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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 \(x=\sqrt[3]{1}=1\).

Question : At the end of certain sections such as coordinate geometry there are suggested problems from the OG, my question is there an updated version for OG 13? The Math Book I downloaded only goes up to OG 12

Question : At the end of certain sections such as coordinate geometry there are suggested problems from the OG, my question is there an updated version for OG 13? The Math Book I downloaded only goes up to OG 12

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

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.

Please clarify the statement in GMAT math book: Pg 5 (factors), " If P is a prime number and P is a factor of (ab) then P is a factor of a or P is a factor of b."

It should be "P is a factor of a and/or P is a factor of b."

Please clarify the statement in GMAT math book: Pg 5 (factors), " If P is a prime number and P is a factor of (ab) then P is a factor of a or P is a factor of b."

It should be "P is a factor of a and/or P is a factor of b."

Hi, Valid question. But not necessarily what you say.

For example.

Let the prime number p=2, a=4 and b=3.

ab=12. and P=2 is a factor of ab.

Here p is factor of a not b.

same way if a=3 and b=4. the ab remains same=12. But P is factor of b not a.

In some cases, as you say it can be factor of both a and b. not always.

So it is better to write P is factor of a or P is factor of b.

Please clarify the statement in GMAT math book: Pg 5 (factors), " If P is a prime number and P is a factor of (ab) then P is a factor of a or P is a factor of b."

It should be "P is a factor of a and/or P is a factor of b."

Hi, Valid question. But not necessarily what you say.

For example.

Let the prime number p=2, a=4 and b=3.

ab=12. and P=2 is a factor of ab.

Here p is factor of a not b.

same way if a=3 and b=4. the ab remains same=12. But P is factor of b not a.

In some cases, as you say it can be factor of both a and b. not always.

So it is better to write P is factor of a or P is factor of b.

Hope it helps.

Thanks, you example helps the understanding. However, I feel that by writing "or" , you exclude the option that P may be a factor of both. So, I think mentioning "and/or" would be more clear, at least for me.

None the less. I have understood the concept. Thanks

thanks for the tips. i need to GMAT MATH BOOK.I will get my hands on one of the paper tests, the Barron’s practice tests I had were on the computer only and I did not have the corresponding book with the scale. I did a Veritas test and got a 520 (doing better in the verbal section). Is it reasonable to think I could get 600 or more on the GMAT with good preparation? Thanks

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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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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