 2020, 20:55
Bunuel wrote:
Is triangle \(ABC\) equilateral?
Quote:
(1) \(AB = 1\)
A. AB = 1 - Other sides BC, AC can be / cannot be equal to AB --> Not Sufficient
Quote:
(2) \(BC + AC = 2\)
B. BC+AC=2 - Other side AB can be / cannot be equal to each BC and AC --> Not Sufficient

C. We have AB = 1, BC+AC=2
Quote:
Case 1 - If, BC=AC=1 --> Yes - it is equilateral triangle
Quote:
Case 2 - If, BC=0.6 and AC=1.4

Lets check if this values meets the criteria of properties of Triangles -
1. Any side of triangle will always be less than the sum of other two sides
BC+AC>AB, AB+BC>AC, AC+AB>BC
2. Any side of triangle will always be greater than difference of the other two sides
AC-BC<AB, AC-AB<BC, AB-BC<AC

--> No - It is not an equilateral triangle

E is clearly the right answer. :)
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Re: M03-08 [#permalink]
24 Nov 2020, 20:55
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Bunuel
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