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09 Jun 2021, 08:00
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Question Stats:
51% (01:15) correct
49%
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If pyramid P and rectangular box B are of equal height, what is the ratio, by volume, of P to B?
(1) Pyramid P and rectangular box B have square bases.
(2) Pyramid P and rectangular box B have bases of equal area.
(1) Pyramid P and rectangular box B have square bases.
(2) Pyramid P and rectangular box B have bases of equal area.
09 Jun 2021, 08:31
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Definitely most don’t know the formula for volume of pyramid neither do I know!
But it’s an DS problem, and by reading the question we can conclude that we are not going to find volume of both shapes. We just care about the variables that matter.
For rectangle volume is (l * b * h)
For pyramid,
We can find it.. we know that there are only two shapes that make up the pyramid. A square with side length a and a triangle (when you cut pyramid through mid-section) with base and height. Here the base is same as the side length of square.
So we just care two variables while calculating volume of pyramid (i.e base ‘a’ and height ‘h’
Given, height is same for rectangle and pyramid. We only require two other sides of rectangular box AND base of pyramid
Statement 1:
We don’t know whether the square of rectangular box and pyramid are of same area! INSUFFICIENT
Statement 2:
Okay area is the same; ( i.e l = b = a)
Clearly SUFFICIENT
Posted from my mobile device
But it’s an DS problem, and by reading the question we can conclude that we are not going to find volume of both shapes. We just care about the variables that matter.
For rectangle volume is (l * b * h)
For pyramid,
We can find it.. we know that there are only two shapes that make up the pyramid. A square with side length a and a triangle (when you cut pyramid through mid-section) with base and height. Here the base is same as the side length of square.
So we just care two variables while calculating volume of pyramid (i.e base ‘a’ and height ‘h’
Given, height is same for rectangle and pyramid. We only require two other sides of rectangular box AND base of pyramid
Statement 1:
We don’t know whether the square of rectangular box and pyramid are of same area! INSUFFICIENT
Statement 2:
Okay area is the same; ( i.e l = b = a)
Clearly SUFFICIENT
Posted from my mobile device
09 Jun 2021, 11:32
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You genuinely need to know the general Volume formula for a pyramid here, and you need to know quite a bit about how pyramids are defined, to answer correctly. Since you need to know nothing at all about pyramids for the GMAT, this is not a realistic question.
Often when people think of a pyramid, they think of a square base, connected to a point in the air that is directly above the centre of the square. But in math, the base of a pyramid can be literally any kind of polygon - a square, a scalene triangle, a rectangle, an irregular octagon, etc - and the point in the air connected to that base can be anywhere at all (it doesn't need to be over the centre of the base).
I could easily imagine a test taker who knows what a pyramid is reading this question, and thinking "using Statement 2 alone, I don't even know what kind of base the pyramid has (is it a triangle or a decagon?), and even using both Statements, I don't know if the top of the pyramid is over the centre of the square base, so the answer is probably E". Unless you had studied pyramids in detail, it seems perfectly reasonable to me to think that the shape of the base and the position of the top point both might be important when you need to compute a pyramid's volume. It turns out neither of those things actually matter, but you'd only know that for sure if you knew the general volume formula for a pyramid, which is a formula you'd never need on the GMAT. Any pyramid, regardless of the shape of the base, and regardless of the location of the top point, has a volume of (1/3)(Area of base)(height). That's why in this question Statement 2 is all we need to find the ratio requested (since we know the heights are equal), but this question is well out of the scope of the GMAT.
Posted from my mobile device
Often when people think of a pyramid, they think of a square base, connected to a point in the air that is directly above the centre of the square. But in math, the base of a pyramid can be literally any kind of polygon - a square, a scalene triangle, a rectangle, an irregular octagon, etc - and the point in the air connected to that base can be anywhere at all (it doesn't need to be over the centre of the base).
I could easily imagine a test taker who knows what a pyramid is reading this question, and thinking "using Statement 2 alone, I don't even know what kind of base the pyramid has (is it a triangle or a decagon?), and even using both Statements, I don't know if the top of the pyramid is over the centre of the square base, so the answer is probably E". Unless you had studied pyramids in detail, it seems perfectly reasonable to me to think that the shape of the base and the position of the top point both might be important when you need to compute a pyramid's volume. It turns out neither of those things actually matter, but you'd only know that for sure if you knew the general volume formula for a pyramid, which is a formula you'd never need on the GMAT. Any pyramid, regardless of the shape of the base, and regardless of the location of the top point, has a volume of (1/3)(Area of base)(height). That's why in this question Statement 2 is all we need to find the ratio requested (since we know the heights are equal), but this question is well out of the scope of the GMAT.
Posted from my mobile device
