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# Is this a rt triangle

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Manager
Joined: 17 Nov 2009
Posts: 234

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Is this a rt triangle [#permalink]

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20 Jul 2010, 08:26
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Difficulty:

45% (medium)

Question Stats:

67% (01:36) correct 33% (01:10) wrong based on 6 sessions

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Is this a rt triangle

1. The sides are in the ratio 3:4:5
2. The angles are int he ratio 3:4:5

pls explain: I need to know if the sides are in the ratio 3:4:5 is that triangle always a rt triangle -even though I do not know the angles?
[Reveal] Spoiler: OA

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Manager
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WE 1: 2 yrs - Oilfield Service

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20 Jul 2010, 08:52
Yes, if the sides are in the ratio 3:4:5 the triangle must be a pythagorean triplet right triangle. The sides will be some multiple of that ratio such as 6, 8 and 10 etc.

This can be easily proved by observing that if the sides are 3x, 4x and 5x => (3x)^2 + (4x)^2 = 9x^2 + 16x^2 = 25x^2 = (5x)^2... which is simply a verification of the pythagorean theorem - this is sufficient to figure out that the triangle is right-angled.

This is why statement 1 is sufficient.

Statement 2 is easier: The sum of the angles must be 180

=> 3x + 4x + 5x = 180 => 12x = 180 => x = 15

Thus the angles are 45, 60 and 75... which means the angle is NOT right-angled.

This is unusual for the GMAT that the two statements contradict eachother. However, this is still fair-game as the GMAC doesn't officially dismiss this possibility.

Pick D.

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20 Jul 2010, 11:39
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AbhayPrasanna wrote:
This is unusual for the GMAT that the two statements contradict eachother. However, this is still fair-game as the GMAC doesn't officially dismiss this possibility.

Pick D.

For (1) we've got that the triangle is right and for (2) we've got that triangle is not right, so statements contradict each other.

This will never occur on GMAT as: on the GMAT, two data sufficiency statements always provide TRUE information and these statements never contradict each other.
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07 Aug 2010, 10:24
Bunuel wrote:
AbhayPrasanna wrote:
This is unusual for the GMAT that the two statements contradict eachother. However, this is still fair-game as the GMAC doesn't officially dismiss this possibility.

Pick D.

For (1) we've got that the triangle is right and for (2) we've got that triangle is not right, so statements contradict each other.

This will never occur on GMAT as: on the GMAT, two data sufficiency statements always provide TRUE information and these statements never contradict each other.

Bunuel
I need some clarification on this point. Clearly by (1) we know that it is a rt triangle. From (2) we know it is not. So why is it a problem to say - D. Each can independently answer the question? Why can't they contradict each other?
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07 Aug 2010, 10:37
mainhoon wrote:
Bunuel wrote:
AbhayPrasanna wrote:
This is unusual for the GMAT that the two statements contradict eachother. However, this is still fair-game as the GMAC doesn't officially dismiss this possibility.

Pick D.

For (1) we've got that the triangle is right and for (2) we've got that triangle is not right, so statements contradict each other.

This will never occur on GMAT as: on the GMAT, two data sufficiency statements always provide TRUE information and these statements never contradict each other.

Bunuel
I need some clarification on this point. Clearly by (1) we know that it is a rt triangle. From (2) we know it is not. So why is it a problem to say - D. Each can independently answer the question? Why can't they contradict each other?

Because:
On the GMAT, two data sufficiency statements always provide TRUE information and these statements never contradict each other.

This is the rule of GMAT.

In original question statements contradict each other and this violates the above rule. That's why this is not a good question.
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20 Aug 2010, 21:34
I was confused at first, because I didn't remember the ratios of the angles to be the same as the ratio of sides, so I thought I was missing something.

On the plus side, if you saw this on the GMAT, I would guess it's more likely than not an experimental question that slipped though, and I would do minimal work on it.
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Re: Right Angled triangle   [#permalink] 20 Aug 2010, 21:34
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