GMAT Math Book

Second Post of converted files

Marcel

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.

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.

Answer: D.

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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Seventh Post of Converted files

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

9. Inequalities

• Theory
  Inequalities Made Easy!
  Inequalities: Tips and hints
  Arithmetic with Inequalities
  Wavy Line Method Application - Complex Algebraic Inequalities
  Solving Quadratic Inequalities: Graphic Approach
  Inequalities - Quadratic Inequalities
  Graphic approach to problems with inequalities
  Inequalities trick
  INEQUATIONS(Inequalities) Part 1
  INEQUATIONS(Inequalities) Part 2
  
  • Questions
    Inequality and absolute value questions from my collection
    DS Questions
    PS Questions

For more check Ultimate GMAT Quantitative Megathread

Thanks a ton, This helps a lot

Hi there,
Can anybody help with this:-
how many 3 digit no. are possible using the digit 0, 1, 4, 5, 7 & 9?

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.

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?

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.

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