Lesson 1: Fractions- Repeating decimal sequences upon division or con

Question

Here is my first post on topics that I am learning on the go through my practice of multiple questions and which you will generally not find in any of the GMAT courses (even the most extensive ones). I have been preparing for a year and have always taken every new concept that came my way as a new challenge and found it extremely intimidating to absorb it because even after hours of dedicated course prep, I did not know such things which are actually ESSENTIAL but still noone provides. I hope to keep posts like these coming so it becomes an extensive resource directory, however, given my personal limitations, there is only little I can be sure of circumstances but surely do keep me following along as it certainly is on my agenda for now.

Lesson 1: Fraction- Repeating decimal sequences upon division

First - We use the number that is repeating and the denominator has as many "9" digits as there are different digits in the block that repeats. e.g.
0.555555 = 5/9
0.13131313 = 13/99
0.432432432432 = 432/999
You can thus remember: If a fraction (in lowest terms) can be written as a repeating decimal and the number of decimal digits repeating is n, then the denominator must be a factor of 10^n - 1.

Second - If the sequence starts to repeat after some zeros, add the same number of zeros in the denominator. e.g.
0.005555 = 5/900
0.013131313 = 13/990
0.0004324324324...=432/999000=54/124875=2/46250.0004324324324...=432/999000=54/124875=2/4625

Third - Terminating decimals + Repeating Decimals. e.g.
2.31555555=2.31+0.00555555=231/100+5/9002.31555555=2.31+0.00555555=231/100+5/900
0.745454545=0.7+0.0454545=7/10+45/9900.745454545=0.7+0.0454545=7/10+45/990

Last one - The reciprocal of a prime number "p", except 2 and 5, has a repeating sequence of p-1 digits, or a factor of p-1 digits. e.g.
1/7=0.142857142857142857...1/7=0.142857142857142857... - As you can notice, the sequence has 6 digits = p-1 = 7-1 = 6 digits.
And if you multiply this fraction by a number you will only change the beginning of the sequence. e.g.
4/7=4∗1/7=0.57142857142857...

Borrowed content from- coelholds

Additional: You must know when the answers will be terminating or not.
1. Any integer divided by 2 or 5 or both (or their multiples) will always be a terminating decimal. Hence any number divided by 4, 8, or 10 will be a terminating decimal
2. Any integer divided by 9 will be a repeating decimal that will follow the repeating sequence mentioned in point 1 in the above section
3. Any integer divided by 3 and 7 will have a repeating sequence of 2 or 6 respectively, or factors of them (as per point 4 in above section)
4. 6 does not seem to have any defined pattern as 2/6=Repeating decimal with single-digit sequence and 3/6=0.5= Terminating decimal

Hope you liked this. Please do give me kudo so I know it helped you and gave you a useful strategy. It will also help me come up with more such posts.

Question to apply this strategy on: https://gmatclub.com/forum/if-each-of-t ... 59213.html

NarayanaGupta007 · Answer

Value of 1/9 is 0.11111.....you are manipulating this 
value of 1/11 is 0.09 ......we can learn this two two division in parallel 
if want to add new lesson add something really that not covered by extensive course....
1-if any no added to factorial is divisible by every no less than that factorial.
2-X/Y is less than something the anything added in both num and den is always less then that soemthing 
jusT for instance i added there are lot more

NarayanaGupta007 · Answer

Kids concepts (No offence)

Elite097 · Answer

That means you did not understand the post (no offence)

NarayanaGupta

Elite097 · Answer

This is a fairly easy lesson and to some it might seem rather obvious. However, note that the purpose of this post to tell about how to interpret slopes intuitively. On certain hard questions, we often do not recall the application of this method and this actually happens to save a lot of time rather than a long Math to solve these. However, if you are fairly advanced into your prep, please feel free to skip and the rest of you, hang on because this will come in handy if you really spend some time to think through what ensues,

Lesson 2: Interpreting the slope of a line intuitively

The concept of slope is extremely important on the GMAT – it is not sufficient to just know how to calculate it using (y2 – y1)/(x2 – x1).

In simple terms, the slope of a line specifies the units by which the y-coordinate changes and the direction in which it changes with each 1 unit increase in the x-coordinate. If the slope (m) is positive, the y-coordinate changes in the same direction as the x-coordinate. If m is negative, however, the y-coordinate changes in the opposite direction.

For example, if the slope of a line is 2, it means that every time the x-coordinate increases by 1 unit, the y-coordinate increases by 2 units. So if the point (3, 5) lies on a line with a slope of 2, the point (4, 7) will also lie on it. Here, when the x-coordinate increases from 3 to 4, the y-coordinate increases from 5 to 7 (by an increase of 2 units). Similarly, the point (2, 3) will also lie on this same line – if the x-coordinate decreases by 1 unit (from 3 to 2), the y-coordinate will decrease by 2 units (from 5 to 3). Since the slope is positive, the direction of change of the x-coordinate will be the same as the direction of change of the y-coordinate.

Now, if we have a line where the slope is -2 and the point (3, 5) lies on it, when the x-coordinate increases by 1 unit, the y-coordinate DECREASES by 2 units – the point (4, 3) will also lie on this line. Similarly, if the x-coordinate decreases by 1 unit, the y-coordinate will increase by 2 units. So, for example, the point (2, 7) will also lie on this line.

Summary: So here is the thing, when the slope is positive, y will always move in the same direction of x irrespective of whether x is moving downwards on the line or upward. Note that in our example, when x decreased by 1, y decreased by 2 but that does not mean that the line is negatively sloped so be aware of this. On the other hand, if the slope is negative when x decreases, y increases.

Link to previous post: https://gmatclub.com/forum/extra-quant- ... l#p3035798

Disclaimer: I am not an expert and an aspirant like you all who has been super focused on developing nuances behind the strategies used and also identifying ways to save some time which I often struggle with. Here is my attempt to document my learnings as I go through my journey so everyone can benefit from it. However, if you so happen to find anything fundamentally wrong or debatable, happy to consider that feedback and deep dive further. Usually however, these posts will be either be based on some validation or observation across questions. These posts are also usually aligned to topics that are not usually covered in most test prep materials so you can give a quick read to specific concepts and strategies before your exam.
PS: Pardon me as these might not be structured as I will be sharing my learnings as and when I interact with certain concepts.

ShwetaSingh1 · Answer

Seems that the post has been only created to ask for Kudos (one of the reason the post has been marketed in every possible group, including GMATClub chat, WhtsApp etc).

To be honest, the content is pretty basic and lame and has a huge scope of improvement. May be helpful for someone who is below 400, definitely useless for anyone who is targeting above 600.

No offense

bumpbot · Answer

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Lesson 1: Fractions- Repeating decimal sequences upon division or con

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