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Need help on divisibility and primes

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Need help on divisibility and primes

by jscpba » Thu Dec 09, 2010 8:53 am
I took the GMATprep yesterday and scored 530. I need to get to at least 650. I completed the mgmat fundamentals of math guide prior to the CAT. I started on mgmat guide one, number properties, today and the divisibility and primes problem set is giving me fits. Does anyone have some tips to help this information sink in?

Question examples- (I have the explanations, but am struggling to figure out how to answer them before looking at the answers)

Given that 8 is not a factor of g, is 8 a factor of 2g?

If s is a multiple of 12 and t is a multiple of 12, is 7s+5t a multiple of 12?

If 80 is a factor of r, is 15 a factor of r?

Thanks guys!
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by roshnipat1610 » Thu Dec 09, 2010 9:50 am
Hi,

I will try and explain. I have not completed this lesson all the way through, so there might be a few points that I have not considered.

1. Given that 8 is NOT a factor of g, is 8 a factor of 2g ?

Ans: I dont think there is sufficient information to say for sure. It could be or it need not be.

You can simply plug in numbers:

For eg. if g = 15 , 2g = 30 - 8 is not a factor of g as well as 2g
if g = 12, 2g= 24 -8 is not a factor of g, but is a factor of 2g


2. s is a mulitple of 12 so can be written as s=12.x
similairly, t is a multiple of 12 and can be written as t=12.y

7s+5t = 7.12.x+5.12.y = 12(7x+5y) ...therefore is a multiple of 12

3. Prime factors of 80 are 2,2,2,2 and 5. Prime factors of 15 are 3, 5

Since they dont have enough factors in common, based on this information, 15 is not but we dont know if n has other factors that have 3 in its primes, so we cannot conclude.

Hope this helps
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by iridebikes » Thu Dec 09, 2010 10:27 pm
OK, so 8 is not a factor of g, is 8 a factor of 2g? We can't determine the answer because obviously, we don't know g. lets say g is 4, 8 is NOT a factor of 4, but 8 is a factor of 2g. So yeah this does work in this particular case but what if g were 2? In that case the answer is no.

If 80 is a factor of r, is 15 a factor of r?

In this case it really helps to create a prime box
80= 2,2,2,2,5
15= 3,5

There is the possibility that 15 is a factor of r. For example if r is 240, 15 is a factor of r. However if r is equal to 160, then r is not divisible by 15.

I should add, I too hated the divisibility and primes stuff. What you should do is go on the mgmat website, download the flashcards, and also make flashcards for each question you get wrong, and write down the explanation on the other side. This will help a ton. The questions in the end of the chapter do help a lot despite what some may say.
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