The expenses of a hostel are partly fixed and partly

Thank you Bunuel! Totally clear now!

Great explanation

Because he's the hero GMATclub Needs, but don't deserve. So, we'll ask him 700level questions, because he can take it. He's a silent guardian. A watchful protector. A Bunuel.

(in case you didn't notice it, I modified a quote from the movie "The dark Night"

+1 C

Fixed costs: $ 1,000
Variable costs per head: $70

Can you kindly explain how 20y & 25y are taken?

The variable cost is \($y\) per head, thus for 20 students it's 20y and for 25 students it's 25y.

Hope it's clear.

I solved the problem using an approach similar to Bunuel's. However, it took me 2:31 min to read the question and solve the problem. I wonder if there is a faster way to solve this problem because these additional seconds (~31 seconds) all add up.

My steps:
F + 20 * V = 120 * 20
F + 25 * V = 110 * 25

5 * V = 50 (55 - 12 * 4)
5 * V = 50 * 7
V = 70
F = 2400 - 1400 = 1000
Total = 1000 + 70 * 40 = 3800
At this time I looked at the answer choice and did not see anything matching and quickly realized I need per head cost
So I divided the above result by 40 to get 95.

I could potentially save few seconds if I am more alert but I still feel the above steps would take me 2 min or more.

I would like to know how much time other people are taking to solve the same problem

Fun question if you don't overthink it! I spent way too long wondering if the variable cost had a linear relationship with the number of students.

Given: The expenses of a hostel are partly fixed and partly variable. It costs $120 per head per day if there are 20 students and $110 per head per day if there are 25 students.

Asked: What will be the cost per head per day if the number of students increases to 40?

Let the fixed cost be $x and variable costs be $y/student per day.

120*20 = x + 20y
110*25 = x + 25y

20(120-y) = x = 25(110-y)
480 - 4y = 550 - 5y
y = 70
x = 1000

The cost per head per day if the number of students increases to 40 = (x + 40y )/40 = x/40 + y = 25 + 70 = $95

IMO C

Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.