ronniebassist wrote:

there was this certain question :

What is the volume of a certain rectangular cuboid ?

(1) Two adjacent faces of the solid have areas 30 and 48 , respectively .

(2) Each of the two opposite faces of the cuboid has area 60 .

It might sound ultra dumb , but I couldnt even get started with this . What kind of strategy should I have adopted here ? , and is there a different approach for DS problems from different areas i.e algebra , geometry etc.

Sounds like you just need to become comfortable with what DS questions are asking.

A DS question is asking "Do I have enough to solve this problem". The answer can be yes or no and be sufficient, but the key is it MUST be definitive either way.

Spend some time becoming familiar with DS questions and how to approach them.

As for your specific question:

This is a geometry problem, trying to validate the minimum data needed to solve for the volume.

Since it is a rectangular cuboid, you have a minimum of two different leg lengths, and potentially three.

Volume is simply length x width x height right? So we need to be able to solve for three distinct variables, and it's possible two of them are the same.

Let's start with option two. Option two opposite faces have area 60. If we factor out 60 for the possible retangble dimension combinations we find: are 60x1 30x2 20x3 15x4 12x5 10x6

We also are not given any information regarding the third leg (that could be the same or different with one of the other two), as opposites side of a rectangular cube are exactly the same.

Options two is not sufficient on its own.

One tells us information about two adjacent sides. This means one leg between them must be shared, and you also come out with the third leg, so this one looks promising (but don't jump to conclusions just yet).

Factoring out 30 we get 30x1 15x2 10x3 5x6

Factoring out 48 we get 48x1 24x2 16x3 12x4 8x6

We have quite a few that share a common length. Namely the factors w/ 1, 2, 3, 6, with different volumes accordingly.

Thus two on its own is not sufficient.

If we think about how a cube is shaped, we can go through to see if these combination actually work by combining option 1 and option 2.

We know the area of each rectangle. 60, 30 and 48.

Start matching up each one until you get a set that works. If you have more than one combination that works (and yield different volumes) then you know both together are NOT sufficient. If no matter what you only have one result, together they ARE sufficient.

I would solve it right now, but my brain is entirely dead. I will try to remember to come back to this one later.

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