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

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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, 19:24
Hi Nums99,

I've posted an explanation for this question here:

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

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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, 01:49
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, 13:48
1
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.

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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, 04:08
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, 10:20
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)?

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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, 18:11
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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, 18:33
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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.

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

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New post 03 Mar 2020, 04:45
What would be the y-intercept of a vertical line that passes through the origin?
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Re: EMPOWERgmat PS Forum Expert - Ask Me Anything about PS and Math  [#permalink]

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New post 03 Mar 2020, 15:14
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Louis14 wrote:
What would be the y-intercept of a vertical line that passes through the origin?


Hi Louis14,

The Origin on a graph is the point (0,0) - and is a point on both the X-axis and the Y-axis. Thus, the Y-intercept of a line that passes through the Origin is Y = 0.

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

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New post 03 Mar 2020, 15:22
EMPOWERgmatRichC wrote:
Louis14 wrote:
What would be the y-intercept of a vertical line that passes through the origin?


Hi Louis14,

The Origin on a graph is the point (0,0) - and is a point on both the X-axis and the Y-axis. Thus, the Y-intercept of a line that passes through the Origin is Y = 0.

GMAT assassins aren't born, they're made,
Rich


But, correct me if I'm wrong, wouldn't it be true that the line would have already intersected the y axis before it crosses the the origin? Essentially then it should have a different y intercept than 0. No?
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Re: EMPOWERgmat PS Forum Expert - Ask Me Anything about PS and Math  [#permalink]

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New post 03 Mar 2020, 15:47
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Hi Louis14,

You might find it easier to think in terms of a real-world example:

Consider the line Y = 2X

What is the Y-intercept and what steps do you go through to find it...?

......

The Y-intercept is the point on a line in which X=0 (so plugging X=0 into the equation for your line is how you find the Y-intercept). For the Y-intercept of a line to be something OTHER than 0, there needs to be some additional number that is either added or subtracted. For example:

Y = 2X + 3 has a Y-intercept of "3"

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

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New post 06 Apr 2020, 12:22
Hi

Is there any particular method to approach DS questions. Some format or defined process. Difficult DS questions usually trap you in some of the cases that you miss to consider.

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

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New post 06 Apr 2020, 12:58
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zs2 wrote:
Hi

Is there any particular method to approach DS questions. Some format or defined process. Difficult DS questions usually trap you in some of the cases that you miss to consider.

Pls suggest.


Hi zs2,

DS questions are interesting because they're built to 'test' you on a variety of skills (far more than just your 'math' skills), including organization, accuracy, attention-to-detail, thoroughness and the ability to prove that your answer is correct. DS questions also have no 'safety net' - meaning that if you make a little mistake, then you will convince yourself that one of the wrong answers is correct. Thankfully, the 'math' behind most DS questions isn't that complicated, but you have to be thorough with your work and take advantage of any 'shortcuts' that are built into the prompt.

Almost every GMAT question that you face will be built around a pattern (and sometimes more than one!), so the 'steps' that you have to work through to answer any individual DS question will depend a bit on what information you're given and the specific question that you're asked. That having been said, there is a standard set of steps that you'll work through on every DS question that you face. From what you describe, I assume that you already know most of this, so do you have any specific DS prompts that you found challenging?

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

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New post 24 Apr 2020, 04:44
Hi Rich,

I have a really silly question about exponents. Since Xm * Xn = Xm+n
If we are given, 3n + 3n + 3n = 12
Can we write 3n+n+n = 12
Substitute it as n+n+n = 12
3n= 12
N= 4

Apparently the approach I have taken is wrong and the answer is 11. Could you please guide me on where I am going wrong!

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

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New post 24 Apr 2020, 12:17
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Hi taniasingh,

The Exponent rules that you will be expected to know for the GMAT are really about multiplication and division (although sometimes you will simply be asked to "rewrite" an exponent-based calculation).

When MULTIPLYING numbers that have the SAME base, you ADD the exponents. For example:

(3^2)(3^2) = 3^(2+2) = 3^4

You can actually prove that this is correct by doing the arithmetic....
(3^2)(3^2) =
(9)(9) = 81

3^4 = (3)(3)(3)(3) = 81

When dealing with variables, the same rules still apply....

(X^M)(X^N) = X^(M+N)

When you're ADDING identical numbers, you can almost always 'rewrite' that calculation. For example:

3^N + 3^N + 3^N =
3(3^N) =
(3^1)(3^N) =
3^(N+1)

The last part of your post is a bit unclear; if you are referring to a specific GMAT question, then can you provide a link to the original post? I would like to see the original prompt and the specific question that are trying to answer.

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Re: EMPOWERgmat PS Forum Expert - Ask Me Anything about PS and Math   [#permalink] 24 Apr 2020, 12:17

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