Monthly rent for units in a certain apartment building is

VJesus12 wrote:Monthly rent for units in a certain apartment building is determined by the formula \(k\cdot \frac{5r^2+10t}{f+5}\) where \(k\) is a constant, \(r\) and \(t\) are the number of bedrooms and bathrooms in the unit, respectively, and \(f\) is the floor number of the unit. A 2-bedroom, 2-bathroom unit on the first floor is going for $800/month. How much is the monthly rent on a 3-bedroom unit with 1 bathroom on the 3rd floor?

(A) $825
(B) $875
(C) $900
(D) $925
(E) $1,000

[spoiler]OA=A[/spoiler]

Source: Manhattan GMAT

Hi Vjesus12.

Using this fact

A 2-bedroom, 2-bathroom unit on the first floor is going for $800/month

we can find the value of \(k\), so let's do it.

We have that \(r=2, t=2\) and \(f=1\), so $$800=k\cdot\frac{5\left(2\right)^2+10\cdot2}{1+5}\ \Rightarrow\ 800=k\cdot\frac{40}{6}\ \ \Rightarrow\ k=120.$$ Now, let's compute the monthly rent on a 3-bedroom unit with 1 bathroom on the 3rd floor.

In this case we have that \(r=3, t=1\) and \(f=3\). Then $$Rent=120\cdot\frac{5\left(3\right)^2+10\cdot1}{3+5}\ \Rightarrow\ \ Rent=120\cdot\frac{55}{8}=825.$$ Therefore, the correct answer is the option _A_.

I hope it helps you. <i class="em em-sunglasses"></i>