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# If 3^r/(9^2*k^(-2)) = 25, what is r?

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Re: If 3^r/(9^2*k^(-2)) = 25, what is r? [#permalink]
sb0541 wrote:
Bunuel wrote:
If $$\frac{3^r}{9^2*k^{(-2)}} = 25$$, what is r?

(1) k = 5

(2) $$\frac{1}{k^{(-1)}} = k$$

$$3^r. k^2 = 3^4 . 5^2$$

From Statement 1: $$3^r. 5^2 = 3^4 . 5^2$$
$$3^r = 3^4$$ => r =4 . Sufficient

Statement 2 says . k = k . clearly Not sufficient

Got the same answer, am curious though. can we deduce that K = 5 based on the 3^r * k^2 = 3^4 * 5^2. Looks tempting, but would it be wrong to say r = 4 and k = 5 by just looking at the equation.
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Re: If 3^r/(9^2*k^(-2)) = 25, what is r? [#permalink]
jkolachi wrote:
sb0541 wrote:
Bunuel wrote:
If $$\frac{3^r}{9^2*k^{(-2)}} = 25$$, what is r?

(1) k = 5

(2) $$\frac{1}{k^{(-1)}} = k$$

$$3^r. k^2 = 3^4 . 5^2$$

From Statement 1: $$3^r. 5^2 = 3^4 . 5^2$$
$$3^r = 3^4$$ => r =4 . Sufficient

Statement 2 says . k = k . clearly Not sufficient

Got the same answer, am curious though. can we deduce that K = 5 based on the 3^r * k^2 = 3^4 * 5^2. Looks tempting, but would it be wrong to say r = 4 and k = 5 by just looking at the equation.

I am not sure if i fully understand your clarification .
This equation $$3^r. k^2 = 3^4 . 5^2$$ is derived based on the equation from the question.
Now we are moving to statement 1 to check whether we can get a single value of r .

From statement 1 . we will be able to get the value of r . So, this statement is sufficient .
k = 5 is provided in statement 1 and it is not deduced .

Statement 2 is not sufficient .
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Re: If 3^r/(9^2*k^(-2)) = 25, what is r? [#permalink]
Bunuel wrote:
If $$\frac{3^r}{9^2*k^{(-2)}} = 25$$, what is r?

(1) k = 5

(2) $$\frac{1}{k^{(-1)}} = k$$

We are given the following equation:

3^r/[9^2 x (k)^-2] = 25

We can multiply the entire equation by 9^2 x (k)^-2 and we have:

3^r = 25[9^2 x (k)^-2]

3^r = 25 x 81 x (1/k)^2

We need to determine a value for r.

Statement One Alone:

k = 5

We can substitute 5 for k in our given equation:

3^r = 25 x 81 x (1/5)^2

3^r = 25 x 81 x (1/25)

3^r = 81

r = 4

Statement one alone is sufficient to answer the question.

Statement Two Alone:

1/[(k)^-1] = k

We can multiply the entire equation by (k)^-1 and we have:

1 = k x (k)^-1

1 = k x 1/k

The equation above is true regardless what the value of k is so long as k is not 0. Since we cannot determine a value for k, statement two alone is not sufficient.