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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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19 Sep 2019, 21:25
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Competition Mode Question If \((3k)^x = 1\), what is the value of k ? (1) k > 0 (2) x is a positive integer What does k equal if \((3k)^x=1\)?
(1) \(k>0\)
(2) x is 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
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Updated on: 21 Sep 2019, 01:42
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
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19 Sep 2019, 22:01
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
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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
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19 Sep 2019, 23:16
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
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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
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19 Sep 2019, 23:38
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
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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.> (3k1)(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.> (3k1)(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
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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
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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
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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
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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
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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 or1/3 so still insufficient.
Together we know k is positive so we can say k is 1/3.
ANswer is C




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