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EMPOWERgmat PS Forum Expert - Ask Me Anything about PS and Math

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EMPOWERgmat Instructor
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Re: EMPOWERgmat PS Forum Expert - Ask Me Anything about PS and Math  [#permalink]

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New post 09 Aug 2019, 20:24
Hi Nums99,

I've posted an explanation for this question here:

https://gmatclub.com/forum/the-product- ... l#p2334197

GMAT assassins aren't born, they're made,
Rich
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EMPOWERgmat PS Forum Expert - Ask Me Anything about PS and Math  [#permalink]

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New post 31 Aug 2019, 02:49
Hi EMPOWERgmatRichC

I am very confused about this one inequality concept even though it is very simple

when they say x^>9
does it mean -3<x<3
or does it mean -3<x>3
please help this concept misunderstanding is leading me to make silly mistakes in easy answers
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Re: EMPOWERgmat PS Forum Expert - Ask Me Anything about PS and Math  [#permalink]

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New post 31 Aug 2019, 14:48
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Hi Nums99,

When you're dealing with a 'squared term', it's likely that you are going to have more than one type of answer.

For example, if X^2 = 16.... then X can be +4 or -4.

In that same way, when you're dealing with a 'squared term' and an inequality, you will likely have more than one 'group' of numbers that fits the inequality.

For example if Y^2 > 9.... then Y can be any number that is GREATER than 3 OR any number that is LESS than -3.
so...
X > 3 or X < -3

Those are two separate groups of numbers though (one is positive numbers, the other is negative numbers), so you would not write that as one 'big' inequality; it's two separate inequalities.

GMAT assassins aren't born, they're made,
Rich
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Re: EMPOWERgmat PS Forum Expert - Ask Me Anything about PS and Math  [#permalink]

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New post 27 Sep 2019, 05:08
My problem Solving score has been consistently below the DS section. Hope to practice more!
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Re: EMPOWERgmat PS Forum Expert - Ask Me Anything about PS and Math  [#permalink]

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New post 27 Sep 2019, 11:20
Hi Jagwik,

From your message, it's not clear how long you have been studying - or how much lower your performance on PS questions has been relative to your performance on DS questions. Before I can offer you any advice for your studies, it would help if you could provide a bit more information on how you've been studying:

1) How long have you studied? How many hours do you typically study each week?
2) What study materials have you used so far?
3) On what dates did you take EACH of your CATs/mocks and how did you score on EACH (including the Quant and Verbal Scaled Scores for EACH)?

GMAT assassins aren't born, they're made,
Rich
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Re: EMPOWERgmat PS Forum Expert - Ask Me Anything about PS and Math  [#permalink]

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New post 25 Oct 2019, 19:11
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Hi Rich,

I was hoping why you can explain why the opposite of this statement doesn't hold true? "The number of unique prime factors in a number does not change when that number is raised to a positive integer exponent." How come the number of unique prime numbers will change when the number is raised to a negative integer exponent?

For example: 4 has 1 unique prime factor, 4^2 has 1 unique prime factors; but what about 4^(-2)? Doesn't this become (1/16), which means this has one unique factor of (1/2) raised to 4? So the number of unique prime factors would stay the same.
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Re: EMPOWERgmat PS Forum Expert - Ask Me Anything about PS and Math  [#permalink]

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New post 26 Oct 2019, 19:33
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Hi stanleyelnats,

Your general approach to this issue is perfect (TESTing VALUES can help to define rules and patterns that you might not immediately recognize), but you have to be clear on the definitions of the 'terms' that you're using.

When you raise an integer to a positive integer exponent, the number of UNIQUE prime factors does NOT change - since you're just multiplying a number by itself a certain number of times, you're not dealing with any 'new' prime numbers (it's just more of the same prime numbers that you already had.

For example

6^1 = 6... and its prime factors are 2 and 3
6^2 = (6)(6).... so its prime factors are still 2 and 3
6^3 = (6)(6)(6).... so its prime factors are still 2 and 3
Etc.

When raising a positive integer to a NEGATIVE integer exponent, you end up with a "fraction under a 1"... but fractions do NOT have prime factors (since they're fractions).

6^(-1) = 1/6.... this is not even an integer, so it has no factors, much less prime factors. Thus, going from "6" to "1/6", we went from 2 prime factors to 0 prime factors.

6^(-2) = 1/36... same issue here though - this is a fraction and it has no factors.

The number 1 is its own unique situation, since 1 has NO prime factors. No matter what power you raise 1 to, you still end up with 1 (so you're still dealing with 0 prime factors).

1^(-1) = 1/1 = 1
1^(-2) = 1/1^2 = 1/1 = 1
1^(-3) = 1/1^3 = 1/1 = 1
Etc.

GMAT assassins aren't born, they're made,
Rich
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Contact Rich at: Rich.C@empowergmat.com
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Re: EMPOWERgmat PS Forum Expert - Ask Me Anything about PS and Math   [#permalink] 26 Oct 2019, 19:33

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