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Are all angles of triangle ABC smalled than 90 degrees? 1)

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Are all angles of triangle ABC smalled than 90 degrees? 1) [#permalink] New post 03 Oct 2007, 23:54
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Are all angles of triangle ABC smalled than 90 degrees?

1) 2*AB = 3*BC = 4*AC
2) AC^2 + AB^2 = BC^2


Pls. explain.
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 [#permalink] New post 04 Oct 2007, 04:11
1) SUFF

from pythagoras we know that triangle with sides 3,4 and 5 is rectangular

here we have (picking numbers) 6,4 and 3

6 > 5 -> angle is greater than 90

2) pythagoras: SUFF

not really a structured explanation but I hope this will clarify
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 [#permalink] New post 04 Oct 2007, 05:52
statement I

2*AB = 3*BC = 4*AC

Since the sum on angles in triangle is 180 then the ratio of degrees is 180/9 = 20

2*20:3*20:4*20 = 40:60:80

sufficient

statement II

In order for all the angles of the triangle ABC be smaller than 90 degrees you cannot have a right angle. If you did then you could express the ratio of this triangle sides by the Pythagoras Theorem A^2+B^2 = C^2.

AC^2 + AB^2 = BC^2

Comply with Pythagoras Theorem. At least one angle is at 90 degrees.

sufficient

the answer is (D)

:)
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 [#permalink] New post 04 Oct 2007, 07:57
Statement 1 & 2 gives us diff answers,
Stat 1->40,60,80
Stat 2 ->one angle is 90

Is that possible??
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 [#permalink] New post 04 Oct 2007, 08:12
from 1)
We know the ratios of line so we can find out the ratios of angle.
No need to calculate it.
Sufficient

from 2)
From Pythagoras Theorem one angle is 90 n others are less than 90.
Sufficient

D.. Answer
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 [#permalink] New post 04 Oct 2007, 08:14
abiswas wrote:
Statement 1 & 2 gives us diff answers,
Stat 1->40,60,80
Stat 2 ->one angle is 90

Is that possible??


Its possbile in GMAT,Though it rarely happens in GMAT.
  [#permalink] 04 Oct 2007, 08:14
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