har from Gman ninja here and in today's video we're going to talk about arithmetic on the GM or we might say that this is one of the worst named videos in this series because we're going to talk about how to avoid arithmetic on the gmap what we're going to look at is what to do when the gmap throws something that looks intimidating at you or when Midway Through Your solution you get to a horrible division or horrible calculation horrible appplication and what you can do to make that a bit simpler now to do that I've got six questions coming your way the first four of them are not going to be that tough we're probably looking at somewhere between a 75 and an 80 on the scoring level then question five we're going to D the difficulty level up a bit we're going to get into the 80s and then question six we're going to put a real Challenge on you and and question six will be tough now having said that the first part of the video is not that difficult please stay with us because some of the concepts we're going to look at are going to be some of the most important you see in throughout the entire series one of the worst things you can do on the GMAT is to miss a question that you know how to do and really the calculations are the bit that you know how to do if you've if you've broken through the concept if you've understood the question but you mess up the multiplication or division somewhere you're now you're really losing points that you should be getting so today's video while it's not going to be that tough is going to be really important we do have one data sufficiency question in there it's going to be the final question we know that data sufficiency is now on the data Insight section but it's still using the same math concepts underpinning it so we're doing them together in the same video all right without any further Ado I'll get the first question up on the screen take a couple of minutes and have a look at this and I'll see you to look at the solution after you've had that time e e e hey everybody Charles here sorry for the interruption before we get you back to that Quant content three quick things I'd love for you to be aware of first of all this video is part of our full free complete GMAT course that's available up on our YouTube channel if this course is saving you money that you would otherwise spend on a course or a tutor please Center donating some of that savings to charity either a charity that you love if you don't have a charity that you love we've got a list of Charities that we love to support on our website GMAT ninja. com second thing if you love that presenter that you're watching in this video not me the other one they offer oneon-one tutoring if you're interested in that GMAT ninja. com and we can set you up third thing finally if you're doing great on the GMAT doing great on the GRE starting to look for admissions help with your applications for grad school we would love to refer you to a bunch of our favorite companies so just hit us up there is a contact form on our website G ninja.
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people in the family so that final sentence that gives us the gives us the the ability to set up a bit of an equation here so the number of people in the crowd we could say that's 40,000 but the number of people in the crowd after the family leaves so this family of four has has disapp period has gone away um that is how many times the number of people in the family so that is equal to number of people in the family is four but we want to know what we need to multiply that by in order to match the 40,000 minus 4 on the other side so at this point 40,000 minus 4 that that that's not difficult I'm going to jump straight in 39,99 is equal to 4X so in order to find the value of x that I want the the multiplier that I'm looking for in this question I need to do 39,99 96 / 4 now this is what I want to get into in some of these videos this ad admittedly is not the most difficult calculation and yeah I'm sure that loads of you have got the right answer to this but this is the principle that I want to get to this doesn't look nice and in the question you might get at there might be something that's even nastier than this so what can we do about it I'm going to come back to come back to this line and sort of Branch off and we'll go to one side yeah the subtra fraction was it was the obvious thing to do first but maybe it wasn't the best thing to do first if I rewrite this over here so we had 40,000 - 4 is equal to 4X and then think may maybe I do the division first so my x value that's going to be 40,000 - 4 all divided by 4 now what what we can do here is we could split this up so I can split the top of a fraction up just to be careful I can't split the bottom of a fraction up if this was the other way around I wouldn't be able to separate it you can only split the top of the fraction up in this way and we could say that's 40,000 / 4 minus 4 / 4 well 40,000 ID 4 that's just going to give us 10,000 and four divid 4 that's yeah that's just going to give us one and so the final answer we're going to get here is 99,999 and so C is the answer to this question now as I said that that is hopefully an easy question for you um but the thing that I want to focus on is is that principle what can we do to make this calculation a bit simpler maybe I don't just want to think about kind of bashing my face into the wall and doing a really nasty Division if I don't have to maybe I can find a way around it do two divisions yeah I'm going to do two processes rather than one but each of those processes are going to be simpler and the most important thing I'm less likely to make a mistake in doing them and I get to the answer yeah maybe it takes me 5 10 seconds longer but as I say I'm not going to screw this up or I'm going to be less likely to screw this up than I am doing something horrible all right that that's the sort of principle I want to carry through in these videos so next question's coming up give you two minutes have a go at this one e e e all right another question that on the surface of it isn't that tough but the numbers the calculations are going to make it look more difficult than it than it really is because what what we're asked to do we we want to find the arithmetic mean we want to find the average cost of a ticket so I mean concep actually we can we can think of that it's quite simple I want to know the total cost of all the tickets and then divide it by the number of tickets available so we can set that calculation up um the average the thing that I'm looking for well I want the total price of all the tickets so working them through at the silver level I've got 4,000 tickets and they're $50 each so the total cost of the silver ticket is going to be 4,000 Times by 50 and then I do the same thing for all the other tiers so gold is going going to be 3,000 tickets Times by $100 each Platinum is going to be 2,500 tickets time $150 each and the diamond I've got 500 tickets multiplied by $250 each and then I need to divide that whole thing by the total number of seats that we've got going on so that's 4,000 + 3,000 plus 2,500 + 500 and so we end up with this which is is right there nothing has gone wrong here that this is the right way to do it but yeah the calculations are are going to build up pretty quickly I don't really want to do 4,000 * 50 and then do I don't know 3,000 time 100 isn't that tough but you can see that the the amount of time this is going to take is going to build up very quickly what I could do instead is is look for common factors now this becomes a very big thing on the GMAT it's it's quite common it's surprisingly common it's just maybe we don't see it as often as we could there's a common factors in each of these the number of seats at each tier well there were all multiples of 500 so I could pull a 500 out of the front of this calculation and this whole thing suddenly will become a bit simpler I've got 8 * 50 + 6 * 100 + 5 * 150 + 1 * 250 and I could do the same on the bottom of this bottom of this fraction I've got 500 and that's now 8 + 6 + 5 + 1 right so I think things are looking a bit nicer here and yeah we can go ahead we can cancel the 500s then what I could do again right bottom line yeah I'm just going to add these numbers up but Top Line we've got multiples of 50 here again you might not need to do it at this stage but maybe the calculation the question you're doing or in a different question is going to be a bit tougher and yeah we can just we can keep factoring things out so Top Line let's factor out of 50 here so I've got 8 * 1 + 6 * 2 + 5 * 3 + 1 * 5 and bottom of the fraction yeah I'm going to add these numbers up so 8 + 6 is 14 + 5 is 19 + 1 is 20 so now I've got 50 multiplied by 8 * 1 is 1 6 * 2 is 12 5 * 3 is 15 1 * 5 is 5 all of this is still over 20 8 + 12 is was 20 35 40 so I've got 50 ultip by 40 ID by 20 and I can start to start to cancel things 40 and 20 they cancel so 40 is 2 * 20 so the whole thing simplifies right down to 50 * 2 which will give me 100 and so my final answer for this question is B all right again same same with the last question I don't want to focus too much on this question there are loads of different ways of answering this question and if you yeah if you had a different Solution please punch it into the comments the more different ways of solving a question like this we've got wonderful the thing that I want to focus on is this again the principle of you look for common factors see if you can pull them out the front stick a set of parentheses in rewrite your equation but the the calculations that you do inside that equation are go or sorry the inside that set of parentheses are going to be simpler that's the aim we're doing here we want to take what look like horrible calculations and make them into something simpler I would rather do 8 * 1 and 6 * 2 and 5 * 3 than I would something like 2,500 * 150 this is going to take some time okay writing a few lines out is going to take a little bit of time but it's going to be far easier for me to do 5 time three than it is 2,500 * 150 and that's the sort of thing I want you to take away from this video I want you to think about all right we're going to keep these rolling question three is coming take a couple of minutes to have a look at this one e e e all right another nasty looking question hopefully the calculations aren't going to be quite so bad after we've done a bit of work on it but yeah not nice looking to begin with as always if you want a bit more time now's your chance to pause it before we really dive into this but yeah let's take take a look at this one um so the first thing I I want to notice here is that we're not asked for a precise answer we don't want to know whether p is going to be I don't know 02341 or or something quite so precise we we we just got a range now what that means is with something that look looks like this something that looks so precise we don't need to be quite so accurate with it I I can do a bit of estimation I can do a bit of rounding here so let me tell that Top Line 7197 that's really close to 72 so let me just simplify that a little bit I can't I can't move it too far but I I can estimate it a little bit and we can do the same with a couple of these other bits so 294 that's very similar to 0. 3 and 739 you let's call that something very similar to 74 so we've taken something that looks awful and made it look that little bit nicer but it's still not great I don't like the decimals that's the next bit I'm going to deal with here now I'm I'm sure yeah we've all seen something like I don't know f x is uh 54,000 over 2,000 well then I can take this and I can start canceling out zeros and we can make the numbers smaller but what you don't often see is we can go the other way and make the numbers bigger if we need to so if I if I take this if I'm if I look at the 72 and the 3 first I could times Well I can times both of those by 10 I can times top of the fraction by 10 bottom of the fraction by 10 and that will at least give me a whole number here so my Top Line is now going to be something like Point uh well zero it's going to be something like 7. 2 and the point 3 is now going to be three and I've I've got a whole number there I like whole numbers whole numbers make this whole thing nicer and I'm still with that 74 so if I want to get rid of the 74 well I'm going to times the top and bottom of this um fraction by 100 to make that 74 into a whole number now Top Line If I multiply that by 100 I'm going to get 720 I've still got the three and the 74 is now 74 and now we've taken something that looked horrendous up at the beginning and it it it's still not nice I still don't really want to do 720 divided by 74 divid it's still not wonderful but it's much better than it was and now our next job we're just going to go and simplify this step by step there's loads of different ways of doing this different orders however you want to do it totally fine but what what I would say is try and make these steps as small as possible I don't really want to try and do long division of 720 over 74 that that that's going to it's going to take forever it's going to be awful if you can see it we can spot that 720 and three they're both in the three times table 720 does divide by 3 and what we're going to get there is 240 / 74 and from there I'm just going to go step by step I I don't know what 240 divided by 74 is I do know they're both even though so let's divide both of them by two that's going to give me 120 over 37 Now 37 is a prime number so I'm I'm not going to be able to take this any further but 120 divid by 37 that that's something that I can begin to work with what we could do is is say 37 if I times that by two I get to 74 if I times if I add on another 37 I'm going to get 111 and the next one's going to be 148 so 120 well that's going to be sitting somewhere between 3 * 37 and 4 * 37 which means that my overall answer here this value of P it's going to be somewhere between three and four and D is going to be the answer to this question all right so couple couple of different things going on there and again the order you do them in doesn't doesn't really matter that much I estimated the first so made 717 into s sorry made 7197 into 72 first and then multiplied up to make them a whole number you could do the opposite way you could make them all whole numbers and then estimate and then simplify down here I did 720 divid 3 first you could do 720 / 2 and 74 divided by 2 you can do them in that order the the order doesn't really matter again it this video is all about the principles behind this thing we're taking something that looks terrible we're taking something that looks nasty and intimidating and making it into something that looks much nicer which enables us to answer the question all right racing through these questions question four coming up now take a couple of minutes and have a look at this e e e all right up till now in this video it's all been about simplifying the calculations and that's still going to be important in what we do but here I want to think about sort of systematizing the process I want want you to think in terms of a process rather than just in terms of I've got to calculate calculate calculate calculate because we might look at a question like this so which of the following numbers is closest to a half and think well now I'm going to have to do something like a half minus 9/16 and a half minus 1019 and a half mine and just there's a lot of calculation in that we're going to do something similar but let's just think about how we could structure this in order to minimize the amount of calculation we need to do and when we're looking at fraction and certainly when we're thinking about either addition or subtraction and fractions I want you to be thinking about denominators how can we make the denominators the same in order to make the calculation as simple as possible so what I'm going to do is underneath each of these I'm going to write the equivalent fraction to a half using each of these denominators now what that means is so a half is equivalent to if we're doing something over 16 it's equivalent to 8 over 16 so 9 over 16 is 1116 away from a half now here we've got 9.
59 again I'm not not too keen on the 0. 5 there but we'll run with it for a bit now that means that 1019 is 0. 519 away from um away from a half or that's equivalent to 1 over 38 if I want to use nice round hole numbers which I generally do I like nice big round hole numbers so 116th away for a 130 e away for B because the denominator because we've got a one on the top we've got a one on the top we've got ones and we're going to get ones everywhere the denominator on B is bigger than denominator on a this means that this Gap the gap between 1019 and a half is smaller for B than it is for a a is not going to be the answer between these two it's going to be B but we've got CD and E to check so denominator of 24 if the equivalent fraction to a half is 12 and so C is 1 24 away from a half let's keep going for d for a denominator of 30 well a half would be 15 30th so 16 30th is 130th away from a half and finally if I've got something over 36 well the equivalent fraction 18 over 36 is the same as a half so e 19 over 36 is 136 away from a half and now as I as I look across this list again I've got ones for each of the numerators here yeah I had to do a little bit of extra work for B but the reason I did that is so I can have ones in all the numerators which means that the what I'm looking for is the smallest gap between one of these numbers well the smallest gap between one of these numbers and a half which is I want the smallest of these numbers down at the bottom and that is going to be 138 because the denominator is the biggest because the 38 is the biggest which means B is the answer here now again we we actually did a half minus each of these fractions but because we systematized it because I just went what is the equivalent to a half if I had each of these denominators it made the whole process as simple as as simple as I could make it anyway this is another question where I'm sure there are lots of different solutions so if you've got a different way of doing it please punch it into the comments it'd be great to Great to learn of a new way to answer this question all right those are the the four of what we might call the more simple questions we're going to start turning the difficulty level up a little bit question five it's it's not the toughest but it's equally not the nicest think about the stuff we've done in this first four questions and and try and apply those principles as we move into this one um we'll give you a couple of minutes and see you back here soon e e e all right we said we're turning the difficulty level up but the difficulty level here is a little bit more about just the intimidation Factor than the difficulty of the actual calculations because again looking at this question I mean the numbers that we're given you they they just look awful they just they're so big or or they're so small and and there's just there's a lot going on here so if we're going to get to an answer if we're going to get to An Answer efficiently sort of within the time we've got available on the gmap we're going to have to do a few things to to simplify these numbers and make them look nicer and and really that's where we're going with this now if you remember back a couple of questions I said I I don't like working with decimals when I can avoid it I really want to be working with whole numbers and that gives us a bit of a clue as to where to start with in this question Q here I mean it again it doesn't look nice because 0 235 but it's got the least going on I don't have to do a division or a multiplication so I'm I'm going to start with q and say well.
235 * 10 12 well I want a whole number here instead of 235 I would need to multiply that by a th000 or 10 to the 3 in order to make that a whole number so I could say to to go through the steps that's the same as saying 235 * 10 3 * 10 9 and this bit 235 * 10 3 that will give me 235 * 10 9 okay so from now I've just got a format that I can work with in here Q is 235 * 10 9 and if I can turn the other numbers here into a similar format then I can start to compare them and we might get something we can work with here so let's take a look at P now 400,000 that is the same as saying that's 4 * 1 2 3 4 5 I'm moving that decimal point five times so 4 * 10 5 multiplied by 5 * 10 5 or in other words I've got 20 * 10 10 but to get it into that same format with the 10 9 going on I'm going to call that 200 * 10 9 and so we got those first two numbers here and I can say that P is less than Q so we could cross out a number couple of the answer choices now before we move any further but let's leave that till the end I'm going to deal with r and s right so R first of all 100,000 + 25,000 we could say that that is 125,000 and we'll simplify that more in a second 10 ^ 3 to the^ of two um rules of exponents would tell us that that is the same as saying times 10 the 6 here now 125,000 I could call that 125 * 1,000 or * 10 3 and I got time 10 6 there so R is going to be 125 * 10 9 and that is the smallest out of the three numbers we have so far so R is going to be less there one more s here again top so Top Line 500 million so that is the same as saying sort of I'm going to call that 500 because we've been dealing dealing with um dealing with three figure numbers in all of these so I'm going to call that 500 to start with but that's the same I've move the decimal point 6 * or 500 * 10 6 that's the same as 500 million and then dividing that by 4 * 10 to the 1 2 3 * 10 Theus 3 there all right so I could split this up 500 over 4 and I've got time 10 6 / 10 -3 500 ID 4 that's the same as 125 and rules of exponents again I've got 10 6 / 10us 3 so that's the same as 10 6 take away -3 6 take away3 is going to give me 9 and I've got 125 * 10 9 here and so s is the same as R Which is less than P Which is less than q and now I just need to find something that matches here so s is R is equal to S Which is less than p is less than q c is going to be our answer to this question all right so big chunk of work to do here and really that's where the difficulty comes it's not so much the difficulty of the calculations because the the sort of we did 500 divid by 4 and we did four * 5 okay there's a bit of exponent work to go on there's a bit of understanding of um scientific notation but the calculation is not that hard it's the intimidation Factor if you can see your way into these question questions I I went with Q first you you might have jumped in on P again different ways of doing these questions but if you can simplify if you can make the question look nicer to you and just work your way through it steadily methodically it's hopefully going to be not that bad all right final question for you today coming up and we're going to take a a jump in the difficulty level here we we need to challenge you a little bit in each of these videos so here's your challenge for today it's a data sufficiency question as well so challenge coming at all different kinds of levels have a couple of minutes and take a look at this e e e all right two last things thank you so much for making it to the end of the video if you've made it this far you're one of those awesome people that's obviously really engaged in this GMAT thing we would love your comments and your feedback if there's anything else you'd love to see in our videos hit us up in the comments we'll do our best to oblige second thing if you're enjoying it hit that like button hit the Subscribe button helps other test takers like you find our full free video course you need anything else you know where to find us Gat ninja.
