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

My problem Solving score has been consistently below the DS section. Hope to practice more!

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

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.

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

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?

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"

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

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?

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

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

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.

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

Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.