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Relative speed

by Mo2men » Sat Apr 29, 2017 7:38 am
Pam gets on an elevator at the 12th floor of a building going up to the 70th floor. Hilary gets on the elevator on the 63rd floor at the same time in the same building going down to the 1st floor. At what floor will their paths cross?

(1) Pam's elevator is moving twice the rate of Hilary's elevator.
(2) Hilary's elevator is moving at a rate of 4 floors per second.


OA:A
Last edited by Mo2men on Sun May 28, 2017 3:26 am, edited 2 times in total.
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by [email protected] » Sat Apr 29, 2017 10:00 am
Hi Mo2men,

The answer that you originally listed is not correct. I'm going to give you some 'hints' so that you can attempt this question on your own:

[spoiler]This is essentially a Combined Rate question, since we have two entities approaching along the same path. While the prompt does not state it, we're mean to assume that the elevator cars will not stop along the way up/down. To answer this question, we either need to know the specific speeds of the two cars OR we need to know the ratio of the two speeds (since if we have that information, then the actual distance between the two cars won't matter....[/spoiler]

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by GMATGuruNY » Sat Apr 29, 2017 12:59 pm
Mo2men wrote:Pam gets on an elevator at the 12th floor of a building going up to the 70th floor. Hilary gets on the elevator on the 63rd floor at the same time in the same building going down to the 1st floor. At what floor will their paths cross?

(1) Pam's elevator is moving twice the rate of Hilary's elevator.
(2) Hilary's elevator is moving at a rate of 4 floors per second.
The problem should indicate that the floors are equally spaced and that the two elevators move at constant speeds.
Number of floors between Hilary and Pam = (Hilary's floor) - (Pam's floor) = 63-12 = 51.
Since Pam and Hilary are moving toward each other, they are WORKING TOGETHER to cover the 51 floors between them.

Statement 1: Pam's elevator is moving twice the rate of Hilary's elevator.
Implication:
Of every 3 floors between Pam and Hilary, Pam travels 2 floors, while Hilary travels 1 floor, with the result that Pam travel 2/3 of the 51 floors between her and Hilary.
Since Pam begins on the 12th floor, we get:
(12th floor) + (2/3)(51) = 12 + 34 = 46th floor.
SUFFICIENT.

Statement 2: Hilary's elevator is moving at a rate of 4 floors per second.
Without information about the speed of Pam's elevator, we cannot determine at what floor Hilary's elevator will pass Pam's elevator.
INSUFFICIENT.

The correct answer is A.
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by Jay@ManhattanReview » Sun Apr 30, 2017 12:54 am
Mo2men wrote:Pam gets on an elevator at the 12th floor of a building going up to the 70th floor. Hilary gets on the elevator on the 63rd floor at the same time in the same building going down to the 1st floor. At what floor will their paths cross?

(1) Pam's elevator is moving twice the rate of Hilary's elevator.
(2) Hilary's elevator is moving at a rate of 4 floors per second.

Source: Gmatfree

OA:A
Between the two, they have to cover 63 - 12 = 51 floors to meet. By looking at the statements we get to know that Pam's and Hilary' elevators move at different speeds, otherwise, they would meet between 37 and 38 floors, had each elevator moved at the same speed. No need for any statement! :)

Statement 1: Pam's elevator is moving twice the rate of Hilary's elevator.

Say speed of Hilary's elevator = 1 floor per second, thus speed of Pam's elevator = 2*1 =2 floors per second

Their combined speed (relative speed) = 1+2 = 3 floors per second (since they are moving in the opposite direction, we must add the speeds)

Time to meet = 51/3 = 17 second

In 17 seconds, Hilary's elevator would come down 17 seconds * 1 floor per second = 17 floors

Thus, they meet at 63 - 17 = 46th floor. Sufficient

Statement 2: Hilary's elevator is moving at a rate of 4 floors per second.

We do not have the speed of Pam's elevator. Cannot calculate. Insufficient.

The correct answer: A

Hope this helps!

Relevant book: Manhattan Review GMAT Data Sufficiency Guide

-Jay
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