I'm writing a public service exam soon and need some help on number series.

For example: 1, 2, 3, 4, X, what is X?

Now that's an easy and obvious one, but the test I'm going to do has some extremely difficult questions. How do I go about studying this? I've tried googling but haven't found an effective method? Any of you math people have a good idea of a way to learn how to identify and do these number series quickly?

infinitestory

United States4053 Posts

October 14 2011 05:20 GMT

http://oeis.org/

United States3249 Posts

October 14 2011 05:22 GMT

On October 14 2011 14:20 infinitestory wrote:
http://oeis.org/

Can this help me train for a closed-book test?

infinitestory

United States4053 Posts

October 14 2011 05:24 GMT

most likely not; it's very good at finding the formula behind integer sequences, and not much else

if you haven't already, you should learn to derive a polynomial sequence by finite differences

United States3249 Posts

October 14 2011 05:26 GMT

On October 14 2011 14:24 infinitestory wrote:
most likely not; it's very good at finding the formula behind integer sequences, and not much else

Yeah, it's definitely a beast for that. I need basically:

1) Some examples of integer sequences from medium to hard
2) How to solve them
3) Their solutions

I just need a thought process here. I can almost just go with steps 1 and 3 though, and work it out from there - I assume there a limited number of patterns that you can realistically give for a general public service test, and if I solve 100 or so of them before the test the ones on the best will fit somewhat closely to the ones I practiced.

Anyone have a bunch of medium to hard number sequences to solve and break down?

United States3249 Posts

October 14 2011 05:28 GMT

On October 14 2011 14:24 infinitestory wrote:
most likely not; it's very good at finding the formula behind integer sequences, and not much else

if you haven't already, you should learn to derive a polynomial sequence by finite differences

How do I do that? Also I just need to find the next number in the series, not find an expression that would generate the series.

There's also trick stuff like 1,5,2,6,X with X being 3 as it's basically 1,2,X and 5,6,Y basic +1 pattern being interspliced together.

super_sonic

Singapore5 Posts

October 14 2011 05:38 GMT

try learning some basic series, like arithmetic, geometric, Fibonacci. and check if they have something to do with what you are given. Alternatively, you may look for some patterns, like how fast a series is growing, let's say you have a series of 2,10,26,50,X, the differences between two consecutive members are 8, 16, 24, so it is natural to assume that the next is number is 32 plus previous one, 50. So the answer is 82. In fact, that series is (2*n+1)^2+1, for n = 0,1,2,3

Plexa

Aotearoa39261 Posts

October 14 2011 05:40 GMT

Well its hard to know what you define as medium to hard difficulty though

for instance what level would you consider 1 1 2 6 24 120 X to be?

btw these are sequences not series :3

whatthefat

United States918 Posts

October 14 2011 05:40 GMT

I would make sure you know the most commonly used sequences. Specifically:
1) Know your squares and cubes
2) Know the Fibonacci sequence
3) Know the triangular numbers
4) Also be aware of modular arithmetic. The example you gave:

There's also trick stuff like 1,5,2,6,X with X being 3 as it's basically 1,2,X and 5,6,Y basic +1 pattern being interspliced together.

is actually an arithmetic progression in mod 7 (1, 1+4=5, 5+4=2, 2+4=6, 6+4=3).

United States3249 Posts

October 14 2011 05:49 GMT

#10

On October 14 2011 14:40 Plexa wrote:
Well its hard to know what you define as medium to hard difficulty though

for instance what level would you consider 1 1 2 6 24 120 X to be?

btw these are sequences not series :3

Medium. Right in the middle.

Plexa

Aotearoa39261 Posts

October 14 2011 05:49 GMT

#11

Somehow I get the feeling modular arithmetic isn't covered in this!

United States3249 Posts

October 14 2011 05:50 GMT

#12

I basically don't have much time to spend on this either. Think 2-4 hours tops. I just need to get through the basic stuff, then I have to move on to studying the logic puzzles and some other basic math.

whatthefat

United States918 Posts

October 14 2011 05:53 GMT

#13

On October 14 2011 14:49 Plexa wrote:
Somehow I get the feeling modular arithmetic isn't covered in this!

Perhaps not! Although it can help with some puzzles, even if it isn't the necessary or intended way to solve the puzzle. I'm not sure what difficulty level this test is at though.

EDIT: In that case, definitely don't worry about modular arithmetic. I would just familiarize yourself with some well known types of number sequences.

United States3249 Posts

October 14 2011 05:54 GMT

#14

On October 14 2011 14:53 whatthefat wrote:

Show nested quote +

Perhaps not! Although it can help with some puzzles, even if it isn't the necessary or intended way to solve the puzzle. I'm not sure what difficulty level this test is at though.

Test spans all difficulties. Starts off really easy then goes up to insanely hard / impossible. I'll find my level of competence / skill, and want to use a few hours of studying to increase that while I can. I'm just not sure how exactly.

PlutoNZ

New Zealand410 Posts

October 14 2011 05:54 GMT

#15

On October 14 2011 14:40 Plexa wrote:
Well its hard to know what you define as medium to hard difficulty though

for instance what level would you consider 1 1 2 6 24 120 X to be?

btw these are sequences not series :3

The next value is 720.

You could read this page: http://www.purplemath.com/modules/nextnumb.htm

If you want more help, give me some examples of the problems you will be doing.

United States3249 Posts

October 14 2011 05:55 GMT

#16

Also guys, since this is a government exam, sample questions are not given. I did it last year and remember that in general it starts really easy and gets ridiculously hard, and you start to fail at some point. Besides that there is no knowledge of it and no way to find out.

Jonoman92

United States9110 Posts

October 14 2011 06:01 GMT

#17

Not sure how one would study for this. But the advice already posted sounds decent.

On October 14 2011 14:40 whatthefat wrote:
I would make sure you know the most commonly used sequences. Specifically:
1) Know your squares and cubes
2) Know the Fibonacci sequence
3) Know the triangular numbers
4) Also be aware of modular arithmetic. The example you gave:

Show nested quote +

is actually an arithmetic progression in mod 7 (1, 1+4=5, 5+4=2, 2+4=6, 6+4=3).

Nevermind, just got it upon thinking what the modulus operator did back in Java.

United States3249 Posts

October 14 2011 06:02 GMT

#18

On October 14 2011 14:54 SearingShadow wrote:

Show nested quote +

The next value is 720.

You could read this page: http://www.purplemath.com/modules/nextnumb.htm

If you want more help, give me some examples of the problems you will be doing.

Thanks!! This is what I was looking for. I'm going to go through it tomorrow and see where I can get. After that I'll have to find some pretty hard sequences and see if I can do them.

United States3249 Posts

October 14 2011 06:03 GMT

#19

On October 14 2011 15:01 Jonoman92 wrote:
Not sure how one would study for this. But the advice already posted sounds decent.

Show nested quote +

Hmm, could you explain that a bit more? I don't really see how from just 1,5,2,6,X it is clear that X=3 is next. Seems like there's insufficient information.

Yeah I guess it could be other stuff, but it was just as an example. I could rewrite it to 1,5,2,6,3,X and X = 7. It's just to show that sometimes there are very basic patterns (+1) but they are spliced together with another parallel sequence. There's also stuff like 1/2, 2/4, 3/8, 4/16, where it's adding +1 to the numerator and x2 for the denominator. If you were to rewrite that as a decimal it's hard/impossible to solve.

Shelke14

Canada6655 Posts

October 14 2011 07:06 GMT

#20

On October 14 2011 14:40 Plexa wrote:
Well its hard to know what you define as medium to hard difficulty though

for instance what level would you consider 1 1 2 6 24 120 X to be?

btw these are sequences not series :3

X= 720?

OH shit, I didn't see the guy answered it a few posts above mine sorry! lol