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If (3k)^x = 1, what is the value of k ? (1) k> 0 (2) x is a positive

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If (3k)^x = 1, what is the value of k ? (1) k> 0 (2) x is a positive [#permalink] New post   19 Sep 2019, 21:25
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If \((3k)^x = 1\), what is the value of k ?

(1) k > 0

(2) x is a positive integer

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What does k equal if \((3k)^x=1\)?

(1) \(k>0\)

(2) x is a positive integer
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C
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Re: If (3k)^x = 1, what is the value of k ? (1) k> 0 (2) x is a positive [#permalink] New post   Updated on: 21 Sep 2019, 01:42
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if x not equal to 0 then k should be 1/3,-1/3 depends on x - odd/even
if x = 0 then k can be any value

(1) no use OF KNOWING ABOUT K, without x....insuff
(2) x is not 0 then k has to be +1/3 or -1/3...insuff

If K>0 AND x not equal to 0 then k has to be 1/3

SO OA:C

Originally posted by madgmat2019 on 19 Sep 2019, 21:36.
Last edited by madgmat2019 on 21 Sep 2019, 01:42, edited 1 time in total.
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Re: If (3k)^x = 1, what is the value of k ? (1) k> 0 (2) x is a positive [#permalink] New post   19 Sep 2019, 22:01
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If \((3k)^x\) = 1, what is the value of k ?

\((3k)^x\) = 1 =>after analysis, we can say that k=any value and x=0, e, only then the equation could be equal to 1

(1) k> 0
k could be any number from 1 to ∞. INSUFFICIENT!

(2) x is a positive
From our analysis, we know x has to be zero. Since we don't know anything about k, can't comment. INSUFFICIENT!

(1) + (2)
k> 0 and x is a positive
only when k=\(\frac{1}{3}\) and x=1 satisfies the equation \((3k)^x\) = 1. Hence, k=\(\frac{1}{3}\). SUFFICIENT!

IMO answer is option C
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Re: If (3k)^x = 1, what is the value of k ? (1) k> 0 (2) x is a positive [#permalink] New post   19 Sep 2019, 22:07
I would go with B
For (1) k>0, k can be any number, if x is zero.
For (2) x is positive integer, That means x must be 1. Hence, there is only one solution for K, which is 1/3.

Hence, option B
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Re: If (3k)^x = 1, what is the value of k ? (1) k> 0 (2) x is a positive [#permalink] New post   19 Sep 2019, 23:16
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We are to determine the value of k given that (3k)^x = 1

From statement 1, we are given that k>0
Clearly this is insufficient because when x=0, k has infinite possibilities as a value.

From 2, we know that is positive implying x>0. This is also insufficient because k can be either -1/3 or 1/3 as long as x is an even number.

1+2 however is sufficient. We are able to determine that k=1/3 in order to satisfy the given equation.

The answer is C.

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Re: If (3k)^x = 1, what is the value of k ? (1) k> 0 (2) x is a positive [#permalink] New post   19 Sep 2019, 23:23
A is sufficient but B is not sufficient. Because irrespective of the value of x positive or negative if k>0 then 3*1/3= 1

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Re: If (3k)^x = 1, what is the value of k ? (1) k> 0 (2) x is a positive [#permalink] New post   19 Sep 2019, 23:38
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if \((3k)^x\) = 1 what is the value of k?

STATEMENT (1)-- k > 0
if x = 0 k can be any value such as --2,3,4.....
if x = 1 k = \(\frac{1}{3}\)

from this statement, we can't find the definite value of k
hence, INSUFFICIENT

STATEMENT (2)-- x is a positive integer
if x = 1 then k = \(\frac{1}{3}\)
if x = 2 then k = \(\frac{-1}{3}\)
both satisfy the equation
so, we cant get definite value of k
INSUFFICIENT

combining both statements together
we know k>0 and x is a positive integer
only for k = \(\frac{1}{3}\)
\((3k)^x\) = 1 (x can be any positive integer value )
SUFFICIENT

C is the correct answer
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Re: If (3k)^x = 1, what is the value of k ? (1) k> 0 (2) x is a positive [#permalink] New post   20 Sep 2019, 00:40
If \((3k)^{x}\)=1, what is the value of k ?

Statement1: k > 0
Still no info about what x is.
--> If x=0, then k could be any positive number.
Insufficient

Statement2: x is a positive integer

-> If x=1, then \((3k)^{1}\)=1. --> k=\(\frac{1}{3}\)
-> if x=2, then \((3k)^{2}\)=1.--> (3k-1)(3k+1)=0 --> k=\(\frac{1}{3}\) or k=\(\frac{-1}{3}\)
Insufficient

Taken together 1&2,
k>0 and x is positive integer

--> If x=1, then \((3k)^{1}\)=1. --> k=\(\frac{1}{3}\)

-> if x=2, then \((3k)^{2}\)=1.--> (3k-1)(3k+1)=0 --> k=\(\frac{1}{3}\) or k=\(\frac{-1}{3}\)
(k>0) --> k=\(\frac{1}{3}\)

--> no matter of what positive integer x is, k must be equal to \(\frac{1}{3}\)
Sufficient

The answer is C.
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Re: If (3k)^x = 1, what is the value of k ? (1) k> 0 (2) x is a positive [#permalink] New post   20 Sep 2019, 01:17
If \((3k)^x = 1\), what is the value of k ?

For \((3k)^x = 1\) → x = 0 only Thus k can be either positive or negative.

(1) k > 0
For any value of k, \((3K)^x = 1\) where x = 0
INSUFFICIENT.

(2) x is a positive integer

Now, x > 1

For that \((3K)^x = 1 → k = \frac{1}{3}\) always.

SUFFICIENT.

Answer (B).
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Re: If (3k)^x = 1, what is the value of k ? (1) k> 0 (2) x is a positive [#permalink] New post   20 Sep 2019, 05:22
Quote:
If \((3k)^x=1\), what is the value of k ?

(1) k > 0
(2) x is a positive integer


\((3k)^x=1\)…
[1] \(x=0,… k=any\)
[2] \(x=any,… k=1/3\)
[3] \(x=even,… k=-1/3\)

(1) k > 0: k=(any,1/3) insufic.
(2) x is a positive integer: x=(even≠0,any≠0) and k=(-1/3,1/3) insufic.
(1&2) x=(any≠0) and k=1/3 sufic.

Answer (C)
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Re: If (3k)^x = 1, what is the value of k ? (1) k> 0 (2) x is a positive [#permalink] New post   20 Sep 2019, 12:06
Statement I
k > 0
k can have any positive value.
For k = 1/3 and x = can be have positive value--> meets the condition
For k = any positive value and x = 0 --> meets the condition

Not sufficient

Statement II
x is a positive.
For x to be positive and (3k)^x = 1, value of k must be 1/3

Hence sufficient.

Answer B
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Re: If (3k)^x = 1, what is the value of k ? (1) k> 0 (2) x is a positive [#permalink] New post   21 Sep 2019, 01:33
A difficult one indeed.

A alone doesn't say anything. As we need to find the value of k, and it only says that k is positive.

B alone isn't sufficient either. K can be 1/3 or -1/3(for X=1).

However when both of these stems are used together, we only have one option k=1/3.

Hence C.

The thing to remember here is that 0 is not considered as a positive integer.

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Re: If (3k)^x = 1, what is the value of k ? (1) k> 0 (2) x is a positive [#permalink] New post   21 Sep 2019, 19:25
Statement 1 is insufficient because k could take one of so many values

Statement 2 means K could be 1/3 or-1/3 so still insufficient.

Together we know k is positive so we can say k is 1/3.

ANswer is C
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Re: If (3k)^x = 1, what is the value of k ? (1) k> 0 (2) x is a positive [#permalink]
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