If k is divisible by 6 and 3k is not divisible by 5, is k di

Question

If k is divisible by 6 and 3k is not divisible by 5, is k divisible by 10?

Is this correct way to solve this ?

k can be any multiple of 6 except the one that end in 0. since 3k is not divisible by 5 ...thus k is also not divisible by 5 therefore k is not divible by 10 as well since 10 = 2*5....

Please explain in detail your solutions as well...

nammers · Answer

If k is not divisible by 5 we know that 5 is not in the prime box of k.
If k is divisible by 6, we know 2 and 3 are in the prime box of k.
For k to be divisible by 10 we need 5 and 2 to be in the prime box of 3k, but this is impossible as there is no 5 in the prime box of k alone.

Numbers that we can tell are in the prime box are 2,3,3 (the last 3 is from 3k)

Hope this helps

Spidy001 · Answer

k is divisible by 6 => 2 and 3 are factors of k.

3k is not divisible by 5 => k is not divisible by 5( as 3 is not divisible by 5).

For a number to divisible by 10 , it needs to have both 2 and 5 in it. 
In K as we only have 5 and no 2,it is not divisible by 10.

nammers · Answer

3k is NOT divisible by 5

Spidy001 · Answer

You are right . I read that as "3k is divisible by 5".

Spidy001 · Answer

the part highlighted in red is not correct. Just because there is a 3 in 3k, does not mean k should have another 3 because of that.

That being said ,We know that K is a multiple of 6.

if k = 6 , there is only 2 and 3 in the prime box.

if k =18 , there are 2,3,3 in the prime box.
 
 So depending upon what multiple of 6 we chose we may or may not an additional 3. So we can say 2,3 are there in the prime box for sure.

bholakc · Answer

Anybody! Can explain it better please?

fluke · Answer

k is divisible by 6:
Means: k has at least 2 prime factors, 2 & 3, one each. We can't say anything other than that about k.

3k is not divisible by 5:
Means: k does not have 5 as its prime factor. The multiplication by 3 doesn't hurt the inference in any way.

Using the two inferences above, we can definitely say k IS NOT divisible by 10, because an integer to be divisible by 10, it must have at least 2 and 5 as its factors.

So, it is a definite NO and thus sufficient.

jitbec · Answer

Clearly k is not divisible by 10 if it does not have prime factor of 5 and as 3k is not divisble by 10 ;so k is not having prime factor of 5

KarishmaB · Answer

Contrary to what I say in most of my posts, using Mathematical representation actually helps in divisibility questions!

Here are my thoughts:

'If k is divisible by 6', 
It means k = 6a (where 'a' is any integer)

'3k is not divisible by 5', 
It means 3k is actually 3*6a = 18a. 18a is not divisible by 5 means 'a' is not divisible by 5 (We can see that 18 is obviously not divisible by 5 either)

'Is k divisible by 10?'
Since 'a' is not divisible by 5, 6a cannot be divisible by 10 since there is no 5 there to make a 10.

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If k is divisible by 6 and 3k is not divisible by 5, is k di

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