iamschnaider wrote:
A tank is filled with gasoline to a depth of exactly 2 feet. The tank is a cylinder resting horizontally on its side, with its circular ends oriented vertically. The inside of the tank is exactly 6 feet long. What is the volume of gasoline in the tank?
(1) The inside of the tank is exactly 4 feet in diameter.
(2) The top surface of the gasoline forms a rectangle that has an area of 24 square feet.
A student asked me to explain why statement 2 is sufficient. So,......
Target question: What is the volume of gasoline in the tank? Statement 2: The top surface of the gasoline forms a rectangle that has an area of 24 square feet.We know that the tank is
6 ft long
Let
x = the width of the surface
We have the following:
Area of rectangle = (base)(height)So, we can write: 24 = (
6)(
x)
Solve get:
x = 4So, the diagram looks like this:
IMPORTANT: For geometry Data Sufficiency questions, we’re typically checking to see whether the statements "lock" a particular angle, length, or shape into having just one possible measurement. This concept is discussed in much greater detail in the following video:
https://www.gmatprepnow.com/module/gmat ... /video/884So we want to determine whether there is exactly one tank size such that when the gasoline is
2 feet deep, the surface of the gasoline is
4 feet wide.
So let's start with some random tank like this...
... and fill it with gasoline to a depth of
2 feet
When we measure the width of the surface, we get
3 feet
So, this particular tank is too small.
Let's try slightly bigger tank. Here's one.
Still too small.
As we can see, if we gradually make the tank bigger and bigger and bigger, there will be EXACTLY ONE tank such that the width of the surface is
4 feet.
Since there is EXACTLY ONE tank that meets the given conditions, we know that statement 2 is SUFFICIENT
Answer: D
ASIDE: Some people might be wondering, "Sure, but what is the actual volume of the gasoline in the tank?"
Fortunately, we don't need to find the actual volume. We need to only demonstrate that we COULD find the volume.
One way to do this would be to use geometric properties and formulas. But we can also find the volume in other ways.
For example, if I had very precise measuring equipment and a way to construct cylindrical tanks of any shape, then I COULD keep testing actual tanks until I find one that meets the given conditions. Then, I'd fill that tank with gasoline to a depth of 2 feet. Then I'd pour that gasoline into a very precise measuring cup. Done!!
Cheers,
Brent
Thank you for the detailed images. However, I still need some help understanding why it is not possible for the width=4 to be below/above halfway mark, and still have depth=2. For instance in the below image, is it not possible?