Translate what the question says into math.

x is inversely proportional to y²: x decreases as y² increases, and x increases as y decreases, and there is a constant, k, such that x * y² = k or x = k/y²

Now continue translating to math.

y is divided by 3a: If y is divided by 3a we get x = k/(y/3a)² or x = k(3a)²/y² or x = k(9a²)/y².

So initially x = k/y² and after dividing y by 3a, x = k(9a²)/y².

The correct answer is E.

Hacking tip: If you didn't know exactly what inversely proportional means, you could still have gotten this one right by figuring out that if directly proportional means that there is some constant ratio of x and y that holds such that when x increases y increases, then inversely proportional means that there is something going on such the when y² decreases x increases somehow.

If y is divided by 3a, then y² is divided by (3a)²= 9a². So if y was divided by 9a², then it makes sense that 9a² would have something to do with the increase in x. So of all the answer choices E seems to make the most sense.

lucas211 wrote:The variable x is inversely proportional to the square of the variable y. If y is divided by 3a, then x is multiplied by which of the following:

a) 1/9a
b) 1/(9a^2)
c) 1/3a
d) 9a
e) 9a^2

a and b are INVERSELY PROPORTIONAL if their product is always THE SAME:
ab = k, where k is a constant.

The variable x is inversely proportional to the square of the variable y.
Since x and y² are inversely proportional, we get:
xy² = k, where k is a constant.

Let x� = 1 and y� = 6.
Plugging x� = 1 and y� = 6 into (x�)(y�)² = k, we get:
(x�)(y�)² = (1)(6²) = 36, implying that k=36.

If y is divided by 3a, then x is multiplied by which of the following?
Let a=2.
Dividing y� by 3a, we get;
y₂ = y�/3a = 6/(3*2) = 1.

Plugging y₂ = 1 and k=36 into (x₂)(y₂)² = k, we get:
(x₂)(1²) = 36
xâ‚‚ = 36.

Since x� = 1 and x₂ = 36, the value of x is multiplied by 36. This is our target.
Now plug a=2 into the answer choices to see which yields our target of 36.
Only E works:
9a² = (9)(2²) = 36.

The correct answer is E.