Elevator

[kumard24]

7. A certain elevator has a safe weight limit of 2,000 pounds. What is the greatest possible number of people who can safely ride on the elevator at one time with the average (arithmetic mean) weight of half the riders being 180 pounds and the average weight of the others being 215 pounds?
(A) 7
(B) 8
(C) 9
(D) 10
(E) 11

Can anyone help???

[AleksandrM]

Here is how I went about it:

First, conceptualize what you are told:

180x + 215y is < or = 2000

Then, just plug in answer choices.

You can eliminate all of the answer choices with odd numbers, because you cannot split a person in half (the problem tells you that HALF are 180 and the other HALF are 215).

So just pick B, and you see that it is 180(4) + 215(4) = 1580

So go on to the next choice, 180(5) + 215(5) = 1975, that's your answer.

Hope I am right![/u]

[rros0770]

I agree with Aleksandr, I got D also

[rros0770]

I agree with Aleksandr, I got D also

[Stuart@KaplanGMAT]

Here is how I went about it:

First, conceptualize what you are told:

180x + 215y is < or = 2000

Then, just plug in answer choices.

You can eliminate all of the answer choices with odd numbers, because you cannot split a person in half (the problem tells you that HALF are 180 and the other HALF are 215).

So just pick B, and you see that it is 180(4) + 215(4) = 1580

So go on to the next choice, 180(5) + 215(5) = 1975, that's your answer.

Hope I am right![/u]

Great solution!

Instead of backsolving, we could have also solved algebraically.

Using your summation:

180x + 215y

and taking into account that x=y (since each group is half of the people),

we know that 395 is the weight of one person from each group. So, to find the answer, we can divide 2000 by 395 and then double our result to get the total number of people.

2000/400 would be 5, so 2000/395 will be 5 and a bit. Since we don't want bits of people in the elevator (that would be really bad for our shoes), we know that 5*2 = 10 will be the maximum number of people that we can fit inside: choose (D).

[resilient]

PLEASE: can you please keep the answer to the question in your post.

we are giving you answers and trying to help you get your score but you are in essence leaving us in the dark with no answer. ALso please put the source of the question.

QA is D and backsolving is awesome here. This is also a perfect reason why to start with d or b.

[kumard24]

Apologies for the delayed response.

Firstly..thanks for the answer...once again it looks so easy now.

Secondly, the source for this question was from a friend. I think he mentioned that he sourced it from wiki 500 PS Questions