Chapter 1 -- Divisibility and Primes Problem Set

[WriteCoreyMarsh]

Hello,

I've just come out of my first MGMAT class, and I feel overwhelmed and disheartened. I didn't understand much of anything the teacher spoke about. He put up a 300 level question, and I couldn't answer it. Then he put up a 700 level question, and it might as well have been a different language. I thought reading the strategy books would help, so as soon as I finished class, I spent 2 hours trying to get through chapter 1: divisibility and primes. The information appears to be straightforward, but then the problem sets are anything but. I went through the first few questions, and couldn't answer any of them. I stopped at question #6, which seemed to contradict the material just taught 2 pages earlier. Can someone please help me with this question:

"If J is divisible by 12 and 10, is j divisible by 24?" (The answer can be: Yes, No, Cannot be determined)

Now, the book spent most of this chapter hitting home the idea of prime boxes. The main example it used was 72, and this is how it broke that number down:

72-->12 x 6 --->2,2,2, 3, 3 (prime factors)

Now, for the question stated above, I think I'm supposed to break 12 and 10 down to prime factors, which would be:

12---> 2, 2, 3 10---> 2, 5

So the prime factors of J are 2, 2, 2, 3, 5, right? WRONG!!! I am utterly confused, because the answer says the prime factors include: 2, 2, 3, 5. What happened to the third "2"? Please explain and help me answer this question.

...Also, can anyone attest to feeling incredibly lost on the first day/first reading, but went on to score 700+? I don't have a full understanding of how the course is setup, but I'm guessing the teachers don't go through every single question in each strategy book, do they?

[tylrhllnbch]

You have to factor out the overlap - you can't just combine all of the prime factors.

Couple of ways to think about this:

First, try some numbers. If J is divisible by 12, what are some possible values for J? 12, 24, 36, 48, 60, 72, ...
If J is divisible by 10, what are some possible values for J? 10, 20, 30, 40, 50, 60, 72, ...

Now, if I'm going to use both statements, I can only take the overlapping possibilities: 60, 120, 180, etc.

Is 60 divisible by 24? No.
Is 120 divisible by 24? Yes.
So the info isn't sufficient.

Now, notice that my smallest possibility for J when looking at both statements was 60. What are the prime factors of 60? 2, 2, 3, 5. Hmm... that's what the answer said, too! How to understand what's going on theoretically so I don't have to list out a bunch of numbers?

Picture a small, one-room building. This building has two windows in it, on different sides of the building. You can't see in either window. Susie goes up to Window 1, looks in, and comes over to tell you that there are a 2, a 2, and a 3 inside that room. (2, 2, and 3 are the prime factors of 12).

So what do you know? There are a 2, a 2, and a 3 in that room.

Then Amy goes up to Window 2, looks in, and comes over to tell you that there are a 2 and a 5 inside that room (2 and 5 are the prime factors of 10).

So what do you know? There are a 2 and a 5 in that room.

Now think about what you definitely know based on the info from BOTH Susie and Amy. There's definitely a 3 in the room. There's also a 5. What about the 2's? Are there definitely three 2's in there? Or could Susie and Amy have been looking at the same 2? We know there are at least two 2's in the room, because Susie reported two separate 2's. But that one 2 that Amy saw - that could have been one of the 2's that Susie saw. So I don't know for sure that there is a 3rd 2 in the room - there might be, but I just don't know.

What's that amount to? 2, 2, 3, 5 - just like we figured out from trying numbers. In other words, each statement gives us true BUT potentially overlapping information - and we have to strip out the overlap when we combine the statements.

[rfernandez]

I'm sorry to hear that the first day was overwhelming! It can be hard to "reclaim" subject matter that you haven't seen or used in a long time, so if that's what's going on for you, know that you're not alone.

tylrhllnbch did a great job answering your content question. Does that make sense?

To answer your other question: there's too much new material to cover in class to make going over HW possible in class. You do have some resources available to you to this end, however:
- ask your instructor about specific questions before or after class or during a break.
- sign up for office hours (you get a free 30 minutes per week)
- use these forums as you did

Also, are you aware that we have a Foundations of Math course? Here's the write-up from our website:

This workshop is designed for students who have gone an extended period of time without being exposed to GMAT math concepts and/or students who score below 50th percentile on the Quantitative Section of practice exams. In addition, students who score above 50th percentile, but who take unsystematic approaches or make frequent careless mistakes, should also consider this program.

Check it out and if you're interested, call up Student Services with any questions.

[Guest]

Can you please explain how the explanation for Chapter 1, Question #5 from the Problem Set of Number Properties is different from the explanation provided under the sum and differnce are aslo divisible heading at page 14 (same chapter, same book).

5. If j is divisible by 12 and 10, is j divisible by 24?

adding them we got 22 and by sustracting them we got 2
prime box for 22 =2 x11
prime box for 2 =2 x1
according to explaination written on page page 16 j should also divisible by 22 and 2 .How is this possible plz explain.

You have to factor out the overlap - you can't just combine all of the prime factors.

Couple of ways to think about this:

First, try some numbers. If J is divisible by 12, what are some possible values for J? 12, 24, 36, 48, 60, 72, ...
If J is divisible by 10, what are some possible values for J? 10, 20, 30, 40, 50, 60, 72, ...

Now, if I'm going to use both statements, I can only take the overlapping possibilities: 60, 120, 180, etc.

Is 60 divisible by 24? No.
Is 120 divisible by 24? Yes.
So the info isn't sufficient.

Now, notice that my smallest possibility for J when looking at both statements was 60. What are the prime factors of 60? 2, 2, 3, 5. Hmm... that's what the answer said, too! How to understand what's going on theoretically so I don't have to list out a bunch of numbers?

Picture a small, one-room building. This building has two windows in it, on different sides of the building. You can't see in either window. Susie goes up to Window 1, looks in, and comes over to tell you that there are a 2, a 2, and a 3 inside that room. (2, 2, and 3 are the prime factors of 12).

So what do you know? There are a 2, a 2, and a 3 in that room.

Then Amy goes up to Window 2, looks in, and comes over to tell you that there are a 2 and a 5 inside that room (2 and 5 are the prime factors of 10).

So what do you know? There are a 2 and a 5 in that room.

Now think about what you definitely know based on the info from BOTH Susie and Amy. There's definitely a 3 in the room. There's also a 5. What about the 2's? Are there definitely three 2's in there? Or could Susie and Amy have been looking at the same 2? We know there are at least two 2's in the room, because Susie reported two separate 2's. But that one 2 that Amy saw - that could have been one of the 2's that Susie saw. So I don't know for sure that there is a 3rd 2 in the room - there might be, but I just don't know.

What's that amount to? 2, 2, 3, 5 - just like we figured out from trying numbers. In other words, each statement gives us true BUT potentially overlapping information - and we have to strip out the overlap when we combine the statements.

[Guest]

.
Can you please explain how the explanation for Chapter 1, Question #5 from the Problem Set of Number Properties is different from the explanation provided under the sum and differnce are aslo divisible heading at page 14 (same chapter, same book).

5. If j is divisible by 12 and 10, is j divisible by 24?

adding them we got 22 and by sustracting them we got 2
prime box for 22 =2 x11
prime box for 2 =2 x1
according to explaination written on page page 16 j should also divisible by 22 and 2 .How is this possible plz explain.

[esledge]

Looks like we have two threads with identical questions. Please try to avoid posting the same question in multiple places. Since there are other discussions in each thread, I will leave them as is, but for the answer to the last couple questions, please see the following.

http://www.manhattangmat.com/forums/hol ... t2210.html

[guest612]

i really improved my score with hard work and commitment. and i'm confident you can too. just stick with it and you will improve dramatically. it can seem overwhelming but just be diligent about it and you'll do well. no one can guarantee a specific score but if you're scoring below 500, i've heard and can understand how it's easier to improve from there even more than when scoring in the upper range. good luck!