Number Properties-Divisibility & Primes- Problem 10- Page 23

[rockrock]

Question: If k is divisible by 5 and 3k is not divisble by 5, then is K divisible by 10?

i would think the easiest way to think of this that since the prime factors of 10 are 2 and 5...the only way for 3k to be divisble by 10, is if it includes these two prime factors, which the question already tells us it doesn't include 5.

i thought the book explanation was a bit confusing...

[parthatayi]

is the question correct?
Because if k is divisible by 5
=> k = 5m
=> 3k =15m=5n which is divisible by 5.

[rockrock]

Sorry -the question was mistyped:
Question: If k is divisible by 6 and 3k is not divisble by 5, then is K divisible by 10?

The first part then (k is divisible by 6 doesn't seem to be relevant). The fact that you know 3k is not divisble by 5, and 5 is one of the prime factors of 10 should tell you that K is not divisible by 10.

Instead the explanation states- Since 5 is prime and 3 is not divisble by 5, we know that 3k is not divisible by 5. I don't quite get why 3 not being divisible by 5 is relevant?

[parthatayi]

Sorry -the question was mistyped:
Question: If k is divisible by 6 and 3k is not divisble by 5, then is K divisible by 10?

The first part then (k is divisible by 6 doesn't seem to be relevant). The fact that you know 3k is not divisble by 5, and 5 is one of the prime factors of 10 should tell you that K is not divisible by 10.

Instead the explanation states- Since 5 is prime and 3 is not divisble by 5, we know that 3k is not divisible by 5. I don't quite get why 3 not being divisible by 5 is relevant?

Yes you are correct.We can conclude with the second statement of the question.

[tim]

i answered this question in another thread:

number-properties-divisibility-primes-problem-4-page-23-t8167.html