If k is a non-negative integer, and 6^k is a factor of 345,136

Question

If k is a non-negative integer, and  6^k  is a factor of 345,136 what is  6^k−k ?

A. −6
B. −1
C. 0
D. 1
E. 6

GMATinsight · Accepted Answer

Non-Negative Integers are { 0  , 1, 2, 3, 4, 5.... }

When a question uses term  Non-negative integer  then always suspect the role of 0

Given Number = 345,136 
6 = 2*3 i.e. for a number to be divisible by 6, it must be divisible by 2 as well as by 3

Divisibility test of 3 = Sum of the digits of the number must be divisible by 3 for a number to be divisible by 3

Sum of digits = 3+4+5+1+3+6 = 22  (i.e. Not divisible by 3)

i.e. 345,136 is NOT divisible by 6
For 345,136 to be divisible by  6^k , k must be 0 so that  6^k=1  which is factor of every number

i.e.  6^k - k = 6^0 - 0 = 1 - 0 = 1

ANswer: Option D

Bunuel · Answer

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sumitkrocks · Answer

The given number is not a multiple of 6 
For a number to be a multiple of 6, it has to be a multiple of 2 and 3 both.

Sum of the digits of the the given number = 22 i.e not a multiple of of 3

hence k =0 
and expression  6^k−k  = 1-0 = 1 
D is the answer IMO

kantapong · Answer

6^k is factor of 345136

Let's see if 345136 is divisible by 6 -> no
Hence k = 0 -> 6^k - k = 1 - 0 = 1 D

Sanya15 · Answer

since both 345 and 126 aren't divisible by 6, k=0 , therefore, answer is 1 
option- D

asishron29181 · Answer

6^k is a factor of 345,136 what is 6^k−k
Sum of all the digits of the number = 3+4+5+1+3+6 =22
Not divisible by 3

Clearly not div by 6
k = 0
6^k - k = 1 -0 = 1

IMO D

Sanya15 · Answer

Bunuel  -- pls clarify if 345,136 is a single number or 2 different numbers

Bunuel · Answer

_________________________
It's one number: 345,136.

HarshaBujji · Answer

As 345,136 is not divisible by 3, It's also not divisible by 6;

So the only value of k it is valid is k=0 which is 1;
 
IMO D

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If k is a non-negative integer, and 6^k is a factor of 345,136

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If k is a non-negative integer, and 6^k is a factor of 345,136

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