Problem Solving

Hi All,

We're told that two trees have a combined height of 60 feet and the taller tree is X times the height of the shorter tree. We're asked to find the height of the shorter tree in terms of X. This question can be approached in a couple of different ways, including by TESTing VALUES.

IF the shorter tree is 10 feet tall and the taller tree is 50 feet tall, then X = 5. Thus, we're looking for an answer that equals 10 when we plug X=5 into it. After checking all five answers, there's only one that matches...

Final Answer: A

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

swerve wrote:Two trees have a combined height of 60 feet, and the taller tree is x times the height of the shorter tree. How tall is the shorter tree, in terms of x?
$$A.\ \frac{60}{1+x}$$
$$B.\ \frac{60}{x}$$
$$C.\ \frac{30}{x}$$
$$D.\ 60\ -2x$$
$$E.\ 30\ -5x$$

Let y = the height of the shorter tree

The taller tree is x times the height of the shorter tree. Ho
So, yx = the height of the taller tree

The two trees have a combined height of 60 feet
We can write: y + yx = 60

How tall is the shorter tree, in terms of x?
We must solve the equation y + yx = 60 for y.
Factor left side: y(1 + x) = 60
Divide both sides by (1 + x) to get: y = 60/(1 + x)

Answer: A
Cheers,
Brent

swerve wrote:Two trees have a combined height of 60 feet, and the taller tree is x times the height of the shorter tree. How tall is the shorter tree, in terms of x?
$$A.\ \frac{60}{1+x}$$
$$B.\ \frac{60}{x}$$
$$C.\ \frac{30}{x}$$
$$D.\ 60\ -2x$$
$$E.\ 30\ -5x$$
The OA is A.

Source: Manhattan Perp

We can create the equation in which s = the height of the shorter tree, and xs = the height of the taller tree.

s + xs = 60

s(1 + x) = 60

s = 60/(1 + x)

Answer: A