You know the drill. Five points per correct answer. Show your work.
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Update: 17 and 19 have been answered on Facebook.
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You know the drill. Five points per correct answer. Show your work.
***
***
***
***
Update: 17 and 19 have been answered on Facebook.
This entry was posted on August 12, 2010 at 6:50 pm and is filed under Uncategorized.
Tags: geometry, GRE, math problems
August 13, 2010 at 12:17 am
I’ll give 18 shot because I’m slightly less stupid at algebra than geometry. My answer = 12 miles
Distance = Rate * Time
So I solved simultaneously for:
D = 40mph * (T + 10/60)
D = 30mph * (T + 16/60)
to get T, then plug into either equation to get D.
40 * (T + 1/6) = 30 * (T + 4/15)
40T + 40/6 = 30T + 120/15
10T = 120/15 – 40/6
10T = 8 – 20/3 = 24/3 – 20/3 = 4/3
T = 4/3 * 1/10 = 4/30 = 8/60 = 8 minutes
D = 40mph * (8/60 + 10/60) = 40 * 18/60 = 36/3 = 12 miles
D = 30mph * (8/60 + 16/60) = 30 * 24/60 = 24/2 = 12 miles
August 13, 2010 at 7:14 am
Very nice. Five points!
August 25, 2010 at 1:41 am
20 is pretty easy to solve by drawing a diagram, but I’m not sure how to express it algebraically.
If you were to draw a line perpendicular to PQ and RS, intersecting x, it would make 2 right triangles.
The angles on the side made by PQ would be 90, and 60. The angles on the side made by RS would be 90 and 50 (180-z).
Since the interior angles of a triangle add up to 180, this leaves their third angles as 30 and 40 respectively. These angles make up a 180 arc with x, making x = 180 – 30 – 40 = 110.
That would have been so much easier with a picture. 🙂
August 25, 2010 at 8:09 pm
Five points to you, sir. Collect 20 for a free blog post.