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19 Mar 2008, 14:34
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In a certain triangle, the ratio of the smallest angle to the largest angle is 2:7 and the ratio of the smallest angle to the next smallest angle is 1:3. What is the measure of the largest angle..
(A) 24 deg
(B) 62 deg
(C) 84 deg
(D) 142 deg
(E) 168 deg
(A) 24 deg
(B) 62 deg
(C) 84 deg
(D) 142 deg
(E) 168 deg
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19 Mar 2008, 19:12
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Nothing wrong with the real math, but it's good to be armed with many methods, and this question is a great one to work backwards on. Since we are looking for the largest angle, we can rule out the answer choices smaller than 60. (If the largest angle is smaller than 60, then the other two are even smaller, and there's no way it can add up to 180).
So, you know it's going to be one of the larger ones, and even 62 looks a little unlikely.
(B) 62 deg
(C) 84 deg
(D) 142 deg
(E) 168 deg
Now, a little more. We are looking for the largest angle, which is in a 2:7 ratio with the smallest. That means that the largest angle has to be a multiple of 7 (unless the angles aren't integers, which is very unlikely in a problem like this). Only C and E are multiples of 7 (try subtracting large multiples of 7 from each number and look at what's left, to see if they're multiples of 7).
Now, 168 looks a little unlikely, as it looks a bit too big. If the largest angle is 168, then there's only 12 degrees to go for the other two. If the largest is 168 and it's in a 2:7 ratio, then the smallest would be 48. No way.
Gotta be C.
So, you know it's going to be one of the larger ones, and even 62 looks a little unlikely.
(B) 62 deg
(C) 84 deg
(D) 142 deg
(E) 168 deg
Now, a little more. We are looking for the largest angle, which is in a 2:7 ratio with the smallest. That means that the largest angle has to be a multiple of 7 (unless the angles aren't integers, which is very unlikely in a problem like this). Only C and E are multiples of 7 (try subtracting large multiples of 7 from each number and look at what's left, to see if they're multiples of 7).
Now, 168 looks a little unlikely, as it looks a bit too big. If the largest angle is 168, then there's only 12 degrees to go for the other two. If the largest is 168 and it's in a 2:7 ratio, then the smallest would be 48. No way.
Gotta be C.
