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# GMAT Math Book

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Concentration: Entrepreneurship, Other
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GMAT Math Book  [#permalink]

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Updated on: 25 Jan 2015, 09:14
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GMAT MATH BOOK
Open GMAT Club project

Authors: bb, walker, Bunuel, shrouded1

--------------------------------------------------------
Get The Official GMAT Club's App - GMAT TOOLKIT 2.
The only app you need to get 700+ score!

[iOS App] [Android App]

--------------------------------------------------------

- GMAT math diagnostic test

- Number theory
- Percents
- Absolute value
- Algebra
- Triangles
- Polygons
- Circles
- Coordinate geometry
- Standard Deviation
- Probability
- Combinatorics
- Sequences and Progressions
- 3-D Geometries

A downloadable PDF of the GMAT Club's Math Book is available here

Resources:

materials that are not currently included in the Math Book.

- Statistics Made Easy - All in One Topic! - Bunuel
- Collection of math-related links - timetrader
- Graphic approach to problems with inequalities - walker
- Everything about Factorials on the GMAT - Bunuel
- Compilation of tips and tricks to deal with remainders. - sriharimurthy
- Word Problems Made Easy - sriharimurthy
- 'Work' Word Problems Made Easy - sriharimurthy
- 'Distance/Speed/Time' Word Problems Made Easy - sriharimurthy
- Guide to series and sequences... arithmetic and geometric - benjiboo
- How to draw Venn diagrams - new!- whiplash2411

- Official Guide for GMAT® Review, 13th Edition Quantitative Question Directory

--------------------------------------------------------
Get The Official GMAT Club's App - GMAT TOOLKIT 2.
The only app you need to get 700+ score!

[iOS App] [Android App]

--------------------------------------------------------

Spoiler: :: Images
Attachment:

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Originally posted by walker on 29 Nov 2009, 14:56.
Last edited by walker on 25 Jan 2015, 09:14, edited 43 times in total.
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Concentration: Entrepreneurship, Other
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Re: GMAT Math Book  [#permalink]

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29 Nov 2009, 14:56
11
2
RULES FOR AUTHORS

Colors

- black/white/gray + green (#459926). Please, do not use any other color highlighting.

Images

- Maximum size: 290px*290px. Format: PNG. Transparent background.
- No long formulas. They are images in a final document and have to be not wider than 290px.

Attachments

Embed Attachments (Images) using img-tag with url
Code:

Attachments at the end of posts have to be hidden using spoiler-tag:
Code:
[spoiler=Images]................[/spoiler]

Structure and content

- Keep structure as simple as possible. Don't forget that the book will be also used for a mobile application.
- Avoid long blocks.
- Avoid redundancy in headers, text and structure.
- Use more "formal" language.
- Go from simple definitions to the hardest concepts.
- Weight of any concept in your post should be as close as possible to frequency of using this concept in GMAT.
- Use only own examples, don't copy-past problems.
- Don't forget about "Resources" list at the end of your post.
- Test your post in a simple way: Choose a random problem from your topic. Does your post help to solve this problem? How easy anyone can find related to the problem information?

Code:
[size=150][color=#459926][b]TITLE[/b][/color][/size]

.... {header information: author, editors and so on}

text + images

text + images

[b]Example #1[/b]
[b]Q[/b]:text
[b]Solution:[/b] text

[b]Example #2[/b]
[b]Q[/b]:text
[b]Solution:[/b] text

.....

[size=150][color=#459926][b]Resources[/b][/color][/size]

New topics

If you are going to create a new topic, please, include following information into Book's table of contents to avoid creating the same topic at the same time by different authors:

Code:
- [color=#999999][b]Standard Deviation[/b][/color] - [color=#999999][i]walker: next topic[/i][/color]

The name of a new topic should begin with "Math: " and be as short as possible.
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##### General Discussion
Intern
Joined: 06 Oct 2009
Posts: 9
Re: GMAT Math Book  [#permalink]

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21 Feb 2010, 20:29
2
1
Hello everybody,

This is my first post. I converted everything I could find in the GMAT math project and more into an ADOBE file to make it look sharper. All the information that you guys post is wonderful stuff and I just wanted to share these files I converted with everyone. I can do more later if anyone wishes.

Marcel
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Re: GMAT Math Book  [#permalink]

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21 Feb 2010, 20:32
4
4
Second Post of converted files

Marcel
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Re: GMAT Math Book  [#permalink]

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21 Feb 2010, 20:37
2
2
Third Post
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Re: GMAT Math Book  [#permalink]

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21 Feb 2010, 20:39
2
1
Fourth Post
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21 Feb 2010, 20:41
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1
Fifth Post
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21 Feb 2010, 20:43
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Sixth Post
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21 Feb 2010, 20:45
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Seventh Post of Converted files
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Re: GMAT Math Book  [#permalink]

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21 Feb 2010, 20:49
1
Last Post of GMAT Open Math Project

As a note I also converted the Verbal tips posted by the members and practice problems including the 3000 reading comp passages if any one would like those as well.

All the best,

Marcel
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Re: GMAT Math Book  [#permalink]

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30 Apr 2010, 12:25
Hi there,
Can anybody help with this:-
how many 3 digit no. are possible using the digit 0, 1, 4, 5, 7 & 9?
Math Expert
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Posts: 60727
Re: GMAT Math Book  [#permalink]

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30 Apr 2010, 14:57
1
1
sheetalsanjana wrote:
:-D Hi there,
Can anybody help with this:-
how many 3 digit no. are possible using the digit 0, 1, 4, 5, 7 & 9?

If repetition is allowed, then:
5(any digit out of 6, but 0)*6(any digit out of 6)*6(any digit out of 6)=180, we can not have 0 as the first digit, as in this case number won't any longer be 3-digit and becomes 2-digit.

If repetition is not allowed, then:

5(any digit out of 6, but 0)*5(any digit out of 6-first digit=5)*4(any digit out of 6-first&second digits=4)=100.
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Re: GMAT Math Book  [#permalink]

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20 Feb 2013, 02:38
Hello to all,

My first post on this forum.

I have a question about the formulas to add an element to a set on p103. Are they also valid for sets which contain a limited amount of numbers, for example a set consisting of four or five numbers? If you use the number two formula, and you add a number to a small set, the mean will change significantly. I think this formula is only valid for large sets in which the mean is more or less invariable when adding numbers?

I just tried it with a small set of numbers, and the formula didn't work.
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Re: GMAT Math Book  [#permalink]

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20 Feb 2013, 10:11
jorisboris, I am not sure if I understand you, but so far I think you are misunderstanding the formulas (are you referring to the formulas labeled as 1), 2), 3) and 4) in p103?)

Translated to words:

1) If the number you add to the set (y) is higher than the standard deviation (in formulas: if the distance from y to the median is higher than the distance of the standard deviation to the median, if y > STD) then the standard deviation of the set will increase (in formulas: the new standard deviation will be higher than the old standard deviation).

Or what is the same: new numbers added to the set will reduce the STD if they present less deviation than the STD (they are closer to the mean than the STD range), will increase the STD if they are further away from the mean than the range of the STD, will keep the STD the same if they are exactly as far away from the mean as the STD and will minimize as much as possible the STD if they are exactly equal to the mean (they add a deviation of 0, so the STD has the same total deviation, +0 is added) but more term to divide, thus decreases as much possible). Of course if you have 5 terms and you add a 6th term to the set that is exactly the same as the mean the STD will decrease much more than if you have 1000 terms with a huge STD and you just add one new element to the set. Still, the behavior will be the same, as these considerations are QUALITATIVE, not QUANTITATIVE.

Check my notes attached. In summary, these formulas only explain the behavior of the Standard Deviation based on the kind of number that you add to the set. Colors match, so line 1) refers to red point, line 2) refers to orange point, etc.

Does this solve your question?
Attachments

STD.jpg [ 81.79 KiB | Viewed 83131 times ]

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Re: GMAT Math Book  [#permalink]

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19 Jun 2014, 09:06
In the Math Book, page 26 , there is this problem : x^6 - 3x^3 + 2 = 0, then it states let y = x^3, then it goes to y^2 - 3y^3 + 2 (my first question is here, why is it 3y^3?, is it because y = x^3, so we are doubling?) next, this is factored to (y-2) (y-1) = 0 and the solutions are given as y = 1,2 (I understand this) or x^3 = 1,2 (I understand this) or x = 1, cube root 3 (this is where I am confused as to how there solns are found for x , and especially the cube root 3 i can't see where its coming from).
Thank you in advance for the assistance.
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Re: GMAT Math Book  [#permalink]

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19 Jun 2014, 09:19
sagnik242 wrote:
In the Math Book, page 26 , there is this problem : x^6 - 3x^3 + 2 = 0, then it states let y = x^3, then it goes to y^2 - 3y^3 + 2 (my first question is here, why is it 3y^3?, is it because y = x^3, so we are doubling?) next, this is factored to (y-2) (y-1) = 0 and the solutions are given as y = 1,2 (I understand this) or x^3 = 1,2 (I understand this) or x = 1, cube root 3 (this is where I am confused as to how there solns are found for x , and especially the cube root 3 i can't see where its coming from).
Thank you in advance for the assistance.

$$x^6 - 3x^3 + 2 = 0$$ --> $$(x^3)^2 - 3x^3 + 2 = 0$$. Let $$y=x^3$$ --> substitute x^3 with y : $$y^2 - 3y + 2 = 0$$ --> $$(y-2)(y-1)=0$$ --> $$y=2$$ or $$y=1$$.

If $$y=x^3=2$$, then $$x=\sqrt[3]{2}$$.
If $$y=x^3=1$$, then $$x=\sqrt[3]{1}=1$$.

Hope it's clear.
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Re: GMAT Math Book  [#permalink]

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29 Jun 2014, 17:48
Sorry, lazy on my part :

There is a set A of 19 integers with mean 4 and standard deviation of 3. Now we form a new set B by adding 2
more elements to the set A. What two elements will decrease the standard deviation the most?
A) 9 and 3
B) -3 and 3
C) 6 and 1
D) 4 and 5
E) 5 and 5
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Re: GMAT Math Book  [#permalink]

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30 Jun 2014, 03:13
1
3
sagnik2422 wrote:
Sorry, lazy on my part :

There is a set A of 19 integers with mean 4 and standard deviation of 3. Now we form a new set B by adding 2
more elements to the set A. What two elements will decrease the standard deviation the most?
A) 9 and 3
B) -3 and 3
C) 6 and 1
D) 4 and 5
E) 5 and 5

The standard deviation of a set shows how much variation there is from the mean, how widespread a given set is. So, a low standard deviation indicates that the data points tend to be very close to the mean, whereas high standard deviation indicates that the data are spread out over a large range of values.

So when we add numbers, which are far from the mean we are stretching the set making SD bigger and when we add numbers which are close to the mean we are shrinking the set making SD smaller.

According to the above adding two numbers which are closest to the mean will shrink the set most, thus decreasing SD by the greatest amount.

Closest to the mean are 4 (equals to the mean) and 5 (1 greater than the mean), thus adding them will shrink the set most, thus decreasing SD most.

Similar questions to practice:
a-certain-list-has-an-average-of-6-and-a-standard-deviation-97473.html
a-certain-list-of-200-test-scores-has-an-average-131448.html
a-certain-list-of-100-data-has-an-average-arithmetic-mean-87743.html
set-x-consists-of-100-numbers-the-average-arithmetic-mean-103536.html
set-a-consists-of-five-different-numbers-set-b-consists-of-155868.html
new-ds-set-150653-60.html
m03-72087.html
a-team-of-researchers-measured-each-of-ten-subjects-reactio-123873.html

Hope it helps.
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Re: GMAT Math Book  [#permalink]

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29 Oct 2014, 07:37
Hi Bunuel/Karishma,
In the GMAT Math Book (page #5), it says

• If $$a$$ is a factor of $$b$$ and $$b$$ is a factor of $$a$$, then $$a=b$$ or $$a=-b$$.

I can get it but it creates confusion when Veritas Arithmetic book (page # 20) says "Negative numbers are never factors.". So,where is the catch ?

P.S: I hope it's the right place to ask these questions. As I don't post much questions on Math forum so if this is not the right place please move it to the right forum.Thank you!
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Re: GMAT Math Book  [#permalink]

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21 Nov 2014, 05:06
bagdbmba wrote:
Hi Bunuel/Karishma,
In the GMAT Math Book (page #5), it says

• If $$a$$ is a factor of $$b$$ and $$b$$ is a factor of $$a$$, then $$a=b$$ or $$a=-b$$.

I can get it but it creates confusion when Veritas Arithmetic book (page # 20) says "Negative numbers are never factors.". So,where is the catch ?

P.S: I hope it's the right place to ask these questions. As I don't post much questions on Math forum so if this is not the right place please move it to the right forum.Thank you!

Yes, for the GMAT we consider only positive factors.
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Re: GMAT Math Book   [#permalink] 21 Nov 2014, 05:06

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