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A rectangular aquarium provides 36 square centimeters

Expert replies
by BTGmoderatorDC » Tue Jan 02, 2018 5:30 am
A rectangular aquarium provides 36 square centimeters of water-surface area per fish. How many fish are there in the aquarium?

(1) The edges of the aquarium have lengths of 60, 42, and 30 centimeters.
(2) The aquarium is filled to a depth of 40 centimeters.

I'm quite confused, can some experts explain the statements?

OA E
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Source: — Data Sufficiency |

test

by aockert » Fri Jan 05, 2018 3:11 pm
This question is asking about the top-surface area of an aquarium. Instead of giving us the actual surface area, the question stem provides the surface area per fish: 36. The surface area per fish would be equal to the surface area divided by the number of fish:
$$surface\ area\ per\ fish\ =\ \frac{surface\ area\ of\ aquarium}{#\ of\ fish}$$

In order to find the # of fish in the tank, we have to be able to determine the surface area of the tank.

Statement 1 is insufficient by itself. This statement gives us all of the dimensions of the tank, but does not indicate which dimensions match up to length, width, or height. So you can eliminate choice D.

Statement 2 is also insufficient by itself. The depth of the tank MIGHT be helpful given some more information (more on that below), but by itself, it tells us nothing about the surface area. At this point you could eliminate choices A and B.

Now we can combine the two statements to see if they are sufficient together.

Statement 2 tells us that the aquarium is filled to a depth of 40 centimeters. The depth of the water MUST be less than the height of the aquarium. So Statement 2 tells us that of the 3 dimensions given in the question stem, 30 CANNOT be the depth (and therefore must be the length or the width, which we need to find the top-surface area). However, we still do not know WHICH of the two other dimensions would pair with 30 to give the top-surface area. In other words, we know the top-surface area is
42 x 30 = 1260
OR
60 x 30 = 1800

One final issue here is that you could not have a partial number of fish, so we can divide each of these surface-areas by 36 (the area per fish) to see if they provide a whole number value.
$$1800\div36=50$$
$$1260\div36=35$$

So, with both statements taken together we could have 50 OR 35 fish. Thus Choice E is correct, and the two statements taken together are not sufficient.
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