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# GMAT Math Book

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Intern
Joined: 21 Sep 2011
Posts: 2

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19 Dec 2012, 01:17
thank you very much, very handy and useful
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Joined: 02 Jun 2011
Posts: 44
Schools: MIT Sloan (LGO)

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15 Feb 2013, 23:15
Dear walker,

In page 89 there are some mistakes.

1. If the slope of a line is negative, the line WILL intersect quadrants II and IV. X and Y intersects of the line with negative slope have the same sign. Therefore if X and Y intersects are positive, the line intersects quadrant I; if negative, quadrant III.
2. If the slope of line is positive, line WILL intersect quadrants I and III. Y and X intersects of the line with positive slope have opposite signs. Therefore if X intersect is negative, line intersects the quadrant II too, if positive quadrant IV.
3. Every line (but the one crosses origin (0,0) OR parallel to X or Y axis OR X and Y axis themselves) crosses three quadrants. Only the line which crosses origin OR is parallel to either of axis crosses only two quadrants.
4. If a line is horizontal it has a slope of 0, is parallel to X-axis and crosses quadrant I and II if the Y intersect is positive OR quadrants III and IV, if the Y intersect is negative. Equation of such line is y=b, where b is y intersect.
5. If a line is vertical, the slope is not defined, line is parallel to Y-axis and crosses quadrant I and IV, if the X intersect is positive and quadrant II and III, if the X intersect is negative. Equation of such line is x=a, where a is x-intercept.

In addition, I would like to suggest some changes to the explanation of Lines in Coordinate Geometry (page 85). I think there are too many formulas and a systematic approach is not encouraged. For instance:

Page 85

I think using a b c on General Form is confusing. I would recommend to use A B C, such as:

$$Ax+By+C=0$$

The point intercept form is given right away, together with the slope and the y-intercept for the General Form, all using the same letters. I would change the whole explanation to something like:

From the General Form $$Ax+By+C=0$$,

$$By=-Ax-C$$

$$\frac{B}{B}y=\frac{-A}{B}x+\frac{-C}{B}$$

$$y=\frac{-A}{B}x+\frac{-C}{B}$$

Where $$\frac{-A}{B}$$ is the slope and $$\frac{-C}{B}$$ is the y-intercept. From here:

$$y=mx+b$$.

This is a much more intuitive approach and does not require to remember 3 formulas.

Page 86

Why give the formula of a line passing through two points? Following an intuitive approach, I would just:

1. Calculate slope from the line crossing the two given points.
2. Plug in the slope and one of the points in the general equation to get b. No formulas required.

Page 87

Again, another formula is given. Same approach as above can be used with (x,0) and (0,y).

Page 92

Another formula is given. Why not just use the same slope and the point?

Maybe all the formulas can be included at the end as an extra, but using most of them right away somewhat breaks the logic and just give a takeaway that does not ensure that the concept is correctly understood. I think it's much more powerful (and simple!) to use logic and know where everything is coming from.

That come to mind, the basic and most important are: Distance, Mid Point, General Form, Point-Intercept Form, Slope of a Line, Parallel lines = same slope, Perpendicular lines = negative reciprocal, Distance Line-Point.

Best Regards, and great job on this Math Book!
Intern
Joined: 06 Feb 2013
Posts: 42
Location: France
WE: Engineering (Other)

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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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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.

Attachments

STD.jpg [ 81.79 KiB | Viewed 4137 times ]

Intern
Joined: 06 Feb 2013
Posts: 42
Location: France
WE: Engineering (Other)

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20 Feb 2013, 10:38

I was discussing the second formula in which a new element is added: sigma' = sigma if |y-mu| = sigma.

I tried it with an example, a set containing four items: {1, 2, 3, 4}. The mean of this set is 2.5 and the standard deviation is (rounded) 1.118.

Add this standard deviation to the mean, giving: y = 2.5 + 1.118 = 2.618 and add this number to the set: {1, 2, 3, 4, 2.618}. The mean of this new set is 2.724, and the new standard deviation sigma' becomes 1.095.

The standard deviation sigma' of the new set is not equal to the standard deviation sigma of the first set, although |y-mu| = sigma.

Is there something wrong in my reasoning here?

Greetings
Manager
Joined: 12 Dec 2012
Posts: 156
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13 Apr 2013, 05:54
Page 58, bottom:
Where b is the length of the base, a and c the other sides; h is the length of the corresponding altitude; R is
the Radius of circumscribed circle; r is the radius of inscribed circle; P is the perimeter

The Perimeter of the triangle (a+b+c) or of the in-/circum-scribed circle (2*pi*r /*R)?
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13 Apr 2013, 06:42
This is new for me....will sneak peak. But must say great effort walker...I am just starting quant
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15 Sep 2013, 01:30
walker wrote:
GMAT MATH BOOK
Open GMAT Club project

Authors: bb, walker, Bunuel, shrouded1

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

6 topics of the book are included in GMAT ToolKit App (iPhone/iPod Touch)

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

- 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.

- 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

[Reveal] Spoiler: Images
Attachment:

Hi, I couldn't find anything on Mixture/Weighted average problems. Can we have something from that area to in this book?
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Joined: 02 Sep 2009
Posts: 39595

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15 Sep 2013, 03:53
1
KUDOS
Expert's post
shameekv wrote:
walker wrote:
GMAT MATH BOOK
Open GMAT Club project

Authors: bb, walker, Bunuel, shrouded1

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

6 topics of the book are included in GMAT ToolKit App (iPhone/iPod Touch)

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

- 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.

- 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

[Reveal] Spoiler: Images
Attachment:

Hi, I couldn't find anything on Mixture/Weighted average problems. Can we have something from that area to in this book?

Check here:

All DS Mixture Problems to practice: search.php?search_id=tag&tag_id=43
All PS Mixture Problems to practice: search.php?search_id=tag&tag_id=114

Hope it helps.
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29 Sep 2013, 22:56
Hi bb/Bunuel/walker,
Guys, for many chapters in the GC Math book, we don't have practice reference to OG 12(or any other edn.) problems unlike these chapters - Number Theory,Geometry, Coordinate Geometry...

So,do we have any immediate plan to include the same (re practice reference to OG problems) in those chapters (Standard deviation,Probability, Permutation & Combinations, Absolute value,Algebra,Remainders,Word problems-DST and Work-time relted, Overlapping Sets)?

These additions will enrich the book overall,I think.

Look forward to hear from you.
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27 Dec 2013, 05:24
Hello people, I found an error on page 4 of the book. Actually its not an error but there's a shorter way to do the same thing. For verifying whether a no. (say n ) is prime or not we just need to check whether n is divisible by any prime no. less than sqrt(n).

We dont have to check if n is divisible by all the positive integers less than sqrt(n).

If n is not divisible by any prime no. less than sqrt(n), then n is a prime no.

(lets say if a no. is divisible by 6 then it will be divisible by 2 and 3.)

To avoid any confusion : sqrt(n) means square root of n.
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27 Dec 2013, 20:55
hi all,

Please can we have practice questions from QG13 included in Math book? It will be very helpful. Thanks
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28 Dec 2013, 04:18
ankur1901 wrote:
hi all,

Please can we have practice questions from QG13 included in Math book? It will be very helpful. Thanks

Done. Added the following link there: - Official Guide for GMAT® Review, 13th Edition Quantitative Question Directory
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28 Dec 2013, 04:22
bagdbmba wrote:
Hi bb/Bunuel/walker,
Guys, for many chapters in the GC Math book, we don't have practice reference to OG 12(or any other edn.) problems unlike these chapters - Number Theory,Geometry, Coordinate Geometry...

So,do we have any immediate plan to include the same (re practice reference to OG problems) in those chapters (Standard deviation,Probability, Permutation & Combinations, Absolute value,Algebra,Remainders,Word problems-DST and Work-time relted, Overlapping Sets)?

These additions will enrich the book overall,I think.

Look forward to hear from you.

Bunuel - Do we have any update on this?

Thank you.
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14 Feb 2014, 03:47
Bunuel wrote:
ankur1901 wrote:
hi all,

Please can we have practice questions from QG13 included in Math book? It will be very helpful. Thanks

Done. Added the following link there: - Official Guide for GMAT® Review, 13th Edition Quantitative Question Directory

Hey Bunuel,

the link doesn't work for me here can you give an update?
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14 Feb 2014, 03:50
unceldolan wrote:
Bunuel wrote:
ankur1901 wrote:
hi all,

Please can we have practice questions from QG13 included in Math book? It will be very helpful. Thanks

Done. Added the following link there: - Official Guide for GMAT® Review, 13th Edition Quantitative Question Directory

Hey Bunuel,

the link doesn't work for me here can you give an update?

Official Guide for GMAT® Review, 13th Edition Quantitative Question Directory: the-official-guide-quantitative-question-directory-143450.html
The Official Guide For GMAT® Quantitative Review, 2ND Edition Directory: quantitative-review-2nd-edition-directory-164896.html
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14 Feb 2014, 04:33
Thanks for the links. Since there are different practice questions for the different topics in the math book, and they vary from one edition to the other, can you give me a heads up on how you chose the questions for the different topics? This morning I finished number theory and started doing the questions when I realized that they were for edition 12, so I just looked at the question # and figured if they would be fitting for the topic. If not, I randomly chose a question which I THOUGHT would be OK to practice what I learned in the topic. But since I'm no expert on seeing whether it's one topic or another, maybe you could help me here? Would appreciate it!

Thanks!
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04 Mar 2014, 00:42
Bunuel, Walker, Shrouded1, BB - hats off to you guys for writing this GMAT Quant book...you guys rock!
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09 Jun 2014, 02:49
Thanks for sharing with us great post.
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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.
Re: GMAT Math Book   [#permalink] 19 Jun 2014, 09:06

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