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

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EMPOWERgmat Instructor
User avatar
V
Status: GMAT Assassin/Co-Founder
Affiliations: EMPOWERgmat
Joined: 19 Dec 2014
Posts: 12685
Location: United States (CA)
GMAT 1: 800 Q51 V49
GRE 1: Q170 V170
EMPOWERgmat PS Forum Expert - Ask Me Anything about PS and Math  [#permalink]

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New post 03 Oct 2018, 18:52
1
Ask me Anything about GMAT Quant and Math in General


Hello and welcome to my PS Forum Expert Topic. My name is Rich, and I am EMPOWERgmat Lead Expert. I have over 12,000 posts and 4,500 Kudos on GMAT Club, so I should be able to help you with a thing or two ;-) Let me know if you have any Problem Solving questions or perhaps strategy, specific ones, etc.

If you have any specific questions about PS or Math in general such as strategy, approach, etc, please feel free to post them here and I will be happy to address them. Also, feel free to post any PS Questions links with your specific comments and what you would like me to clarify about that particular question. I intend to have this thread be as a "Everything You Need to Know about PS" type of thread and will include some FAQ's over time.


Some of my topics you may find helpful:

https://gmatclub.com/forum/760-what-gma ... 37959.html - a series on breaking the 99th percentile and what it takes.

Thank you all - good luck on the GMAT and look forward to seeing you in the PS forum!
Rich.

_________________

760+: Learn What GMAT Assassins Do to Score at the Highest Levels
Contact Rich at: Rich.C@empowergmat.com

Rich Cohen

Co-Founder & GMAT Assassin

Special Offer: Save $75 + GMAT Club Tests Free
  Official GMAT Exam Packs + 70 Pt. Improvement Guarantee
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EMPOWERgmat Instructor
User avatar
V
Status: GMAT Assassin/Co-Founder
Affiliations: EMPOWERgmat
Joined: 19 Dec 2014
Posts: 12685
Location: United States (CA)
GMAT 1: 800 Q51 V49
GRE 1: Q170 V170
Re: EMPOWERgmat PS Forum Expert - Ask Me Anything about PS and Math  [#permalink]

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New post 03 Oct 2018, 20:55
2
Hi All,

Regardless of how you might feel about the Quant section of the GMAT, it's worth noting that the GMAT is NOT a ‘math test’ – it’s a ‘critical thinking test’ that uses math as the subject through which you can prove your critical thinking skills. While the Quant section does require that you complete lots of basic calculations as you work through it, the GMAT will NEVER require that you complete complex calculations to get to the correct answer… so if you CHOOSE to approach questions in that way, then you will likely limit how high you can score. If one of your goals is a Q51, then you would find it really helpful to build up a multitude of Quant skills, instead of focusing on complex, long-winded ‘math approaches’ that often take longer to implement than other more-strategic options (and inherently increase the chances of you making little mistakes along the way).

The GMAC Official Guide is a fantastic book of practice questions – and if you don’t have a copy, then you should absolutely purchase one for your studies. Consider the following question that appears in the Diagnostic Test of the GMAC Official Guide. It’s question #8 in the Problem Solving section of the Diagnostic – and has appeared in the last several versions of that book:

If a certain toy store’s revenue in November was 2/5 of its revenue in December and its revenue in January was ¼ of it’s revenue in November, then the store’s revenue in December was how many times the average (arithmetic mean) of its revenues in November and January?

1/4
1/2
2/3
2
4

Final Answer:

This is a fairly mid-level prompt; it’s a little wordy but the ‘math’ behind it isn’t too difficult. How would you approach it? Would you use algebra? Do you recognize that there are at least two OTHER ways to get to the correct answer (and one of those approaches requires almost no math…)?

Take a moment to answer this question in whatever way you choose. Write everything down and then compare your approach to the options listed below. Would one of the other options potentially have been faster or easier for you....?
.
.
.

1st Approach: Algebra

The explanations provided in the Official Guide often focus on the ‘math approach’ as that is that standard approach taken in most math books. However, that type of approach is often step-heavy and arguably takes the longest to complete.

For this prompt, we can create 3 variables:

N = revenue in November
D = revenue in December
J = revenue in January

With the information in the first half of the prompt, we can create two equations:

N = (2/5)(D)
J = (1/4)(N)

We’re then asked to calculate (D) / [(N+J)/2]

With the given equations, we can translate each variable ‘in terms of’ D and plug in… Again, this is tedious, step-heavy work, but here goes...

J = (1/4)(2/5)(D) = (2/20)(D) = (1/10)(D)

With the above values for N and J, we have the following fraction to simplify:

D / [(2D/5 + D/10)/2]
D / [(4D/10 + D/10)/2]
D / [(5D/10)/2]
D / (5D/20)
D / (D/4)
4D / D
4

2nd Approach: TESTing VALUES

Many questions in the Quant section can be solved with a Tactical approach (and part of your training should focus on learning those approaches and when certain Tactics are applicable). Here, we are given no actual values to work with, so we can choose our own.

Based on the fractions involved, the common denominator would be 20, so let’s start with D = 20…

IF….
D = 20 then
N = (2/5)(D) = 8
J = (1/4)(N) = 2

Now, we just have to place D = 20, N = 8 and J = 2 into the question….

(20) / [(8 + 2)/2] = (20) / (5) = 4

This IS the answer to the question - and you’ll get that same result regardless of the values that you choose to TEST (as long as your numbers ‘fit’ the given equations). This approach has the benefit of being fast and easy (consider the work involved - we’re really just adding and multiplying small numbers together). With fewer steps, you’re also less likely to make a little mistake along the way.

3rd Approach: Logic (and using the ‘spread’ of the answers to your advantage)

Certain questions in the Quant section are designed with really fast ‘concept shortcuts’ in mind. This is done on purpose to reward strong critical thinkers. Business Schools are looking for EXACTLY that type of critical-thinking applicant, but the GMAT has no way to give you extra points for ‘being clever’ – it can only provide you with potential shortcuts that will save you time and decrease whatever pacing-related anxiety that you might have. As a result of finding these shortcuts, your chances of scoring higher should increase, since you’ll have more time to answer the remaining questions than someone who is using lengthy math approaches and losing time as a result.

Here, consider how the given monthly revenues relate to one another….

1 - November’s revenue is 2/5 of December’s revenue. This means that the December revenue is MORE THAN DOUBLE November’s revenue.

2 – January’s revenue is ¼ of November’s revenue. Since January’s revenue is so much smaller than November’s revenue – and we already know that December’s revenue is MORE THAN DOUBLE November’s revenue, then this means that December’s revenue is a LOT greater (FAR MORE than double) than January’s revenue.

We’re asked to compare December’s revenue to the AVERAGE of November’s and January’s…. Averaging those two smaller numbers will lead to a result that is SMALLER than November's. By extension December’s revenue will be far GREATER than double than average. Looking at the answer choices, there’s only one answer that fits that description…. 4.

Now, consider how much actual work went into the 2nd and 3rd approaches to this prompt (especially relative to the work that went into the 1st approach). Assuming that you had an equal ability to tackle this question using all 3 approaches, which one would be fastest and easiest to implement? If you’re training to be a 760+ Assassin, then you know that it’s NOT the 1st approach.

GMAT Assassins aren’t born, they’re made,
Rich
_________________

760+: Learn What GMAT Assassins Do to Score at the Highest Levels
Contact Rich at: Rich.C@empowergmat.com

Rich Cohen

Co-Founder & GMAT Assassin

Special Offer: Save $75 + GMAT Club Tests Free
  Official GMAT Exam Packs + 70 Pt. Improvement Guarantee
www.empowergmat.com/

*****Select EMPOWERgmat Courses now include ALL 6 Official GMAC CATs!*****

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

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New post 07 Oct 2018, 08:04
EMPOWERgmatRichC wrote:
Ask me Anything about GMAT Quant and Math in General


Hello and welcome to my PS Forum Expert Topic. My name is Rich, and I am EMPOWERgmat Lead Expert. I have over 12,000 posts and 4,500 Kudos on GMAT Club, so I should be able to help you with a thing or two ;-) Let me know if you have any Problem Solving questions or perhaps strategy, specific ones, etc.

If you have any specific questions about PS or Math in general such as strategy, approach, etc, please feel free to post them here and I will be happy to address them. Also, feel free to post any PS Questions links with your specific comments and what you would like me to clarify about that particular question. I intend to have this thread be as a "Everything You Need to Know about PS" type of thread and will include some FAQ's over time.


Some of my topics you may find helpful:

https://gmatclub.com/forum/760-what-gma ... 37959.html - a series on breaking the 99th percentile and what it takes.

Thank you all - good luck on the GMAT and look forward to seeing you in the PS forum!
Rich.



Hey Rich, nice to e-meet you :) i am Dave:)

can you please give some tips/strategies/approaches on how to master techiques of solving 700 level PS questions ? :) it looks like I have started solving most 600-700 level questiions, but when it comes to 700 level questions i am stuck :) or does it all come down to practising more ?? :lol:

thank you,

D
EMPOWERgmat Instructor
User avatar
V
Status: GMAT Assassin/Co-Founder
Affiliations: EMPOWERgmat
Joined: 19 Dec 2014
Posts: 12685
Location: United States (CA)
GMAT 1: 800 Q51 V49
GRE 1: Q170 V170
Re: EMPOWERgmat PS Forum Expert - Ask Me Anything about PS and Math  [#permalink]

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New post 07 Oct 2018, 19:16
1
Hi Dave,

You're asking an incredibly broad question, but here are some things to keep in mind as you approach any type of Quant question (of any difficulty level).

1) NOTHING about a GMAT question is ever 'random' - the words are specifically chosen, the numbers of specifically chosen and even the 4 wrong answer choices are specifically chosen. Thus, you should be critical about everything you've been given. Each prompt was written by a human to test you on certain concepts. Thus, you have to think about which concepts are involved based on the design of the prompt - look for references to specific formulas, number properties and math rules. Sometimes the simple act of taking notes can help you to organize the information in a way that makes it easier to 'make a connection' and/or answer the question that is asked - so you should always take notes and do your work on the pad.

2) In the broader sense, almost all GMAT questions are 'critical thinking questions' that can be approached in more than one way. If "your way" of handling a question takes a long time and involves a lot of difficult 'steps', then you're likely missing out on a pattern, Tactic or design element that you can use to approach the question in an easier/faster way. Practicing those Tactics on easy/medium level questions will make it easier to do that same work on harder questions.

3) At higher-and-higher levels, the GMAT will test you on concepts that you know, but in ways that you are probably not used to thinking about. For example, you can probably FOIL and reverse-FOIL the following because you recognize the patterns involved.

X^2 - X - 6 = 0
(X-3)(X+2) = 0
X = 3 or -2

Would you recognize that same pattern if there were no numbers though....?
X^2 +XY - XZ - YZ = 0

Notice the "X^2"... isn't this just a Quadratic (it starts with a squared term and has 4 parts)? Can you factor it down into 2 pieces and solve for X?

4) Everything that you face on Test Day should remind you of work that you've already done, so having a reasonable memory is important and doing periodic review of your prior work is also a good idea (so that you don't forget any of the concepts that you've learned).

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

760+: Learn What GMAT Assassins Do to Score at the Highest Levels
Contact Rich at: Rich.C@empowergmat.com

Rich Cohen

Co-Founder & GMAT Assassin

Special Offer: Save $75 + GMAT Club Tests Free
  Official GMAT Exam Packs + 70 Pt. Improvement Guarantee
www.empowergmat.com/

*****Select EMPOWERgmat Courses now include ALL 6 Official GMAC CATs!*****

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Re: EMPOWERgmat PS Forum Expert - Ask Me Anything about PS and Math &nbs [#permalink] 07 Oct 2018, 19:16
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