BTGmoderatorDC wrote:In the formula \(w = \frac{p}{\sqrt[t]{v}}\), integers p and t are positive constants. If w = 2 when v = 1 and if w = 1/2 when v = 64, then t =
(A) 1
(B) 2
(C) 3
(D) 4
(E) 16
OA C
Source: Official Guide
We can create the equations:
1/2 = p/(^t√64)
(^t√64)/2 = p
And
2 = p/(^t√1)
2(^t√1) = p
Substituting, we have:
(^t√64)/2 = 2(^t√1)
(^t√64) = 4(^t√1)
(^t√64)/(^t√1) = 4
(^t√64) = 4
Thus, t must be 3.
Alternate Solution:
First, we substitute w = 2 and v = 1 into the given equation to obtain:
2 = p / ^t√1
Since t is positive, we know that ^t√1 = 1 for any t. Thus, we have:
2 = p
Now, we substitute w = ½ and v = 64 and p = 2 into the given equation to obtain:
1/2 = 2 / ^t√64
1 = 4 / ^t√64
^t√64 = 4
Raising both sides to the t power, we have:
64 = 4^t
t = 3
Answer: C
