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20 Jul 2010, 08:26
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D
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
45%
(medium)
Question Stats:
64% (01:13) correct
36%
(01:02)
wrong
based on 11
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
Answer: D
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?
1. The sides are in the ratio 3:4:5
2. The angles are int he ratio 3:4:5
Answer: D
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?
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20 Jul 2010, 08:52
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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.
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.
20 Jul 2010, 11:39
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AbhayPrasanna
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.
