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07 Dec 2012, 09:24
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B
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
95%
(hard)
Question Stats:
21% (01:58) correct
79%
(01:41)
wrong
based on 496
sessions
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File comment: Image file
Triangle.png [ 19.09 KiB | Viewed 18310 times ]
If ABD is a triangle, is triangle ABC a right triangle?Triangle.png [ 19.09 KiB | Viewed 18310 times ]
(1) ACD is a right triangle.
(2) AC is the greatest side of triangle ACD.
08 Dec 2012, 04:12
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joylive
IMO answer is B.
The question is basically asking whether any of the angles in triangle ABC is 90.
1) Having told that ACD is a right triangle, doesn't confirms whether any of the angle in ABC is 90. The statement only lets us know that there is a 90 degree angle in ACD, but which one, we dont know yet.
2) This statement tells that angle D is the greatest so in other words it means that angles DCA or DAC cannot be 90. Moreover, since angle C will always be less than 90 degrees hence its supplement will always be greater than 90.
Since one angle in ABC is already greater than 90, therefore either of the other two angles cannot be equal to 90.
Sufficient.
+1B
Updated on: 20 Nov 2019, 11:33
Originally posted by BrentGMATPrepNow on 30 Jul 2019, 08:56.
Last edited by BrentGMATPrepNow on 20 Nov 2019, 11:33, edited 1 time in total.
Last edited by BrentGMATPrepNow on 20 Nov 2019, 11:33, edited 1 time in total.
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joylive
A student asked me to comment on this question. So.....
Target question: Is triangle ABC a right triangle?
Statement 1: ACD is a right triangle.
This means ONE of the 3 angles in ∆ACD is 90°
So, let's examine 2 possible cases:
Case a: ∠DCA = 90°. This means ∠ACB = 90°, in which case, the answer to the target question is YES, ∆ABC IS a right triangle
Case b: ∠ADC = 90°. This means ∠DCA < 90°, which means ∠ACB > 90°. If ∠ACB > 90°, then no other angle in ∆ABC can be 90°. In which case, the answer to the target question is NO, ∆ABC is NOT a right triangle
Since we cannot answer the target question with certainty, statement 1 is NOT SUFFICIENT
Statement 2: AC is the greatest side of triangle ACD
KEY CONCEPT: The angle opposite the longest side will be the largest angle.
This means ∠ADC is the largest angle
If ∠ADC is the largest angle, then the other two angles in ∆ACD must be less than 90°
ASIDE: How can we conclude that the other two angles in ∆ACD must be less than 90°?
Well, let's say that one angle (say ∠ADC) is greater than 90°. Since ∠ADC is the largest angle, this would mean that ∠ADC is also greater than 90°
At this point, we have TWO angles in a triangle that are BOTH greater than 90°. This would mean that the sum of the triangle's angles would be greater than 180°, which is IMPOSSIBLE.
So, it MUST be the case that the other two angles in ∆ACD must be less than 90°
Since ∠DCA is LESS than 90°, we can see that ∠ACB is GREATER THAN than 90° (since those two angles must add to 180°)
Finally, ∠ACB is GREATER THAN than 90°, the two other angles in ∆ABC must be LESS THAN 90° (since we can't have TWO angles in a triangle that are both greater than 90°)
So, ∆ABC had 1 angle greater than 90° and two angles less than 90°, we know that ∆ABC cannot be a RIGHT triangle.
The answer to the target question is NO, ∆ABC is definitely NOT a right triangle
Since we can answer the target question with certainty, statement 2 is SUFFICIENT
Answer: B
Cheers,
Brent
