Question:  An escalator moves downward from street level to a subway platform at a constant rate. When the escalator is turned off, Wesley takes 70 steps to descend from street level to the platform. When the escalator is turned on, Wesley needs only 36 steps to descend from street level to the platform. If Wesley begins at the platform and walks upward, against the escalator’s downward movement, how many steps will he need to take to reach street level? (Assume that Wesley walks at a constant rate in all scenarios.)

(A) Between 50 and 100 steps
(B) Between 100 and 200 steps
(C) Between 200 and 500 steps
(D) Between 500 and 1000 steps
(E) Over 1000 steps

Correct Answer: E

Solution and Explanation:
Approach Solution 1:

Let D be the level distance from the street to the subway.
When the escalator is motionless, let Wesley's movement speed equal u.
Let v be the escalator's up- or down-moving speed.

He needs to take 70 steps if the escalator is not moving.
Consequently, D/u = 70 and u = D/70 (I)

Wesley requires 36 steps when the escalator and both of them go in the same direction.
D/(u + v) = 36, which means that u + v = D/36 (Ii)

When we combine I and (ii), we obtain

——

v= 17D/(35x36) ..........(iii) (iii)
Thus, u - v = D. (35x36)

Consequently, the number of steps needed when Wesley and the escalator are traveling in opposite directions is —

= D/(u-v) (u-v)
= D/ (D/(35x36))
= 35x36
= 1,260 (which is greater than 1000 steps) (which is greater than 1000 steps). Hence, E is the correct choice.

Correct Answer: E

Approach Solution 2:

Let's choose 1260 miles as the distance measurement unit.
In 70 steps, Wesley travels 1260 kilometers. His step rate is 1260/70 = 18 miles per hour.
Together, Wesley and the escalator travel 1260 miles in just 36 steps. Thus, the overall speed is 35 miles per step, or 1260 / 36 = 35 miles/step.
Accordingly, the escalator moves at a speed of 35-18 = 17 miles each step.

The escalator is now moving counter to his pace as he ascends. Therefore, Wesley's speed will equal the result of all rates. - Escalator speed is 18-17 steps per mile.
equals 1260 miles.
Steps per mile equal speed.
Therefore, there are 1260 steps, or 1260/1

E is the correct answer.

Correct Answer: E

Approach Solution 3:

Since Wesley must descend the escalator in 70 steps while it isn't in motion, let's assume that the escalator has 70 steps.
Wesley descends the escalator in just 36 steps when it is activated, which implies that the escalator completes the task of 34 steps in the time it takes Wesley to descend.

Therefore, the escalator "takes" 34 steps for every 36 steps Wesley takes. Wesley "gains" two steps on the escalator in the time it would ordinarily take to descend to the platform if he reverses his trip and moves uphill, against the escalator. In other words, Wesley really goes up the escalator two steps for every 36 that he takes.

He must acquire a total of 2 steps 35 times since he needs to "gain" a total of 70 steps to reach the top of the escalator. He subsequently makes a total of 36(35) steps. There are more than 1,000 of them. Don't do math that you don't have to—the exact number is 1,260 steps.

The right response is (E).

Correct Answer: E

“An escalator moves downward from street level to a subway platform at" - is a topic of the GMAT Quantitative reasoning section of GMAT. This question has been borrowed from the book “GMAT Official Guide Quantitative Review”.

To understand GMAT Problem Solving questions, applicants must possess fundamental qualitative skills. Quant tests a candidate's aptitude in reasoning and mathematics. The GMAT Quantitative test's problem-solving phase consists of a question and a list of possible responses. By using mathematics to answer the question, the candidate must select the appropriate response. The problem-solving section of the GMAT Quant topic is made up of very complicated math problems that must be solved by using the right math facts.

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