Using the formula, then we have that column A is equal to \(P=\frac{8}{5}k\) and column B is equal to \(T=\frac{780}{k}\). Comparing those two quantities and simplifying we finally reach a comparison between \(k^2\) and 487.5. Given that k can be whatever constant, we can't say which one of the two is the greatest, thus answer is D!

Just an example:
If k=0, a=0 b=undefined
k=1 makes a=1.6 b=780
so answer D.

QUANTITY A: The value of P if V = 20 and T = 32
Take given formula, PV = kT, and plug in values to get: P(20) = k(32)
Divide both sides by 20 to get: P = 32k/20
Simplify to get: P = 8k/5

QUANTITY B: The value of T if V = 10 and P = 78
Take given formula, PV = kT, and plug in values to get: (78)(10) = kT
Divide both sides by k to get: (78)(10)/k = T
Simplify to get: T = 780/k

So, we have:
QUANTITY A: 8k/5
QUANTITY B:780/k

Let's TEST some possible values of k

Try k = 1
In this case, we get:
QUANTITY A: 8k/5 = (8)(1)/5 = 8/5
QUANTITY B:780/k = 780/1 = 780
In this case, QUANTITY B IS GREATER

Try k = 1000
In this case, we get:
QUANTITY A: 8k/5 = (8)(1000)/5 = some number greater than 1
QUANTITY B:780/k = 780/1000 = some number less than 1
In this case, QUANTITY A IS GREATER

Answer: D

Cheers,
Brent

The answer is D.
In the first case it becomes P=1.6k whereas in the second case it becomes 780/k.

Since we don't know k we can't determine the answer.

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