Sunday, August 21, 2011

Manhattan GRE's Math Beast Challenge problem for this week

Here it is:

This Week's Problem: "Clement Walks"

Q: Clement walks around an oval-shaped track at a constant rate of 50 seconds per lap. If 18 laps equal a mile, how many miles does Clement walk in 54 minutes?


(A) 2
(B) 2.5
(C) 3
(D) 3.6

This took me about a minute to figure out. It's just quick algebra. The more gifted among you can doubtless do this in your heads. (The answer will be posted later in the comments.)



Horace Jeffery Hodges said...

I think 18 laps is 15 minutes, so one mile takes 15 minutes. In 54 minutes, one would walk more than three miles, so I think "D" is the answer.

And it took me too long to do that in my head . . . a couple of laps worth, I guess.

Jeffery Hodges

* * *

Kevin Kim said...

Bingo. There are several different approaches one can use, but it sounds as if you used this approach:

1 lap is done in 5/6 minutes.


18 laps are done in 15 minutes. (This can be seen by setting up a proportion.)

1 mile in 15 minutes = 4mph.

4 mph for .9 hours (54 minutes) = 3.6 miles.

QED. (Quirky, erotic, delicious.)

Horace Jeffery Hodges said...

Actually, I just thought, "Hmmm . . . at fifty seconds per lap, six laps takes five minutes, so eighteen laps is fifteen minutes."

And I took it from there.

Jeffery Hodges

* * *

Kevin Kim said...

That's probably an easier way to do it.

Surprises Aplenty said...

Since I only had to be close enough to exclude the other answers, I simply looked at 54/18. If it took a minute to do a lap, '3 miles' would be the answer. As the laps were slightly faster, it must be '3.6 miles' or D. I didn't see the need to fine-tune my calculation. Lazy, I guess.

Kevin Kim said...

Even faster!

This problem is so much easier than that damn "spinach rows" problem.