GRE: Understand Quantitative Comparison
Hello and welcome to this lesson where we`re going to be covering understanding quantitative comparison questions now remember as I mentioned the four quantitative comparison questions are very unique only to the GRE exam so if you`re not familiar with quantitative comparison questions this video is imperative for you to watch so the first thing we`re going to do is I`m going to go ahead and tell you some strategies on how to approach quantitative comparison questions what quantitative comparison questions look like and what are some strategies that you can use to perform well on these types of questions so the first thing I want to do is just to give you a brief example a quick example of what a quantitative comparison question looks like so over here you have some directions it reads use any provided centered information to help you compare quantity and quantity B select the answer that describes the relationship between the two quantities now notice in this case we do not have any centered information just because you have a quantitative comparison question does not mean that they will provide you with centered information sometimes they do sometimes they don`t if they do you must go ahead and use that to your advantage because more because that`s going to help you figure out the values of quantity a and quantity B so I`m not even going to read this question because right now the main thing is what can you do to prepare for these types of questions the first thing you need to do is this over here memorize these answer choices it`s not difficult it should take you less than one minute to memorize it`s very simple but you should memorize it because this answer choice order is always the same in all types of quantitative comparison questions where answer choice a is always that quantity a is greater what does that mean well that means that the value of quantity a is always greater than the value of quantity B notice I use the word always and we`ll talk more about that later on answer choice B States quantity B is meaning that quantity be over here and you don`t have to read this but whatever the case is quantity be here is always greater than quantity a and you would select B is your answer choice and moving on to answer choice C the two quantities are equal obviously that means that the quantity a is equal to quantity B and finally answer choice D always reads that the relationship cannot be determined from the information given so here`s a scenario where quantity 8 sometimes so in some cases you have that quantity a is greater than quantity B sometimes you have that quantity B is greater than quantity a and sometimes you simply can`t figure out one of the quantities because there`s not simply enough information provided and therefore you cannot determine the relationship between them so these answer choices this is a first step for you on succeeding on this quantitative comparison type questions you should memorize these answer choices you should automatically know what answers a B C and D is because in your test day time is crucial right you don`t want to waste any you don`t want to waste even five it`s five or ten seconds because you may really need those ten seconds to answer your last question on the GRE math section so that is the first thing.
So let`s move on to the next slide okay here are some very important notes over here quantitative comparison questions usually take less time than problem solving questions that should be a good thing some students love quantitative comparison questions some students prefer problem solving type questions I personally do really really like quantity of comparison questions I do think once you practice them enough that they are they are usually they can usually be done within 60 seconds and it shouldn`t really take you more than two minutes ever even if it`s hard question so moving on to the second bullet point there are roughly 15 total quantitative comparison questions right at sometimes it`s 15 sometimes it`s 16 basically it`s is it`s somewhere that range so 15 total quantitative comparison questions which accounts for 38% of all math questions what does that mean it means that it`s imperative that you understand these questions why because 38% is more than 1/3 of your math score if you`re just going in to take the GRE exam and you don`t know quantitative comparison questions and how to approach them well you are you are putting yourself at great risk because these questions account for more than 1/3 of your grade so this is very very important and lastly the ETS the official test creators of the GRE exam is not interested whether or not you can perform lengthy and tedious calculations what do I mean by that well if a question looks like it is cumbersome in calculation so there`s a lot of calculations going on that means that there is more than often a shortcut or a logical jump and I`ll clarify what I mean by illogical jumped later on in the video that simplifies a question so if you`re working on a question and you keep your computing computing computing adding here subtracting they`re dividing and it`s just crazy 99% of the time you`re doing something wrong the GRE is not interested whether or not you know how to do a multi-step problem by doing you know are all these different arithmetics instead they care more about your logic right how can do you know how to use a logic to simplify the question and I`ll show you a good example of that just later on so here are some bullet points let`s go ahead and actually move on to some example questions in this video I have three examples of quantitative comparison questions.
The first one is a easy one we`re going to start off with a simple question so this is actually the same question that I used just two slides ago so I have here quantity a the area of a circle with a perimeter of 4 pi and you have to compare that to the area of a square with a perimeter of 4 pi so this one is straightforward you can just go ahead and do the calculations because it`s given to you and it`s not so complex it doesn`t require much time so here what do we have to under the area of a circle with a perimeter of 4pi well the perimeter of a circle is the same exact thing as circumference so that`s the first thing you have to understand that the perimeter of a circle is the equivalent of the circumference of a circle and the circumference of a circle is defined as 2 pi r or pi times the diameter either or and now you`re given that the perimeter is 4 pi so I already know the value of CC in this case is 4 pi and I can set that equal to the formula 2 pi R and why am i doing that well and why did I not use pi times D the diameter for the circumference I could have done that as well right well I didn`t do that because take a look at this the quantity a states that the area of a circle eventually I want to find out the area of the circle and the area of the circle is PI R square notice my variable is R the radius and therefore it I shouldn`t even waste my time with figuring out what the diameter is right even if I figure out the diameter then I have to have then I have to take half of that number why go through the trouble when I can just set it up in one shot so now I have this over here 4 pi is equal to 2 PI R and I`m going to solve for R the radius by dividing both sides by 2 pi the new two PI`s cancels out I`m left with the radius is equal to 4 pi divided by 2 pi and 4 pi divided by 2 pi is just 2 so the radius in this case is 2 and now I can plug that right back in to the area of my circle so the area is equal to PI times the radius which is 2 to the second power 2 to the second power is 4 times pi so the area of this circle is 4 pi so the area is equal to 4 pi I`m going to box my answer and now I`m going to move on to quantity B quantity B over here states the area of a square with a perimeter of 4 pi notice we are dealing with a square a square has some unique properties all the all the lengths are the same so are the angles now if the perimeter of a square is four pi so P is equal to 4 pi what does that mean in order to figure out just one side of the square I have to divide that by 4 since all my sides are equivalent so I can divide that by 4 and what do I have the perimeter is equal to 4 PI over 4 this 4 over 4 cancels out and I`m just left with PI meaning that each of my sides have a measurement of pi and of course you can verify your work very quickly because pi plus PI plus PI plus PI is 4 PI which indeed is the perimeter.
My ultimate goal here is to find the area of the square and the area of this area of a square is equal to side squared or rather length times width but the appropriate formula for the area square side squared so here is my side value which is PI and I`m simply going to square that and there you go here is my answer I have PI squared as my area of the square and I have 4 PI as the area of my circle so now we can easily determine which value is greater we know that the value of pi is roughly 3.14 obviously we don`t even have to use a calculator here and just by the way fYI do not reach for the calculator always you know you are you have a calculator accessed on the online platform please do not reach for that calculator when you don`t have to you are wasting your time and that`s a completely separate video that we`ll be talking about on when you should use a calculator but very simply 4 times 3.14 gives us 12 points something I don`t care what that something is it`s just 12 points something and then PI squared is simply 3.14 times 3.14 3 times 3 is 9 and it`s going to be 9 points something right I believe it`s 9 points 8 something like that I don`t care because clearly, 12 is greater than 9 points 8 meaning that quantity a is greater than quantity B and therefore the answer is answer choice a quantity a is greater.
Moving on to the next question here we are we are actually given some centered information where we have X is greater than Y and Y is greater than Z and the second statement reads that x times Z is less than 0 quantity a we`re comparing X the value of x times y and quantity B we`re comparing the value of y times Z so this centered information we need to figure out what to do with the centered information right so I want to focus on the second piece of information we`re given that x times Z is less than 0 well if x times Z is less than 0 that means that one of the numbers a must be positive while the other number is negative right because a positive times a negative results in a negative number which is less than 0 so for example if I have 3 times negative 2 that`s negative 6 which is less than 0 it can`t be both positive because 3 times positive 2 would be 6 which is greater than 0 and the and also X and Z both cannot be negative because a negative times a negative results in a positive so X or Z one of the numbers has to be positive or negative I don`t know which one has to be positive or negative yet until I look at the first piece of information here that X here is actually greater than Z well if X is greater than Z that means that X must be positive and Z must be negative so now that`s a good thing right now we actually have some real information we know that X must be a positive and Z must be a negative number and now here`s the thing though what do we know about Y well Y is in between X and Z and we don`t actually know if Y is a positive number or a negative number we simply don`t know right because if I use hypothetical values and I say hey well is one hundred and Z over here is a negative 100 well Y can be any number in between right it can be negative five or it can be even 99 because it`s between 100 and negative 100 so we don`t know we simply don`t know.
Fantastic so now let`s take a look at quantity a and quantity B so here is one strategy that most students and you are of course used to this strategy all your life because you`ve been practicing it it`s called the plugin method right you`re plugging in hypothetical values and you will go ahead and plug in various scenarios and try to see which quantity is greater I personally would not recommend using the plugging in method for this specific question why well plugging in is a good method but it`s not the perfect method for this question because you can save your time you can save yourself some time by looking at this question logically and this is how you do it so I know that quantity a is X times y and I know that x times y so I know that X is a positive number I don`t know what Y is and for quantity B I have Y times Z and Z over here is a negative number this much I do know so I have only two scenarios here right I have either that Y is a positive number or Y is a negative number so let`s see what happens if in this case that I have a negative number for y what does that mean well x times y in this case is a positive times a negative which results in a negative number and a negative and negative which results in a positive number and therefore quantity B would be greater however what happens if we make Y positive so let me go ahead and rewrite this down so here is one scenario and the other scenario I`m going to write this here I have x times y I know that X must be positive Y times Z Z must be negative but in this case Y is going to be positive happens in this case positive times positive is positive positive times negative is negative therefore x times y is always going to be greater than y times Z and take a look at that we have two different signs right if Y is a negative number quantity B is greater if Y is a positive number quantity a is greater so we have two different scenarios here which automatically means that the answer choice is d that the relationship cannot be determined from the information given why do I prefer this way because if you are using the plug in plug in and plugging in method you have to use different numbers and sometimes you may not be using the right number so you have to do it multiple times right maybe you`re maybe you`re sitting there with your scrap paper on the computerized version of the exam plugging in six or seven or eight different hypothetical numbers just because you`re paranoid or just because you want to see and make sure or just because you know any kind of hypothetical numbers you`re using you keep getting that quantity a is greater so plugging in is a good method particularly I do prefer using plugging in method for multiple choice problem-solving questions because it tends to help more but you should resort to plugging in method for quantitative comparison questions when you really don`t have any kind of idea right you`re not able to make any kind of logical assumptions like this and you`re just lost go ahead and plug in if the question allows you to if not always try to be logical about it and try to do it this way.
Fantastic let`s move on to the next slide will recover well where we`re going to cover one last strategy for this video okay fantastic so in this slide it`s pretty obvious or what the strategy here is the strategy is avoid unnecessary computations earlier on the video I told you that the ETS doesn`t do not really want you to spend 20 minutes to solve a problem during various arithmetic work so in this case, you have to understand how to avoid unnecessary computations by simplifying the problem or Mait or making some loss jumps so let`s go ahead and look at this question first.
I have some centered information here it reads the earth rotates around its axis every 23 hours 56 minutes and four seconds okay so basically like 24 hours right this is just trying to give me a headache right let`s see if this is really important what we`re going to see in a second quantity a state`s the measure of the arc traversed by the hour hand on a clock from 10:15 to 107 and quantity B States the rotation of the earth measured in degrees during the same time.
One of the first instincts of a typical student is, of course, going to be that hey well I have a time problem here and I will draw a clock here and it`s it`s saying that my clock reads from 10:15 so 10 is roughly here 15 is roughly here so 10:15 and it`s going to 107 and 1 let`s say 1 o`clock is roughly here so what is that that`s going to be 1 and O 7 would look something like this as well and now I have to figure out the difference in time right I have to figure out how much time has passed right so I would do well most students would say.
Well from 10:15 to 107 how do I figure that out if I spend 45 minutes that`s I get to I can go to 11 o`clock and then to get to 11 o`clock to 1 o`clock that`s going to be another two hours and then finally right two hours gets me to one o`clock and to get to one hour 107 I need to add the seven minutes right so I`m adding 45 plus 7 plus the two hours so that works out to be I believe two hours and 52 minutes so 2 hours and 52 minutes is a time that has passed and I`m interested in in the measure of the arc traversed by our hand and I want to compare that to the rotation of the earth measured in degrees during the same time so obviously you can see that this requires a lot of calculations right there is actually a much easier way to do it a very simple way as soon as you can make the if you can connect the dots this question does not require any of this kind of computation over here and in order to actually carry this if you were to do it this way you would probably spend I don`t know probably another two minutes working on this problem here is instead what you should be thinking about.
You have to understand okay so here`s my clock and let`s just pretend here`s 12 and here`s the six and here`s the nine and three let`s just pretend it`s 12 o`clock right let`s just pretend it`s 12 o`clock and in order to go around the circle 360 degrees that means that it takes me 12 hours to go to 3:00 to go through the entire circle right so twelve hours is equal to 360 degrees would you agree with me right because if it`s 12 p.m. now the next time it will hit the 12 o`clock well 12 a.m. it will have gone around the circle one entire time and that`s 360 degrees and to go around the clock 24 hours well that means that it`s going to travel around the circle once again so that`s 360 plus 360 which is 720 to 720 degrees that means in a 24 hour whoops sorry about that in a 24 hour time period I I go around my circle 720 degrees I care about this because quantity B States the rotation of the earth measured in degrees during the same time now take a look at quantity B right quantity B well you know that the Earth rotates around its axis basically once every 24 hours but you should know that the earth goes around itself so it makes a complete circle only once in a 24-hour time period that means that within 24 hours here the earth rotates only 360 degrees so take a look at that right this is very important information this comparison compared to this comparison so in Scenario and quantity a we have the situation where 24-hour period we travel 720 degrees and basically that`s twice of in quantity B where the Earth rotates once every 24 hours and only goes 360 degrees that means what does that mean that means that we don`t care about this right take a look at this ok whatever we traveled for 2 hours and 52 minutes that means that my degree measured over here is going to be twice the value here then compared to how much the earth would have rotated in degrees because quantity a is going to be QX what does that mean that means automatically that quantity a is always going to be greater right so notice how we don`t even have to do any of this we simply can understand that hey a 24-hour period where we we go 70 degrees Internet and in quantity B here in a 24-hour period we have 360 degrees so no matter how much time.
I`ve spent in quantity a if the value is always going to be 2 times the value as the degree measure in quantity B so the answer is a the the point that I`m trying to make is you can try to avoid the unnecessary computations by making that illogical jump that concludes this video lesson over here we have one more slide this was a very important slide ok this is the last slide and I just want to emphasize that we do have videos that cover a cover several questions with respect to the video lesson and we`ve just covered so obviously this lesson has to do with quantitative reasoning that`s our a quantitative comparison and therefore on the bottom of the screen you can click and you`ll see that I go over 1 practice question per video and usually you`ll find anywhere from 2 to 3 videos of practice questions and all these questions range from the medium to difficulty range just to give you some just to give you that added extra practice and I highly recommend that you go ahead and check those videos out check out our website at wwlp.com to access our full online platform where you can access over 20 hours of video lectures of 500 plus practice questions and 7 full-length practice tests.