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# QC “Who Cut the Cheese” GRE Challenge Question

This one is a real toughie. It is probably more difficult than any quantitative comparison question you’ll see test day. See if you can crack it under 3 minutes.

A cube of cheese is 3-inches high. The cheese is sliced twice.

Column A Column B
Resulting surface area of all the slices of cheese 90 square inches

1. The quantity in Column A is greater
2. The quantity in Column B is greater
3. The two quantities are equal
4. The relationship cannot be determined from the information given

Good luck! We’ll post the answer and the explanation in a few days, so check back then :).

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### 11 Responses to QC “Who Cut the Cheese” GRE Challenge Question

1. Chris February 5, 2013 at 1:45 pm #

Thanks all for giving this tough question a try :).

A few of you got the correct answer, which is (D).

The way to attack this problem is to recognize that the surface area can equal 90 (as many of you did), but that there are multiple ways to slice the cheese. One way is to not slice straight down, using, instead, a circular cut. By giving the cheese a circular cut, we don’t even have to do any math to know that the answer is going to be some number pi. So it can’t equal 90 (it doesn’t matter whether it is greater of less than 90; it is not 90). Therefore the answer is (D)

Another student above, realized that, given the constraints of the problem, you don’t even have to cut the entire cheese with the second cut. Leaving out one of the halves is going to result in a smaller surface area. Again, you don’t need to do any math, you just have to be able to see that the surface area will be less than 90. Therefore (D).

Hope that helps :).

2. Karan February 5, 2013 at 5:35 am #

Hmm, whichever way I do it, the sum always comes to 90.
C.

3. Guga February 4, 2013 at 11:55 am #

Each slice will have the following dimensions:
h x h x (slice tick)

For each slice we have:
Area = 2*h^2 + 4*(slice tick)*l

So, so for three slices, we got 6*h^2+4*(3*slice tick)*h = 6*h^2+4*h^2 = 10*h^2 = 90

Is that right ?

4. jones February 3, 2013 at 4:02 am #

D

5. siddhant February 2, 2013 at 10:23 pm #

B.) A cube 3 inch high i.e., total surface area 54 square inches . It is then cut into 2 pieces , assuming we get 4 equal slices i.e., a cube of side 1.5 inches , therefore , area of one side of cube is :- 2.25 square inches , total area of one cube =13.5 , now , total area of 4 cubes = 13.5×4 = 54 ….therefore column B is greater…

6. Bhavika Jain February 2, 2013 at 9:39 am #

7. Leah February 1, 2013 at 4:31 pm #

Could be equal (two slices equidistant in the same plane –> 3 equal pieces, 4(1×3) + 2(3×3) = 30 each)

But could cutting it twice mean, for example, that you cut the cheese in half and then only cut one of the half slices for the second cut? Because then you could end up with something like this: three pieces again, but this time 4(1.5×3) + 2 (9×9) for one block and then 2(1.5×1.5) + 4(1.5×3) for the other two, which gets you 81 and therefore A < B.

In that case, D. (Definitely took me longer than 3 minutes, though…had to try out the different possibilities the hard way).

8. Hossein February 1, 2013 at 10:04 am #

C.
(3×3)x6 + (3×3)x4=90

• Chris February 1, 2013 at 4:23 pm #

The tricky thing with QC is just because you found one possible answer, which in this case is 90, this doesn’t mean that you’ve found all the possible answers, given the constraints. Good try :). But have another look :).

• Vanan February 5, 2013 at 11:19 pm #

@Chris,
How to find the Surface area of Cube? Is it not just 6*a*a ..? I find some multiples of 4 and all given in comments.. plz clarify.

• Chris February 6, 2013 at 10:56 am #

Yes, it is just 6a^2. But in this question, two slices can end up in four pieces. Does that make sense?

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