dabaobao wrote:

When an object is dropped from a building, its height above the ground is given by the formula h = y – gt^2 where y is the height of the building in meters, g is a constant, and t is the time in seconds since the object was dropped. What is the height of an object dropped from a 100 meter tall building 2 seconds after being dropped?

(1) An object is 74 meters above the ground 2 seconds after being dropped from a building that is z meters tall.

(2) The height of an object dropped from a 150 meter tall building is 61.2 meters 3 seconds after being dropped.

Official Solution (Credit: Manhattan Prep)

This question contains a Formula. Jot down that formula and any notes needed to keep the variables straight.

h = y – gt^2

y = building height, g = constant, t = time

The question asks about the height of an object in a particular set of circumstances. Fill in the information about this case into the formula.

h = 100 – g(2^2)

h = 100 – 4g

What information do you need to solve for the height h? The value of the constant g: if you knew g, you could plug it into the equation above to solve for h. So the question can be Rephrased as:

What is g?

(1) INSUFFICIENT: Plug the information from the statement into the formula.

74 = z – g(2^2)

74 = z – 4g

Can you solve for g? You can’t. You could rearrange the equation to isolate g, but there is still another variable in the equation.

g=(z−74)/4

This statement is not sufficient. Eliminate choices (A) and (D).

(2) SUFFICIENT: Plug the information from the statement into the formula.

61.2 = 150 – g(3^2)

61.2 = 150 – 9g

In this case, you can solve for g because it is the only variable in the equation. Since this is a data sufficiency problem, you don’t have to go through the exact calculations. This statement is sufficient. Eliminate choices (C) and (E).

The correct answer is (B).

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