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The Quest for 700: Weekly GMAT Challenge (Answer)

Yesterday, Manhattan GMAT posted a GMAT question on our blog. Today, they have followed up with the 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.
 
The correct answer is C.


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