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

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

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New post 03 Oct 2018, 18:52
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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.

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

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New post 03 Oct 2018, 20:55
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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
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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
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New post 07 Oct 2018, 19:16
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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,
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New post 31 Oct 2018, 07:33
Hey Rich :) can you help with my question
https://gmatclub.com/forum/if-x-1-2x-1- ... l#p2162779
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New post 29 Dec 2018, 20:19
Hi Rich can you please help me with this?

https://gmatclub.com/forum/arithmetic-s ... l#p2199096
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Re: EMPOWERgmat PS Forum Expert - Ask Me Anything about PS and Math  [#permalink]

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New post 17 Mar 2019, 03:06
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Can you help me wit this question?

For every positive even integer n, the function h(n) is defined to be the product of all the even integers from 2 to n, inclusive. If p is the smallest prime factor of h(100) + 1, then p is

A. between 2 and 10
B. between 10 and 20
C. between 20 and 30
D. between 30 and 40
E. greater than 40
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Re: EMPOWERgmat PS Forum Expert - Ask Me Anything about PS and Math  [#permalink]

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New post 17 Mar 2019, 12:26
Hi sk0796,

There's a full discussion of this question here (my explanation is in the middle of page 2 and is reprinted below):

https://gmatclub.com/forum/for-every-po ... 21-20.html

For every positive even integer n, the function h(n) is defined to be the product of all the even integers from 2 to n, inclusive. If p is the smallest prime factor of H(100) + 1, then p is:

1. between 2 and 10
2. between 10 and 20
3. between 20 and 30
4. between 30 and 40
5. greater than 40

The main idea behind this prompt is:

"The ONLY number that will divide into X and (X+1) is 1."

In other words, NONE of the factors of X will be factors of X+1, EXCEPT for the number 1.

Here are some examples:
X = 2
X+1 = 3
Factors of 2: 1 and 2
Factors of 3: 1 and 3
ONLY the number 1 is a factor of both.

X = 9
X+1 = 10
Factors of 9: 1, 3 and 9
Factors of 10: 1, 2, 5 and 10
ONLY the number 1 is a factor of both.
Etc.

Since the H(100) is (100)(98)(96)....(4)(2)....we can deduce....
1) This product will have LOTS of different factors
2) NONE of those factors will divide into H(100) + 1.

H(100) contains all of the primes from 2 through 47, inclusive (the 47 can be "found" in the "94"), so NONE of those will be in H(100) + 1. We don't even have to calculate which prime factor is smallest in H(100) + 1; we know that it MUST be a prime greater than 47....and there's only one answer that fits.

Final Answer:

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 11 Jun 2019, 11:14
Need help to Solve the quant Question.

https://gmatclub.com/forum/geometry-297755.html
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New post 13 Jun 2019, 14:24
Two people run the circle with 10 rounds, one runs in the inside and the other runs in the outside. When the difference between the inside and the outside is 15 feet, what is the difference of between two people's distance after running 10 rounds, approximately?
A. 800 B. 850 C. 900 D. 950 E. 1,000
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Re: EMPOWERgmat PS Forum Expert - Ask Me Anything about PS and Math  [#permalink]

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New post 15 Jun 2019, 17:36
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Hi ajaysharma121,

What is the source of this question? I ask because it's poorly-worded and the questions on the Official GMAT would not be written in this way.

Based on the wording, I assume that both people are running around a circular 'track' (in different 'lanes'); we don't know the radius of either circle, but that's actually not an issue.

IF
...the radius of the circle is 16 feet - meaning that the lanes are 1 ft and 16 ft. from the center - then the difference in distance ran is (2)(16)pi - (2)(1)pi = 30pi feet per lap around the track.
...the radius of the circle is 17 feet - meaning that the lanes are 2 ft and 17 ft. from the center - then the difference in distance ran is (2)(17)pi - (2)(2)pi = 30pi feet per lap around the track.

Thus, the difference in the distances run per lap will ALWAYS be 30pi feet. With 10 laps run, the overall difference in the two distances traveled is (10)(30pi) = 300pi feet. = about (300)(3.14) = a little more than 942 feet. The closest answer is...



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New post 16 Jun 2019, 00:16
Hi EMPOWERgmatRichC, Can you please tell me most important quant topics I need to cover. I have a booked GMAT next week. I thought I was good at quant so I concentrated mostly on my verbal ability. Now my mock score is only 45. My target is 50/51. I am ready to put in 100 hours this week.Thanks!
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New post 16 Jun 2019, 15:12
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Hi GittinGud,

Based on the information in your prior posts, you've been studying for about 2.5 years at this point. In early January of this year, you appeared to be scoring Q48 and Q49, so I don't think that you would have 'lost' that ability over the last 6 months. With a Q45, you're likely missing out on a number of 'gettable' questions (meaning that you are not doing the necessary work to EARN those points). In that way, your focus during this last week before Test Day doesn't necessarily have to be on specific subjects - it should be on your 'processes' (the Tactics you use, the 'steps' you work through, your note-taking, etc.).

Beyond that, studying for 100 hours in 1 week is a TERRIBLE idea. By doing so, you would greatly increase your risk of 'burning out' before Test Day (and that is something that we want to avoid). In these last several days before your Exam, you would be better served spending your time on light practice and review; you would also find it beneficial to get some extra rest, so that you can go into Test Day calm, clear-headed and ready to work.

If you'd like to discuss your situation and studies in more detail, then I suggest that you send me a PM (as opposed to having a drawn-out discussion in this post-thread).

GMAT assassins aren't born, they're made,
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New post 24 Jun 2019, 10:48
A code is to be made by arranging 7 letters. Three of the letters used will be the letter A, two of the letters used will be the letter B, one of the letters used will be the letter C, and one of the letters used will be the letter D. If there is only one way to present each letter, how many different codes are possible?

Posted from my mobile device
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Re: EMPOWERgmat PS Forum Expert - Ask Me Anything about PS and Math  [#permalink]

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New post 24 Jun 2019, 16:28
Hi Hass,

I've posted an explanation to that question here:

https://gmatclub.com/forum/a-code-is-to ... l#p2299010

GMAT assassins aren't born, they're made,
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New post 30 Jun 2019, 20:12
HI EMPOWERgmatRichC

Can you pls help me with below problem...

https://gmatclub.com/forum/5-boys-and-5 ... l#p2298571
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New post 30 Jun 2019, 21:36
Hi NandishSS,

I've posted an explanation to that question here:

https://gmatclub.com/forum/5-boys-and-5 ... l#p2302141

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

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New post 11 Jul 2019, 10:10
Hi
Need your help in improving my speed and accuracy for DS questions specially from number properties, sets and combinations.
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New post 11 Jul 2019, 11:33
Hi vibhash,

I've responded to your post here:

https://gmatclub.com/forum/esr-evaluati ... l#p2311617

Once we have a bit more information about your studies and goals, I'll be happy to answer any questions you might have and analyze your ESR for you.

GMAT assassins aren't born, they're made,
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New post 09 Aug 2019, 06:04
Hi!

The product of 3 consecutive positive multiples of 4 must be divisible by each of the following EXCEPT:

A)16
B)36
C)48
D)128
E)192

The OA is B but i don't understand why exactly.
Arent all these numbers divisible by three consecutive multiples of 4
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Re: EMPOWERgmat PS Forum Expert - Ask Me Anything about PS and Math   [#permalink] 09 Aug 2019, 06:04

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