goodyear2013 wrote:

A monument is made by stacking identical rectangular blocks of marble, each measuring 2 feet by 3 feet by 1 foot, into a large rectangular solid. If all the blocks are aligned in the same direction, how many blocks high is the monument?

(1) The length of the monument is 12 feet and the width of the monument is 15 feet.

(2) The height of the monument is 25 feet.

OE

(1): limitless options.

Insufficient

(2): There is only one way for the height to be 25 feet using these blocks (and without cutting them up): use the 1 ft. sides in the vertical dimension. This means that the monument is 25 blocks high.

Sufficient.

Hi, I want to request the clarification of how statement (2) is sufficient, please.

The dimensions of each block are 2 * 3 * 1. We don't know the orientation in which the blocks are stacked i.e. Imagine you are looking at the monument from the front.

|_________|__________|__________| - blocks stacked such that the 3 feet side makes the width of the monument

|_______|_______|_______|______| - blocks stacked such that the 2 feet side makes the width of the monument

|___|___|___|___|___|___|___|___|___| - blocks stacked such that the 1 foot side makes the width of the monument

etc

The question is, how many blocks high is the monument i.e. how many blocks were stacked one on top of another to give the monument its height.

Depending on the orientation of the blocks and the number of blocks stacked, we will get the height of the monument.

(1) The length of the monument is 12 feet and the width of the monument is 15 feet.

The width of the monument could be made 15 feet by stacking 5 blocks next to each other as in orientation 1 above. It could be made 15 feet by stacking 15 bricks next to each other as in orientation 3 above. But we have no information about the height of the tower or the number of bricks stacked on top of each other or the orientation of the bricks. Hence this statement is not sufficient.

(2) The height of the monument is 25 feet.

Now we know the height of the monument. How can you make 25 feet of height? Stacking 25 blocks one on top of another such that the side of 1 foot makes the height (orientation 1 or 2 above). Is there any other way? Can you make the side of 2 feet or 3 feet the height? No because you will need 12.5 blocks to make a 25 foot high monument in case you make 2 foot the height. Or you will need 8.33 blocks to make a 25 foot high monument in case you make 3 foot the height. But the monument is made by sticking identical blocks together so we cannot cut them. Hence the height of 25 feet must have been created by stacking 25 blocks one on top.

This statement alone is sufficient.

Answer (B)

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