Jan lives x floors above the ground floor of a highrise building. It t

Jan lives x floors above the ground floor.
Jan takes 30 seconds per floor to walk.
Time taken by Jan to reach x floors walking = 30x seconds

Jan takes 2 seconds per floor to ride the elevator. Jan has to wait for 7 mins (7 x 60 = 420 seconds) for elevator.
Time taken by Jan to reach x floors in elevator = 2x + 420 seconds

2x + 420 = 30x
28x = 420
x = 15
Therefore Jan lives on 15 floor. Answer D...

30 secs to walk down each floor. So 30*x seconds to walk down x floors.
2 seconds to ride down each floor. So 2*x seconds to ride down x floors.

It is given that total time to walk down = 7*60 + total time to ride down x floors
Therefore 30*x= 7*60+2*x

30*x-2*x= 7*60
28*x=7*60
x= 7*60/28 = 15
Answer is D

Quickest way without algebra.

Eliminate wrong answer:

7 min = 420 sec.

As per the condition .

steps time = elevator time + 420 sec.

Hence ans choice will definitely be > 420 sec


Now scanning answer choices. We can eliminate A, B and C

A) 4 = 4 * 30 = 120 sec

B) 7 = 7* 30 = 210 sec

C) 14 = 14 * 30 = 420 sec

D) 15 = 15 * 30 = 450 sec

E) 16 = 480 sec

Check condition for option D and E

Option D : 15 * 30 = 15* 2 + 420
=> \(450 = 450\)

Option E: 16 * 30 = 16 * 2 + 420
=> \(480\neq{452}\)

x*(1/2)=7+x*(1/30)
x=15
D

Sometimes my ability to write equations for these problems goes AWOL. It did here, initially.

In case others had similar issues, I'm including a good ole RTD chart to clarify my approach.

1. We have rates in seconds and part of a time in minutes. These rates are easy to convert to minutes.

Jan takes 30 seconds per floor to walk down stairs.\(\frac{1 Floor}{30 seconds} = \frac{2 F}{60 secs} = \frac{2 F}{1 min}\), 2 in diagram.

Jan takes 2 seconds per floor to ride the elevator down. \(\frac{1 Floor}{2 seconds} = \frac{30 F}{60 secs} = \frac{30 F}{1 min}\), 30 in diagram

2. Distance / rate = time (in minutes)

Stairs' time: \(\frac{x}{2}\)

Elevator's time: \(\frac{x}{30}\)

3. We are told that elevator time down + 7 minutes equals walking down the stairs' time, and the rates are in minutes, too, so

\(\frac{x}{30}\) + 7 = \(\frac{x}{2}\) --> (multiply all terms by 30)

x + 210 = 15x

210 = 14x

x = 15

Answer D
_________________

Asks for:
x=?

Given:
Walk down = 30x
Ride down = 2x

Condition:
30x=2x+7min

Solution:
First 7 Min. = 420 Sec.
Then:
30x=2x+420
28x=420
x=420/28
x= 15


Correct answer:
(D) 15

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

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:

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

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
_________________

(Walking time) 30X = 7 * 60 (Wait) + 2X (Elev. Time)
X = 420/28 = 15

here is perhaps the quickest (and dirtiest) solution.

the overall time must be a multiple of 30 seconds, because it takes 30 seconds to walk down each floor. (that's ridiculously slow - bad knees?)

also, the 7 minute wait time is itself a multiple of 30 seconds. this means that the actual time taken by the elevator must also be a multiple of 30 seconds, because we need to add it to another multiple of 30 seconds (7:00) and get still another multiple of 30 seconds.
the only answer choice that multiplies by 2 seconds to give a multiple of 30 seconds is (d). done.

Posted from my mobile device
_________________

simple equation is formed with the statement given . 30x= 420+2x . that will give x=15

Time taken by Jan to walk down the steps of x floors = 30x seconds, since she takes 30 seconds per floor.
Time taken by Jan to ride down the elevator and cover x floors = 2x seconds, since she takes 2 seconds per floor.
Note that she had to wait for the elevator for 7 minutes, so that’s an additional 420 seconds

It is given that time taken in both cases is same; therefore, 30x = 2x + 420
Solving for x, we have x = 15; this means Jan lives 15 floors above the ground floor.

The correct answer option is D.
_________________

My 2 cents on this:

I feel like the wording was slightly tricky for my liking. Anyway, If we look at what is being asked

We need to find X, i.e. the number of floors.

Equation is as follows: 30X = 420 + 2X; X = 15.

D

Let's start by converting 7 minutes to seconds:

7 minutes = 7 x 60 seconds = 420 seconds

If Jan walks down the steps, it will take her 30x seconds to get down to the ground floor.

If she takes the elevator, it will take her 2x seconds to ride down to the ground floor.

So the total time for taking the stairs is:

30x = time to walk down to the ground floor

The total time for taking the elevator is:

2x + 420 = time to wait for the elevator (420 seconds) + time to ride down

Since it takes the same amount of time for both options, we can set the equations equal to each other and solve for x:

30x = 2x + 420

28x = 420

x = 15

Therefore, Jan lives 15 floors above the ground floor.

Not sure if everyone feels the same, but I fell for a very stupid trap!

I took 'x' to be the total distance and 30 secs/floor and 2 secs/floor as the speed for the 2 different modes mentioned.

Then I took distance/time to calculate the time, thus going onto do x/30 = 420 + x/2


But well, don't fall for it guys!

The speed given is per floor, so naturally to calculate the time taken in total for the stairs it will be 'the distance' * 'speed', so that the distance part of the equation cancel each other out, and that you are left with the time.

Another way to think about is that you just need the total time, and while time= distance/speed, that is applicable only when you have the speed for the total distance. Here we have it only for one floor. Thus a little bit of thought would help us realize that we can pretty much get the "time" component of the equation just by multiplying the distance with the speed.


--> 30 secs/floor * x = 7 * 60(converting minutes to seconds) + 2 secs/floor *x floors

Solving the above should give you x = 15.

Let's analyze the time it takes for Jan to reach the ground floor using both the steps and the elevator.

If Jan walks down the steps, it takes her 30 seconds per floor. So, the total time taken to walk down x floors is 30x seconds.

If Jan takes the elevator, it takes her 2 seconds per floor. So, the total time taken to ride down x floors is 2x seconds.

According to the problem, the time taken to walk down the steps is equal to the time taken to wait for the elevator for 7 minutes (which is 420 seconds) and then ride down. So, we can set up the equation:

30x = 420 + 2x

Simplifying the equation, we have:

28x = 420

Dividing both sides of the equation by 28, we find:

x = 420 / 28 = 15

Therefore, x equals (D)15.