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# In a triangle ABC, AC=2. Is BC>

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Current Student
Joined: 18 Jan 2017
Posts: 81
Location: India
Concentration: Finance, Economics
GMAT 1: 700 Q50 V34
In a triangle ABC, AC=2. Is BC>  [#permalink]

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14 Jul 2017, 18:40
3
00:00

Difficulty:

95% (hard)

Question Stats:

26% (02:03) correct 74% (01:47) wrong based on 50 sessions

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In a $$\triangle$$ ABC, $$AC=2$$. Is $$BC >3 \sqrt{2}$$?

1) $$\triangle$$ ABC is obtuse
2) $$\triangle$$ ABC is isosceles
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In a triangle ABC, AC=2. Is BC>  [#permalink]

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14 Jul 2017, 20:28
1
Tan2017 wrote:
In a $$\triangle$$ ABC, $$AC=2$$. Is $$BC >3 \sqrt{2}$$?

1) $$\triangle$$ ABC is obtuse
2) $$\triangle$$ ABC is isosceles

obtuse triangle is a triangle that has one angle greater than 90 degree.
isosceles triangle is a triange with two equal sides.

(1) We cant know whether BC is greater than $$3\sqrt{2}$$ or not. Insufficient.

Attachment:

statement 1.png [ 4.96 KiB | Viewed 1040 times ]

(2) As (2), insufficient.

Attachment:

statement 2.png [ 5.16 KiB | Viewed 1032 times ]

Combine (1) and (2):

Attachment:

combine (1) and (2).png [ 3.77 KiB | Viewed 1013 times ]

Case 1: A > 90.
BC < AB + AC = 4 < $$3\sqrt{2}$$. Sufficient.

Case 2: B > 90
C < B => BC < AC = 2 < $$3\sqrt{2}$$

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Re: In a triangle ABC, AC=2. Is BC>  [#permalink]

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14 Jul 2017, 20:38
Tan2017 wrote:
In a $$\triangle$$ ABC, $$AC=2$$. Is $$BC >3 \sqrt{2}$$?

1) $$\triangle$$ ABC is obtuse
2) $$\triangle$$ ABC is isosceles

Hi...

I statement I tells us that ABC is obtuse.
BC can take any value..
Insufficient..

II this tells us that ABC is isosceles triangle.
If 2 is the SAME side..
Two sides are 2,2 and third side will be less than 4. So ans NO as 3√2>4.
If 2 is the THIRD side, ans can be yes or no.. 7,7,2 OR 3,3,2
Insufficient

Combined

It is obtuse isosceles triangle.
If 2 is the EQUAL sides... The third side will be <2+2... Ans NO
If 2 is the UNEQUAL side.... The other two will be<2, as the side OPPOSITE the largest angle ( here obtuse angle) will be the largest..
Again ans will be NO

Sufficient

C
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Re: In a triangle ABC, AC=2. Is BC>   [#permalink] 14 Jul 2017, 20:38
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