Friday, March 19, 2010

GMAT Question of the Day

I decided to walk down the escalator of a tube station. I did some quick calculation in my mind. I found that if I walk down twenty-six steps, I require thirty seconds to reach the bottom. However, if I am able to step down thirty-four stairs I would only require eighteen seconds to get to the bottom. If the time is measured from the moment the top step begins to descend to the time I step off the last step at the bottom,
can you tell the height of the stair way in steps?
(a) 44
(b) 48
(c) 46
(d) 42

Let speed of the escalator be x steps per second.
In 30 second the escalator will come down by 30 x steps and in 18 seconds it will come down by 18 x steps.
Since height of the stair way is same 26 + 30(x) = 34 + 18(x)
x = 2/3.
Height of the stair way = 26 + 30 (2/3)
= 46 steps.