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M03-08

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Math Expert
Joined: 02 Sep 2009
Posts: 56300

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16 Sep 2014, 00:19
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Difficulty:

5% (low)

Question Stats:

77% (00:34) correct 23% (00:40) wrong based on 325 sessions

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Is triangle $$ABC$$ equilateral?

(1) $$AB = 1$$

(2) $$BC + AC = 2$$

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Math Expert
Joined: 02 Sep 2009
Posts: 56300

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16 Sep 2014, 00:19
2
Official Solution:

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.

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Joined: 18 Mar 2015
Posts: 12

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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
Math Expert
Joined: 02 Sep 2009
Posts: 56300

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14 Dec 2017, 05:24
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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Joined: 18 Mar 2015
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29 Dec 2017, 08:35
thanks bunuel for clarifying
Re: M03-08   [#permalink] 29 Dec 2017, 08:35
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