Problem Solving

Hi All,

We're told that Jan lives X floors above the ground floor of a high-rise building; it takes her 30 SECONDS per floor to walk down the steps and 2 SECONDS per floor to ride the elevator. We're asked if it takes Jan the SAME amount of time to walk down the steps to the ground floor as to wait for the elevator for 7 MINUTES and ride down, then X equals which of the following numbers. This question can be solved in a couple of different ways, including by TESTing THE ANSWERS.

To start, there's a significant difference in time between walking and riding the elevator (30 seconds/floor vs. 2 seconds/floor); in the time it takes Jan to walk 1 floor, she can ride the elevator down 15 floors. Given the 5 answer choices, the correct answer will likely be one of the larger options. Let's TEST Answer D first...

Answer D: 15 floors
IF... Jan travels 15 floors, then
the walking time would be (15)(1/2 minute) = 7.5 minutes
the elevator time would be (15)(2 seconds) = 30 seconds = 1/2 minute
The difference in these two times is 7 minutes, which is an exact match for what we were told. Thus, this must be the answer.

Final Answer: D

GMAT assassins aren't born, they're made,
Rich

AAPL wrote:Jan lives x floors above the ground floor of a highrise building. It takes her 30 seconds per floor to walk down the steps and 2 seconds per floor to ride the elevator. If it takes Jan the same amount of time to walk down the steps to the ground floor as to wait for the elevator for 7 minutes and ride down, then x equals
A. 4
B. 7
C. 14
D. 15
E. 16

Let's first convert 7 minutes to SECONDS in order to have uniform units of measurement.
7 minutes = 420 seconds

Let's start with a word equation
Jan's travel time (in seconds) WALKING down = Jan's travel time (in seconds) via ELEVATOR + 420 seconds

It takes her 30 seconds per floor to walk down the steps and 2 seconds per floor to ride the elevator.
There are x floors
So, WALKING time (in seconds) = 30x
And ELEVATOR time (in seconds) = 2x

Plug values into word equation to get: 30x = 2x + 420
Subtract 2x from both sides to get: 28x = 420
Solve: x = 420/28
= 60/4
= 15

Answer: D

Cheers,
Brent

XXXX

AAPL wrote:Official Guide

Jan lives x floors above the ground floor of a highrise building. It takes her 30 seconds per floor to walk down the steps and 2 seconds per floor to ride the elevator. If it takes Jan the same amount of time to walk down the steps to the ground floor as to wait for the elevator for 7 minutes and ride down, then x equals

A. 4
B. 7
C. 14
D. 15
E. 16

Since 7 minutes = 420 seconds, we can create the equation:

Jan's time to walk = Jan's time to ride

30x = 420 + 2x

28x = 420

x = 15

Answer: D