Math Destroyer 2013 PT 6 #15

[Tajlrak]

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I was wondering what is your approach to this problem.

How many different rectangular prisms having a volume of 30ft^3 are there with sides that are each an integer number of feet?

3
4
5
6
7

A: 5

Thanks in advance.

 

[Illfavor]

I recall this one being confusing at first, then I just decided to write them out.

Area = L*W*H

Options: 1,2,15; 1,3,10;1,5,6;2,3,5;30,1,1 I think are the only options, so that's 5. I think I was confused because I didn't immediately realize 1,2,15 is the same as 2,1,15.

A lot of the time on these problems I try and set up some formula when you can actually deduce a great deal from the answer key.

 

[Tajlrak]

I recall this one being confusing at first, then I just decided to write them out.

Area = L*W*H

Options: 1,2,15; 1,3,10;1,5,6;2,3,5;30,1,1 I think are the only options, so that's 5. I think I was confused because I didn't immediately realize 1,2,15 is the same as 2,1,15.

A lot of the time on these problems I try and set up some formula when you can actually deduce a great deal from the answer key.

Cool deal and I see how u wrote it all down. I guess what I am trying to get at is when we are under time constraint and we are writing down all the possible ways, is there a clear cut way to know that you wrote out all the solutions so you wont be 2nd guessing your self? I do not think so.. which is why i this question is bugging me.

 

[Illfavor]

Not that I know of. I'm not great at math, and the explanation in the back didn't really help me per se...This is one of those times I do it the long way. At worst, guess, mark it, and move on.