The length, the breadth and the height of a cuboid are in the ratio...

This question really doesn't make sense - where is it from? First it talks about 'cuboids', which you will absolutely never see on the GMAT. The word 'cuboid' is not a synonym for 'rectangular prism' (your normal rectangular box shape), and you don't get the volume of a general cuboid just by multiplying the lengths of the edges.

Second, the answer choices don't make sense. Filling in the blanks, the correct answer says "the increase in the volume is 17 times". 17 times what? It needs to say something after the word 'times'. The most natural way to interpret the question is to think it asks "the new volume is what times the old volume", and the correct answer to that question is '18'. But that's not what they mean - they mean "the increase in the volume is what times the old volume" which is a very strange way to interpret the question.

Anyway, if we assume, as I'm sure they meant, that we have a rectangular box, then the ratio of the length, height and width is irrelevant. When you increase something by 100%, you're multiplying by 2, and when you increase by 200%, you're multiplying by 3. So if our dimensions originally were a, b and c, our original volume is abc, and our new volume is (2a)(3b)(3c) = 18abc = 18 times the old volume.

CONCEPT: Since there is no absolute value of any dimension of the Cuboid (Rectangular Solid/box) so in such case we can assume any number for the dimensions as per the ration of the dimensions given

Let, Length(L) = 1 Unit, Breadth(B) = 2 Units and Height(H) = 3 units of the Rectangular Solid

Then Volume = L x B x H = 1 x 2 x 3 = 6 Cube Units

New Length = L + 100% of L = L+L = 2L = 2*1 = 2
New Breadth = B + 200% of B = B+2B = 3B = 3*2 = 6
New Height = H + 200% of H = H+2H = 3H = 3*3 = 9

Then Volume = New Length x New Breadth x New Height = 2 x 6 x 9 = 108 Cube Units

New Volume = a * Old Volume

i.e. a = New Volume / Old Volume = 108/6 = 18 times

Since New Volume = 18 times of Old Volume
therefore Volume has increased by 18V-V = 17 times

i.e. Volume has increased by= 17 times

Answer: option

The only reason this question was added is that during my GMAT classes , everyone was considering the ratios part and coming to a solution. This takes more time and as proved by me and others as well considering ratios is NOT required. Hence just to let everyone know about this and SAVE time in the actual exam I added the question.

Sometimes seeing the bigger picture is a lot more important. After all, one of the key factors that makes GMAT difficult is its timing constraints.