Stacy makes a good point that I want to reiterate. I tried very, very hard to fix my timing issues. If you read through my blogs, I mentioned timing in many posts, and I described the many ways I attempted to address the issue. However, I was not successful in completely overcoming my problem, but I was able to improve my timing on the hardest problems, which is still an improvement. My decision to focus on accuracy did not preclude a focus on timing.

During my GMAT CAT I still kept timing on my mind at all times, but instead of letting it be the deciding factor on every decision I made, I used my best judgement on each individual question. If I truly felt I could find the answer within the next 30 seconds with 90% confidence in my answer choice then I would use those 30 seconds; otherwise, I would just move on.

Throughout my prep, timing was the MAJOR focus. It was only after 10 weeks of study with a timing focus, and 3 days before my actual CAT, that I sat down and formulated a timing strategy for my CAT. Ultimately, I chose accuracy over timing, but that does not mean I didn't keep timing in mind. If you have a timing problem, I strongly advise working hard to overcome that problem instead of avoiding it. Even if you cannot finish all 37 problems, a focus on timing will help you think faster on the hardest problems so that instead of taking 5 minutes to solve it only takes 2.5 minutes. There were some problems on my GMAT that I definitely would not have been able to solve quickly had I stuck to my old ways of doing grunt work math.

Improvements in timing may not even be apparent when you are in fact improving. Say, for example, that before I started my timing focus I came across a very hard number properties question that involves picking numbers etc. And let's just assume this problem would have taken me 5 minutes to solve, but only 2.5 minutes after I've studied with a timing focus. That leaves me with 2.5 minutes gained from that very difficult math problem. Now, let's assume, I get another very hard math question and that one also takes me 5 minutes before timing focus, but 2.5 minutes after timing practice. That's a 5 minute difference. Now let's say that these two problems were questions 28 and 29 and the old me has 3 minutes left for the last 8 problems while the new me has 8 minutes. The faster me can spend an additional 5 minutes on solving two more very hard quant questions near the end of the exam, which solidifies/reinforces my score position, and guess on the last 6 while the old me could possibly finish 1 more question with limited confidence then guess on the last 7. Notice that in this scenario both versions of me would have to guess on the last 6 or 7, but the faster me answered 2 more very hard questions with a fairly good degree of confidence at the end of the exam, which helped to verify to the CAT algorithm that I really was a scorer in that range. Yet in both cases, I had to guess on the last 6 or 7!

Stacy put it very well when she suggested that my score perhaps could have been as high as 51 had I gotten to the last 6 or 7 problems. Which would you prefer? 49 or 51?

Thanks Stacy for your invaluable insight!
-Ashish

Anyways, I'm trying to get as many of my lessons learned onto this blog as possible before I forget now that I no longer have to study for the GMAT.

Today's topic: Picking Numbers in Quant

Picking numbers in quant has been a thorny subject for me. At first, I thought of it as a cheap way of doing problems so I tried to avoid it and instead focused on figuring out answers using critical thinking + math knowledge. In addition, I found picking numbers to be very, very time consuming. However, for the hardest quant problems, I found avoiding this strategy to be detrimental since such a large class of problems can be solved partially or entirely using the Picking Numbers strategy.

Once I realized how many problems could be worked out quickly with this strategy, I made a conscious effort to determine the most consistent way of picking numbers quickly - numbers that are relevant to the question at hand. Now, I concede that picking numbers can be a time waster - a very large time waster - but with practice it is very easy to narrow down the choices for number picking to a small subset of real numbers.

In particular, here are some general numbers to used based on the "description" given in the problem:

* x is a number or no info given on x: -2, -1/2, 0, 1/2, 2
* x is positive (not positive integer): 0, 1/2, 2
* x is an integer: -2, -1, 0, 1, 2
* x is a positive integer: 1, 2, 3, 4
* x is a non-negative interger: 0, 1, 2, 3, 4
* x is a non-positive integer: 0, -1, -2, -3

Note the difference among the last three - 0 is included in the last two because 0 is non-negative and non-positive. Also, you can just as easily substitute -1 and 1 for -2 and 2. Either set works, but it just depends on the problem. For example, with a square or square root problem, -1 and 1 are easier, but if the question deals with primes and/or evens then -2 and 2 are probably better.

If you do not wish to memorize the list above, you can memorize just the first one and reduce the range of valid values depending on the description. For example, if the question states that x is positive, you can start out with -2, -1/2, 0, 1/2, 2 then remove the first two numbers because they are negative. Or, if the question states that the number must be an integer, you can start with the above set and remove -1/2 and 1/2. This method is easier to remember and in some ways safer because you start with a baseline set and remove as necessary but since you start with the baseline set you'll still have all the ranges covered. In the last example, if you just tried to pick numbers ad hoc you may have missed the negative integers, but since you started with the baseline set, -2 was already included.

The big time waster in picking numbers is attempting to use this method without an organized attack plan (i.e. picking numbers randomly just to test a lot of numbers). So the lesson in this post is how I organized my number picking strategy to minimize the amount of time wasted. Now, to speed up calculations, you should pay particular attention to the constraints given by two things: 1) the question stem and 2) the given statements (on DS). First look at the question stem and determine how the constraints can affect the problem. Next, look at statements (1) and (2) on DS questions and use the information provided to further reduce the range of valid numbers. REMEMBER that any picked number must satisfy any and all constraints given by the question stem and DS statements.

In my preparation, I learned that the easiest way for me to organize the information was to build a table. The table consists of arithmetic expressions in the columns and picked numbers in the rows.

Here's an example

#154 OG11 DS:

Is x negative?
(1) (x^3) * (1 - x^2) < 0
(2) x^2 - 1 < 0

Do you remember this problem? Do you remember the crazy explanation given by the test writers where they concede, "The reasoning behind this conclusion can seem a bit complex." Well, I read this explanation and thought, "There's no damn way I'm going to be able to reason this out on the GMAT; I need another method." So I came up with MY own solution. This falls in line with my advice the other day about coming up with solutions that YOU can understand - not what the test writers say is the "correct" solution.

Okay, now the fun...

(1) (x^3) * (1 - x^2) < 0

My thinking process: Hmm. This is a bit complex. I know I can add/subtract numbers on either side of inequalities and there's definitely a subtraction there. Let's see what happens if I multiply the x cubed term:

x^3 - x^5 < 0

Oh wait, now I can move it over to the other side:

x^3 < x ^ 5

Hmm. What do I know about exponents? When can a base to an exponent of 3 be lower than a base with exponent 5? I think it has to be a fraction. What do I know about bases raised to odd exponents? Oh wait, the base must be negative if the expression is negative (e.g. x must be negative if x^3 is negative). But how do I combine that info? Well let's just pick numbers and see.

Hmmm what numbers should I use? The question stem says, "Is x negative?" and that tells me nothing because there are no restrictions on the value ranges so let's try my basic test cases: -2, -1/2, 0, 1/2, 2.

Okay time to build my table. What expressions do I need to test? x^3 and x^5.

_x____x^3__x^5
-2 ____-8____-32 (hey wait, let's fill out 2 also since it's almost the same)
-1/2
0
1/2
2_____ 8____32

Now, time to do a quick check. Okay, if x = -2, -8 > -32 and if x = 2, 8 < 32. But wait, the statement says x^3 < x^5 so x cannot be -2. Okay, cross out that row and continue:

_x____x^3___x^5
-------------------- (imagine the row crossed out)
-1/2__-1/8___-1/32 (hey, let's fill out x = 1/2 also!)
0
1/2___1/8____1/32
2_____ 8_____32

Okay, time to check. If x = -1/2, x^3 = -1/8, and x^5 = -1/32. Is -1/8 < -1/32? Yes (verify on the number line because this is tricky and someone not paying attention can say no if not careful). Now, I have two rows where x^3 < x^5, I can go back and check the value of x. If x = -1/2, it's negative, but if x = 2, it's positive. INSUFFICIENT. (All this took less than 1 minute since I'm very used to building these tables and comparing now). Notice I did not check 0 because I have no need to - I already know (1) is INSUFFICIENT.

(2) x^2 - 1 < 0

Add 1 to both sides and x^2 < 1. So build another table. Again, I do not know anything about x so start with the default values:

_X____X^2
-2_____4 (fill in x =2 now)
-1/2
0
1/2
2______4

Quick check: Is 4 < 1? No. Cross out both rows and continue:

_X____X^2
------------
-1/2___1/4
0
1/2____1/4
------------

Is 1/4 < 1? Yes for both x = -1/2 and 1/2. But wait, one is negative the other is positive. INSUFFICIENT.

Now, (1+2) can be confusing but we have both tables built already. Let's merge the columns of each table and eliminate rows again. But wait, we've already eliminated certain rows based on (1) and (2) so we don't even need to incude them!

_X___X^3____X^5___X^2
-------------------------------- (x = -2 eliminated from (1) and (2) above)
-1/2__-1/8____-1/32__1/4
_0____0_______0_____0
1/2___1/8_____1/32__1/4
-------------------------------- (x = 2 eliminated from (2) above)

So now we just need to compare these values. Look at 0 first since it's so easy. Eliminate that row because 0^2 is not less than 1 and x^3 is not less than x^5. So:

_X___X^3____X^5___X^2
-------------------------------- (x = -2 eliminated from (1) and (2) above)
-1/2__-1/8____-1/32__1/4
-------------------------------- (violates both 1 and 2)
1/2___1/8_____1/32__1/4
-------------------------------- (x = 2 eliminated from (2) above)

Look at these last two rows. We cannot eliminate based on (2) since both (-1/2)^2 and (1/2)^2 is less than 1. Evaluate using statement (1) then. We know -1/8 < -1/32 because we evaluated it above for stmt 1. So let's check 1/8 and 1/32: 1/8 > 1/32 so it violates (1)- ELIMINATE! Now we have:

_X___X^3____X^5___X^2
-------------------------------- (x = -2 eliminated from (1) and (2) above)
-1/2__-1/8____-1/32__1/4
-------------------------------- (violates both 1 and 2)
-------------------------------- (violates 1 above)
-------------------------------- (x = 2 eliminated from (2) above)

So now we have only one row left and indeed x is negative. SUFFICIENT. C.

Things to note:
(1) Use the constraints given in (1) and (2) to eliminate rows first then go back to the root question and see whether the statement holds true or not for the rows remaining.
(2) Sometimes the constraints given in (1) and (2) will not eliminate a row, BUT a constaint given in the question stem will. For example, the question stem notes, "if x is not equal y," then if you see a row where x = y you must eliminate that row. In other words, DON'T FORGET about question stem constraints.
(3) As soon as you fill in the value for a row, check it against the constraints and either leave the row in or cross it out.
(4) As soon as you find two rows with contradicting results, you know it is INSUFFICIENT if the question is a DS question. Stop there and do not fill out the rest of the table.

So you see this picked number + constraints + elimination table/process that I've created made the process of picking numbers extremely simple and easy. All I had to do was do some simple calculations, use some logic to eliminate, avoid doing extra work as soon as I found two numbers that gave contradicting results, and combine the tables together (since I reached phase 3 where I had to combine 1 and 2). But this process, when practiced methodically becomes second nature and is very easy to use. Now, do me a favor and open up the OG11 to the official explanation provided for this problem and read that explanation and compare it to what I have just shown you. Which is easier to understand? Which is faster to do? Which will you be able to utilize on the real GMAT? Which one can be used again and again and again on number picking questions?

Does anyone want more examples of the application of this technique? Please say so if you would like more examples of it being applied. I can think of at least one other OG11 problem that can be solved very quickly this way.

Good luck with this technique and you can thank me later. =)

Here are actual pictures from my error log so you can better visual the table handwritten out. My apologies for my terrible handwriting. In the last picture, you can see my lessons in blue ink. The first states that I should consider which strategy for attacking the question seems easiest (e.g. my table or the OG explanation) and the second states that I should stop testing values once I find two contradictory results.

meticulous! indeed! ( files are big though...)

By the way which one is in blue ink

And just noticed cute little kids in your avatar. May I know who are they?

aim-wsc wrote:meticulous! indeed! ( files are big though...)

By the way which one is in blue ink

And just noticed cute little kids in your avatar. May I know who are they?

That's just the cover of the Smashing Pumpkins Siamese Dream album.

Hello again,

I will be leaving for vacation this weekend for two weeks so you will probably not see much of me during that time. I'd like to present one small strategy that I used to help me on CR questions before I leave though.

Disclaimer: This technique is NOT meant to be used stand-alone; instead, it is meant to help you narrow your focus and isolate the good answer choices from the fluff that test writers add in to confuse you. This strategy is very useful for easy/medium level questions, but is harder to apply on hard questions because test writers often use the keywords themselves on hard questions to throw you off course! Use of this technique can increase your score if used wisely. Overuse of this technique can lead to very bad things especially on hard, hard CR.

Keyword/phrase search:

In my previous blog lessons learned on CR, I continuously mentioned the idea of using keywords to help eliminate answer choices and narrow your focus. In this lesson learned, I will show you how I apply this technique and how I used it to answer difficult questions for which I was unsure of the correct answer.

The idea is that you should search the stimulus and question stem for certain keywords. In particular, pay attention to things can that be tangential to those keywords in the answer choices as this usually signals an incorrect answer choice that is out of scope.

In the example question below, I have highlighted in bold the key words and phrases that I feel are the most important ones to focus on

#73 OG verbal review:

The cotton farms of Country Q became so productive that the market could not absorb all that they produced. Consequently, cotton prices fell. The government tried to boost cotton prices by offering farmers who took 25 percent of their cotton acreage out of production direct support payments up to a specified maximum per farm.

The government's program, if successful, will not be a net burden on the budget. Which of the following, if true, is the best basis for an explanation of how this could be so?

(A) Depressed cotton prices meant operating losses for cotton farms, and the government lost revenue from taxes on farm profits.

(B) Cotton production in several countries other than Q declined slightly the year that the support-payment program went into effect in Q.

(C) The first year that the support-payment program was in effect, cotton acreage in Q was 5 percent below its level in the base year for the program.

(D) The specified maximum per farm meant that for very large cottons farms the support payments were less per acre for those acres that were withdrawn from production than they were for smaller farms.

(E) Farmers who wished to qualify for support payments could not use the cotton acreage that was withdrawn from production to grow any other crop.

Okay, so let's take a look at the keywords that I found:
Stimulus - answer choices should have something to do with direct support payments, cotton prices and country Q.
Question stem - choices should have something to do with NET burden on the budget. What does "Net" anything usually involve?
(A) Choice includes info on losses, revenue, profits and cotton prices
(B) Choice talks about other countries
(C) Choice talks about the first year of the program
(D) Choice compares large and small farms
(E) Choice talks about qualification for the payments and also other crops.

How do you use these keywords to eliminate answers? Just do some thinking about the passage. The passage talks about direct support payments in general with no restrictions on size and not within a particular time frame. The question stem asks you to look for something that has to do with net burden and the budget.

Now let's go through the key words and phrases of the answer choices and eliminate those that have keywords that are tangential to the things I've just mentioned:
(A) losses, revenue and profits --> do these have to do with 'net' burden. sounds likely...keep it for now
(B) several other countries? nope passage only mentions Q. eliminate
(C) first year? does the passage have any keywords that restrict time period? nope. eliminate
(D) very large farms vs small farms? does the passage contain any keywords suggesting size restrictions? nope. eliminate
(E) qualifying for payments. other crops. does the passage mention anything about qualifications? nope. how about other crops? nope. eliminate.

So A is the only answer choice that appears to have keywords that relate to the keywords we found in the stimulus and question stem. A is the OA. When I did this practice problem, I was not sure what the answer was after reading the choices. I had eliminated 3 answer choices, but I was stuck on the last two. So I went to my last resort - keyword searching. I went through the passage quickly, scanned for keywords and compared the last two answer choices and chose A because it contained keywords that reflected the keywords found in the stimulus and question stem. I got it right. Note that there are only 83 CR questions in this book so this question is one of the harder ones.

So you can see this technique can be used to help eliminate answer choices and, when stuck between 2 or 3 choices, can help you decide amongst them which is the most likely to be the correct answer. If you would like to practice this technique, go through the easy CR questions found in CR. Scan them and look for keywords in the stimulus, question stem, and answer choices and try eliminating answer choices based on the keywords. Then make a best guess as to which is the correct answer and see if you got it right.

Cheers!

beatthegmat wrote:Thanks for this great post before your trip! We look forward to seeing you when you get back.

I'll definitely have a great trip after all this work.

Hello again,

This next blog post is another CR strategy. In CR, I believe the two most important things are:

1) Sorting out the premises from the conclusion. Being able to quickly separate these two elements is vital to working through CR questions quickly

2) Narrowing your focus to the specific (I mean very specific) topic covered by the stimulus.

Failing to do these two on a CR question can lead to selection of an answer that is out of scope or a tangent to the topic at hand or confusion over what the author is actually trying to get across.

My main method for addressing (2) was discussed in my last post, namely the keyword search technique. My method for dealing with (1) is a technique that I will call "the truthness technique" for lack of a better phrase (if someone finds a better name for it, please make a suggestion). Please keep in mind, that I have never read the MGMAT CR book or the LSAT CR book so I have no idea what kinds of techniques they provide in those books. It may very well be that my ideas are already published in these books - I really don't know. If they are, I am definitely not copying them and taking credit for them. These ideas that I've suggested in my blog are my own techniques that I practiced internally and instinctively as I practiced more and more.

Anyways, I'll begin by reminding everyone that a premise is any evidence that the author uses to support his claim. The important thing to remember is that the author will ALWAYS state a premise as a truth. Think about it, if you were arguing something, would you provide evidence in such a way that it seems disputable? No! Of course not, you would state it like it was absolute truth so no one can weaken your argument. And that is the key fact: premises will almost always be presented as TRUTH. If the author states something in such a way that it appears to be absolute truth, it is most likely a premise.

On the other hand, a conclusion made by the author is rarely ever stated as a given fact. Why? Because the author is ARGUING for his conclusion - there's no point for an author to argue a conclusion if it is absolute fact. For example, would someone argue, "The US gained independence in 1776?" No. We know that is a fact so that statement would more likely be used as a premise: "Since the US gained independence in 1776,..." And this is the other key fact: conclusions will almost never be discussed as TRUTH.

This is why I call this the "the truthness technique" - you can often figure out which statements are premises vs conclusions by determining whether the author presents them as truth or maybe/could be true.

Here is a problem that I answered on a post in the verbal CR forum:

https://www.beatthegmat.com/viewtopic.php?t=3246

Since no one returns from death, we can never be certain about what passes through the mind of the dying person. For the unconscious, the confused, and the heavily sedated, these final moments are probably meaningless. However, for the mentally alert, it is quite possible that death presents itself as an unbelievably glorious experience, a flight into an entirely new universe of sensation. Why should we think so? Some people who have been reprieved from “certain” death at the last moment have experienced what goes through the consciousness of those who are not so fortunate. For example, parachutists who have survived falls report experiences that resemble psychedelic “trips.”

The primary point of the argument in the passage is
(A) no one returns from death
(B) dying can be a glorious experience
(C) we can never know what passes through the mind of a dying person
(D) some people are reprieved from death at the last moment
(E) some people “die”, yet live to report their, experiences

First, I want to note that the keyword search technique is absolutely useless for this question. Each answer choice contains keywords found in the passage so throw that strategy out and look inside your verbal toolbox for other tools that can be used. My method to solve this was the truthness technique.

In the linked post above, I did not fully describe this technique so I will go into my detail here. You can follow the link to see my less detailed response.

The question is asking what the primary point, or conclusion, is.

(A) no one returns from death

"Since no one returns from death, we can never be certain about what passes through the mind of the dying person."
--> How does this statement read to you? How does the author present it? It is stated like it is truth - consider the "since no one" and the "we can never..." PREMISE! ELIMINATE.

(B) dying can be a glorious experience

"it is quite possible that death presents itself as an unbelievably glorious experience,"
--> this statement is not presented as absolute truth - consider the "it is quite possible"
--> since it is not presented as truth, it can plausibly be the conclusion

(C) we can never know what passes through the mind of a dying person

--> this is the second half of the statement shown the choice (A) which I've already classified as a premise. ELIMINATE.

(D) some people are reprieved from death at the last moment

" Some people who have been reprieved from “certain” death at the last moment have experienced what goes through the consciousness of those who are not so fortunate."
--> This also is presented as a truth because it is cited as a fact. People have survived certain death and have lived to tell their story - there is no debate about it. PREMISE! ELIMINATE.

(E) some people “die”, yet live to report their, experiences

--> This is just a restatement of the fact stated in (E), which I classified as a premise. ELIMINATE.

Okay, so A, C, D, and E were presented by the author as TRUTHS. The only statement that was not presented as a truth or fact was B so choose B. This question comes from CR 1000. The poster from the link above did not provide the OA, but I checked the document itself and B is indeed the OA.

The books out there often tell you to look for premise words like {for, since, because, etc etc} but sometimes the author states things in such a way that he does not need to use these words. How boring would an argument be if every other statement started with since or because? When no such keywords can be found, use my truth technique to figure out what is what in CR questions.

Thanks again for reading my blog! And good luck everyone! (time to go pack!)

It seems that people are not sure of my GMAT (Stacy referred to me in an earlier post by "s/he") so I just want to make it clear that I'm male. Oh and my name is Lee. So you don't have to write out Mayonnai5e all the time now.

Anonymous wrote:Your posts rock!

Thanks a lot!

I just want to clarify that I am not suggesting the truth technique over other methods of determining whether a statement is a premise or a conclusion. My idea is mainly useful if the statements are hard to classify because there are none of the usual keywords. If you notice, for choice A above, the related statement begins, "Since no one returns from death." The word since here clearly signals a premise so you really do not need to use my truth technique here. If there is an easier clue, use it! Just because you have a sophisticated tool does not mean you should use it for every case. As they say in software, KISS (keep it simple stupid).