I need some clarification about Prime Boxes:

Can you combine prime boxes in any way (add/multiplication)? Also, when should you be on the lookout for REDUNDANT primes when checking for divisibility by two or more numbers? I see that nuance come up a few times in certain problems but just can't seem to understand it.

Thank you.

this is as good a post as any to talk about my Three Fundamental Rules of Prime Boxes (tm):

1) when you make a prime box for a variable, make sure to include a question mark (to remind yourself that no matter what they do tell you about the box, there could be additional information you don't know about)

2) never place more in a prime box than you absolutely need; you can guard against this by adding one number at a time, but only if you're sure you need it (this should answer your question about redundancy)

3) if you make a prime box for a product, you can split the box into separate compartments; for instance, xy's prime box will contain a section devoted to x and one to y (hopefully this answers your question about multiplication)

you should generally avoid trying to do anything resembling addition with prime boxes..

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Tim Sanders
Manhattan GMAT Instructor

Having viewed Ron's video on Prime Box and Tim's explanation above, I am still a bit puzzled on correctly inputting repeated primes of two integers into a PB. Perhaps, an example would better illustrate my question, and I hope you guys can help


If n is divisible by 40 and n is divisible by 20...

Primes of 40: 2, 2, 2 and 5
Primes of 20: 2, 2, and 5

Should the Prime Box contain:

2, 2, 2, 5, 5...?

OR

2, 2, 2, 5...?

Since I combined a total of four 2's from primes of 40 and 20 and only put two of them in the Prime Box, should I combine the 5 as well? Please help!

Ron's video on PB for those who haven't seen it:
Video I viewed: http://www.beatthegmat.com/mba/2010/06/ ... rime-boxes

Before receiving a reply with the correct answer, my educated guess would be that the prime box should include 2, 2, 2 and 5 PLUS ...?

Following Ron's analogy of "eye witnesses at a crime scene" when dealing with repeated primes, first eyewitness saw suspect "n" carrying three 2s and one 5. Second witness saw the SAME suspect carrying two 2's and one 5.

Given that both of them are telling the truth and describing the same suspect, there should be a total of three 2s and one 5.

Please advise if the above logic is what I should follow when dealing with similar questions in the future.

Here's an easy way to think about it. For every distinct prime integer in a prime box, have a contest. Count the number of each integer among the two numbers. Majority wins.

Let me use your example of n which is divisible by 40 and 20:
40=2*2*2*5
20=2*2*5

The first distinct integer is 2. Which number has the most 2s? 40 has three 2s. Thus, n has at least three 2s.

The other distinct integer is 5. Both numbers have one 5, so this one is a tie. Thus, n has at least one 5.

n's prime box must contain 2, 2, 2, 5 as factors, and it may have others. But we know that it definitely has these.

Let's look at another example. Let's say that n is divisible by 12, 27, 50, and 75.
12=2,2,3
27=3,3,3
50=2,5,5
75=3,5,5

2=12 has the most, two. There are at least two 2s that are prime factors of n.
3=27 has the most, three. There are at least three 3s that are prime factors of n.
5=50 and 75 tie with two. There are at least two 5s that are prime factors of n.

Thus, n's prime box must contain:
2,2,3,3,3,5,5 and it could contain other factors.

Hope this makes sense!

_________________
Jamie Nelson
ManhattanGMAT Instructor

Jack, correct! :-)

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Jamie Nelson
ManhattanGMAT Instructor

Thank you Jamie :)

Your explanation and tip on deciding how to select the correct #s for the Prime Boxes is very useful. Thanks again!

glad this discussion helped!

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Tim Sanders
Manhattan GMAT Instructor