Carcass wrote:
A cube shaped cake is frosted on all sides except the bottom and then cut into 27 equally sized cube shaped pieces.
Quantity A |
Quantity B |
The number of pieces of cake that have exactly two sides frosted |
One more than the number of pieces of cake that have fewer than two sides frosted |
A)The quantity in Column A is greater.
B)The quantity in Column B is greater.
C)The two quantities are equal.
D)The relationship cannot be determined from the information given.
Kudos for the right answer and explanation
QUANTITY A: The number of pieces of cake that have exactly two sides frosted NOTE: The first time I read this question I didn't notice the part about the cake having no frosting on the bottom side.
Now that I've recognized this, the diagram below indicates (in RED) all of the pieces that have exactly TWO frosted sides:
If you can imagine the same pattern on the sides not shown, you will see that there are
12 such pieces of cake
QUANTITY B: One more than the number of pieces of cake that have fewer than two sides frostedFirst, let's determine the number of pieces that have exactly ONE side frosted.
The diagram below indicates (in BLUE) all of the pieces that have exactly ONE frosted side
In total, there are
9 pieces that have exactly ONE frosted side.
Now let's determine the number of pieces that have exactly ZERO frosted sides.
- the middle piece that lies on the lowest layer has has zero frosted sides
- there's also a piece of cake at the very center that has zero frosting slides
So, there are
2 pieces that have ZERO frosted sides.
Quantity B tells us to
ADD 1 to the number of pieces of cake that have fewer than two sides frosted
So, Quantity B =
9 +
2 + 1 =
12So the two quantities are equal
Answer: C
Cheers,
Brent