multiple, factors, x divisible by y

[didieravoaka]

Does anyone can give me all the rules related to multiples and factors of an integer. I'm particularly interested in knowing how to recognize hat a number is divisible by 2,3,5,7,...
I know that a number is divisible by 2 when it ends up by 2,4,6,8...
I know that a number is divisible by 3 when it ends up by 3,6,9...
"""""""""""""""""""""""""""""""""""""5 when it ends up by 5 and 0


If there are some other rules that I forgot, please let me know.

Marc.

[MartyMurray]

Any number that ends in an even number is divisible by 2. Remember that 0 is even.

A number that ends in 3, 6 or 9 is not definitely divisible by 3 though. Consider 13, 16 and 49.

To tell whether a number is divisible by 3, add the digits. If the sum of the digits is divisible by 3, the number is divisible by 3. Here's a surprising one, 111. The digits add up to 3. So 111 must be divisible by 3, and in fact 111 = 3 x 37.

You can do the same for 9. If a number is divisible by 9 the sum of the digits will be divisible by 9. Examples include 27, 36 and 108.

4 - Last two digits are divisible by 4, because 100 is divisible by 4. So you know that everything, 1000, 10,000 etc. to the left of 100 is divisible by 4. So just the last two digits matter.

5 - Any number ending in 0 or 5.

6 - Even number divisible by 3.

8 - Last three digits are divisible by 8.

10 - If ends in 0 is divisible by 10.

Those are all the ones that I use and I don't miss not having the others, and score Q51 no problem without them, though I sometimes wonder whether the ones for 7 and 11 would be helpful.

One thing about the GMAT is that the quant questions are designed to be answered without too much use of arcane math knowledge. So while knowing without having to think about it that, for example, a number that ends in 0 or 5 is divisible by 5 is maybe going to be helpful, memorizing less obvious divisibility rules probably won't make much difference.

Anyway, if you want more, here's a list.

https://www.mathsisfun.com/divisibility-rules.html

[didieravoaka]

Thanks Marty!

I wish I could score Q51 like you lol. If you have other materials or tips to have a high score on quantitative do not hesitate to let me know.

Thanks.
Marc.

[MartyMurray]

Here are a few tips for increasing your quant score.

It almost does not matter what you work on as long as you are working on something that will increase your score. So just keep finding aspects of GMAT quant at which you could be more effective and work on them one after the other.

That having been said, in working on practice questions, focusing on one topic at a time tends to work best. In doing that you give yourself opportunities to really hone your understanding of and skills in handling questions of each particular type.

Meanwhile, many points can be picked up by just being tricked less. I mean without learning one more math concept probably you could increase your score by seeing more clearly what's going on in, for instance, DS questions that use simple math in a tricky way. There are many questions that just use fractions or exponents to make you think, and people don't get them right even though obviously they totally understand the math.

For example, in a previous post you said that numbers that end in 3, 6 or 9 are divisible by 3. Figuring out that that is wrong does not require understanding complex math. It requires seeing the logic of the numbers.

So seeing logic is much of what you need to work on, and in your mind you need to develop a matrix of understanding more than you need to memorize. It's easy, for instance, to remember and apply a formula if you really understand what underlies that formula. In essence you are best off being able to recreate a formula because you understand so well how the formula works.

In any case, you can get a lot of mileage out of getting good at seeing more clearly, as to a large degree GMAT quant is a test of VISION.

Key to developing understanding, skill and vision can be playing the game a lot, by learning how to do things and applying what you learn repeatedly in a variety of scenarios. Just like anything else that you do, GMAT quant can become more natural the more you play it. Don't play haphazardly though. Be intense and tend to work slowly and carefully with a focus on truly understanding and on getting right answers to practice questions.

To save time, there are, in addition to divisibility rules, things you can get good at.

Get good at working with the dimensions of geometric shapes. You can save time by being good at getting from the area of a circle to its other dimensions and vice versa. You can save time by being good at getting from the area of an equilateral triangle to its height or to the length of its sides.

Learn to recognize these key Pythagorean triples, 3 - 4 - 5 and 5 - 12 - 13. Also be good at recognizing and working with 30 - 60 - 90 triangles.

Get good at figuring out the factors of numbers. A great exercise that you could do is to figure out the prime factors of each number from 2 to 100. Count by primes, 2, 3, 2 x 2, 5, 2 x 3, 7, 2 x 2 x 2, 3 x 3, and so on. Being good at finding all of the prime factors of any number can save you LOTS of time.

Know the squares of all the numbers from 1 - 20 or at least play with each of them once or twice so that if they show up on the test you can pretty quickly recognize them. I say definitely know the squares of all the numbers from 1 - 12, and know that 15 x 15 = 225 and that 25 x 25 = 625.

Be good at counting by 15's and 25's.

Another set of things to be good at recognizing is the special quadratics. If you can readily see those when they show up, you will be much more likely to quickly answer certain questions.

I have seen people who thought that they were "not good at math" develop and drive their quant scores up point by point. They just played the game and learned and got better, and people tend to realize that in a sense we are all math geniuses. We just need to tap into that and develop ourselves. So just remain determined, develop your vision and keep looking for ways to increase your score, and you can be sure that you will.

[didieravoaka]

Thank you very much Marty! Also, I think it's better for me to go over each of my previous tests and find weaknesses, then figure out ways to overcome those weaknesses. It's better to stop doing some tests for few days and get a good strategy to overcome quantitative problems as well as verbal problems. I will read and re-read your advice.

Thanks.
Marc.

[MartyMurray]

I think it's better for me to go over each of my previous tests and find weaknesses, then figure out ways to overcome those weaknesses.

Yes, that's a great idea. I am sure that you will get many ideas from those tests. Each weakness is an opportunity!!!

It's better to stop doing some tests for few days and get a good strategy to overcome quantitative problems as well as verbal problems.

I am going to take that further and suggest that you not take another test for at least a week, or ten days. Basically don't take another test until you have reason to believe that you are ready to do at least somewhat better on the next test than you did on the last. Then take a test and see how well what you have been doing has worked.

Test your mind and skills the way you would test a race car that you have been building and tweaking for maximum performance.

GMAT preparation is partly an exercise in project management. Make that score happen by managing the project well.

[didieravoaka]

Ok. But since I scheduled my test for March 16, what do you think I should do? Still waiting for a week before doing a practice test?

What do you suggest?

[MartyMurray]

Hmm. Maybe you have to make that call as you go along.

You might even be best off pushing that test date back a week or two.

If pushing it back does not seem to make sense, then, OK, maybe take another practice test after five or six days.

If I understand correctly and you have already taken many practice tests, it may even make sense to just do the quant and verbal sections of the next test that you take, as your time and energy are somewhat limited by the proximity of your test date. If you have been taking many complete tests, then likely you are already accustomed to the full test experience.

[[email protected]]

Hi didieravoaka,

Since your GMAT is in just 12 days, you shouldn't plan on taking more than 1-2 practice CATs during that time. If you want to push back your Test Date, then you'll have to pay the $50 rescheduling fee AND log-in to do so AT LEAST 7 full days in advance of your Test. Thus, you'll have to make that decision sometime soon.

I don't think that you've mentioned it in your posts, but what were your Quant and Verbal Scaled Scores on your last few CATs? I ask because you seem heavily focused on your Quant studies, but it might be that there are some easy points for you to pick up in the Verbal section.

GMAT assassins aren't born, they're made,
Rich

[didieravoaka]

Yes Marty I'm already accustomed to the full test experience as I have taken many full tests. I think I would go over GMAT PREP 3 and 4 sometime next week before the test date on March 16.

Rich, here are my recent scores:

Manhattan GMAT: 450 (quant 27,verb 26); 530 (quant35,verb28); 500 (quant 39;verb 20); 490(quant 29,verb 29); 420 (quant32,verb22); 460 (32,22)
Veritas: 470 (quant 33,verb 22); 450 (quant28,verb24); 410 (quant 25;verb 22); 330(quant 21,verb 16); 310 (quant17,verb 17); 430 (34,16); 420 (27,21)

Thanks guys!

[Matt@VeritasPrep]

By the way, one general purpose divisibility approach is to think of the number in chunks.

For instance, suppose I want to know if 1508 is divisible by 1300. I'll start by thinking of the closest multiple of 13 to 1508 that I know: in this case, that's 1300. Now I have

1508 = 1300 + 208

Working with the next chunk, I think of a multiple of 13 close to 208. How about 130?

1508 = 1300 + 130 + 78

Now I work with the last chunk: success! 78 = 13*6. So I really have

1508 = 13*100 + 13*10 + 13*6
1508 = 13*(100 + 10 + 6)
1508 = 13*116

As you can probably gather, this works for ANY integer you like, and helps in a pinch.