In XYZ Building, a flight of stairs connects each floor to the next, a

Time taken to cross one landing = \(t\)
Time taken to cross a flight of stairs = \(2t\)

Time taken to cross \(13\) stairs + \(12\) landings (in between stairs) = \([13\)(\(2t\)) + \(12t]\) = \(38t\) = \(13.3\) mins
Time taken to cross \(27\) stairs + \(26\) landings (in between stairs) = \([27\)(\(2t\)) + \(26t]\) = \(80t\) = \(?\)

\(\frac{80t}{38t}\) = \(\frac{?}{13.3}\) mins

\(?\) = \(\frac{80*13.3}{38}\) = \(28\) mins

Answer C

MANHATTAN GMAT OFFICIAL SOLUTION:

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.

Assuming the Speed stays Constant across both Scenarios and the Landings/Flights of Stairs remain the Same Distance:


Since we are NOT Counting either Landings at the beginning or end:

If there is N Flights
There will be (N-1) Landing

Ratio of:

Time to travel 1 Flight : Time to Travel 1 Landing = 2x : 1x

Time to travel 13 Flights: Time to Travel 12 Landings = 13x : 6x

Total Time = 13.3 min = 13x + 16x

13.3 = 19x

x = .7

Total Time to Travel 13 Flights = 13 * .7 = 9.1 minutes

Total Time to Travel 12 Landings = 12 * .7 = 4.2 minutes

Speed on Flights = 13/9.1 flights per min.

Speed on Landings = 12/4.2 landings per min.


To cover 27 Flights, there would be 26 landings.

Time to Cover 27 Flights = 27 Flights / Speed on Flights = (27/1) / (13/9.1) = 245.7/13 =

18.9 minutes


Time to Cover 26 Landings = 26 Landings / Speed on Landings = (26/1) / (12/4.2) = 109.2 / 12 =

9.1 minutes



Answer:

Total Time = 18.9 + 9.1 = 28.0 minutes

Answer - C-

Climbing a flight of stairs is like crossing 2 landings. The question tells us it takes 13.3 minutes to climb 13 flights and cross 12 landings, so it takes 13.3 minutes to cross 2*13 + 12 = 38 landings. We then want to know how long it will take to climb 27 flights and cross 26 landings, which is like crossing 2*27 + 26 = 80 landings. At the same speed it will take 80/38 times as long to travel 80/38 times as far, so the answer is (80/38)*13.3 = 4*133/19 = 4*7 = 28.

Let time per landing be x, time per flight of stairs = 2x,
13 flights of stairs imply 26x for flight+ 12x (12 landings between 13 flights)=> 38x= 13.3 min, x= 13.3/38

27 flights mean 54x+ 26x (26 landings between 27 flights) = 80x= 80*13.3/38 = 28 minutes

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