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In the formula w = p/v^(1/t), integers p and t are positive constants.

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Bunuel
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In the formula w = p/v^(1/t), integers p and t are positive constants. [#permalink] New post   29 Nov 2015, 11:19
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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

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C
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Re: In the formula w = p/v^(1/t), integers p and t are positive constants. [#permalink] New post   30 Sep 2020, 10:55
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Bunuel 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

PS30502.01

1. We are given \(w = \frac{p}{\sqrt[t]{v}}\)

2. Substituting \(v = 1\) and \(w = 2\) in \(w = \frac{p}{\sqrt[t]{v}}\) -> \(2 = \frac{p}{\sqrt[t]{1}}\) -> \(p = 2\)

3. Substituting \(p = 2\), \(v = 64\) and \(w = \frac{1}{2}\) in \(w = \frac{p}{\sqrt[t]{v}}\) -> \(\frac{1}{2} = \frac{2}{\sqrt[t]{64}}\) -> \(\frac{1}{2} = \frac{2}{2^{6/t}}\) -> \(2^{\frac{6}{t}} = 2^2\) -> \(\frac{6}{t} = 2\) -> \(t = 3\)

Ans C
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Re: In the formula w = p/v^(1/t), integers p and t are positive constants. [#permalink] New post   29 Nov 2015, 20:15
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We can rewrite the given formula as, p^t = (w^t * v)
w = 2 when v = 1 --> p^t = (2^t * 1) ----- (1)
w = 1/2 when v = 64 --> p^t = (1/2)^t * 64 --> (2^-t * 2^6) ---- (2)
Equating (1) and (2),
(2^t) = (2^-t * 2^6)
(2^2t) = 2^6
2t = 6 --> t = 3

Answer: C
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Re: In the formula w = p/v^(1/t), integers p and t are positive constants. [#permalink] New post   29 Nov 2015, 20:49
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Bunuel 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


lets see the equation first..

\(w = \frac{p}{\sqrt[t]{v}}\)....
1)w = 2 when v = 1 ..
substitute in the equation , we get p=2 irrespective of the value of 't' as the root is of 1..

2) substitue the value of p=2, since p is constant; w=1/2 and v=64...

we get t=3..
C
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Re: In the formula w = p/v^(1/t), integers p and t are positive constants. [#permalink] New post   24 Oct 2020, 06:36
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We're given: \(w = \frac{p}{\sqrt[t]{v}}\)

We're told w = 2 when v = 1 and w = 1/2 when v = 64.

Lets plug these numbers in:

\(2 = \frac{p}{\sqrt[t]{1}}\)

We know p must equal 2, as the root of 1 is 1.

Lets plug w = 1/2 in:

\(0.5 = \frac{2}{\sqrt[t]{64}}\)

To get 0.5, t must be 3.

Answer is C.
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Re: In the formula w = p/v^(1/t), integers p and t are positive constants. [#permalink] New post   01 Jun 2023, 02:53
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Re: In the formula w = p/v^(1/t), integers p and t are positive constants. [#permalink]
01 Jun 2023, 02:53
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