The Quest for 700: Weekly GMAT Challenge (Answer)

Since it takes Josie twice as long to climb a flight of stairs as it does to cross a landing, let’s start with the smaller time. Let’s take the time to cross 1 landing and call it x. Then the “flight climbing time,” the time to climb 1 flight, is 2x.

 

Josie takes 13.3 minutes to climb 13 flights of stairs and 13 – 1 = 12 landings between them. (We “subtract one before we’re done” to count the landings between the flights.)

 

The relationship can now be written:

 

13.3 = time to climb 13 flights + time to cross 12 landings

13.3 = 13(2x) + 12x

13.3 = 26x + 12x = 38x

x = 13.3/38 = 133/380

 

380 can be factored easily: 380 = 38 × 10 = 2 × 19 × 2 × 5

133 is tricky; it equals 7 × 19.

So 133/380 reduces (with the 19’s canceling) to 7/20. That’s x.

 

Now, the quantity we want is the time to climb 27 flights and cross 27 – 1 = 26 landings.

 

27(2x) + 26x = ?

54x + 26x = ?

80x = ?

80(7/20) = ? Cancel out the 20, leaving 4 × 7 = 28 exactly.