tmipanthers wrote:
Hi guys: This question is from the Number Properties book (5th ed) from Manhattan Guide. My answer is different from that stated in the solutions, so I am wondering if the book is incorrect.
So here is the question. I greatly appreciate the help as I'm about to smash my head into the wall. Thanks!
For questions #1-6, answer each question YES, NO, or CANNOT BE DETERMINED. If your answer
is CANNOT BE DETERMINED, use two numerical examples to show how the problem could
go either way. All variables in problems #1-6 are assumed to be integers.
4. If j is divisible by 12 and 10, is j divisible by 24?
Keep in mind that when you say a is divisible by b, it means 'b' is a factor of 'a'.
i.e. a = n*b
If b = 12, a can be 12/24/36/48/60.... etc
If j is divisible by 12, it means j has 12 as a factor (so j has at least two 2s and a 3 since 12 = 2*2*3).
If j is divisible by 10, it means j has 10 as a factor too (so j has at least one 2 - we already know that from above - and a 5).
So we know that j has at least two 2s, one 3 and one 5. To make 24, we need three 2s and one 3 (because 24 = 2*2*2*3). Do we know whether j has three 2s? No we don't.
j could be 2*2*2*3*5*7
it could be 2*2*3*5*7*11
or it could be 2*2*3*3*5*13
or many other things.
All we know is that it must have two 2s and one 3 and one 5. But this is not sufficient information.
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