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Current time:0:00Total duration:10:34

or on problem 84 on a company sponsored cruise 2/3 of the passengers were company employees and the remaining passengers were their guests so we could say employees is equal to 2/3 of passengers and I guess we could also say that guests are equal to 1/3 of passengers right the remainder are guests if 3/4 of the company employee passengers were managers what was the number of company employee passengers who were not managers ok so statement the second statement in the least the problem statement it says if 3/4 of of let's see if 3/4 of the company employee passengers were managers it's a company employee passenger so 3/4 of E were managers if I read that statement if 3/4 of the company employee passengers or managers what was the number of company employee passengers who were not managers so we essentially so what percentage so essentially they want to know what 1/4 of E is right this is what they're asking because they want to know what were the number of company employee passengers that were not managers in that 3/4 were managers 1/4 were not managers so if we could figure out P we would be able to figure out e and we'd be able to figure out 1/4 e if we were able to figure out guests we could then use that to figure out P which we could use to figure out a which we could then figure out 1/4 e so that's how we should be thinking about it now that we should be spending that much time on it problem number 1 there were 600 90 passengers 690 is equal to P well that we'd be done right because E is equal to 2/3 P and we want to know what 1/4 e is so then our answer is so the non manager employees would be 1/4 times e which is just 2/3 times P time's 690 and that would be our answer so one alone is sufficient and the statement number two there were 230 passengers who were guests of the company employees so they're saying essentially saying that guests are equal two guests are equal to 230 and we could use this information that guests are just one third of P so which is equal to one third of P and then of course from there you could solve you could multiply three times both sides equation to figure out that C is equal to SiC P is equal to six ninety six ninety which is so this is the same information that they gave in one which was enough to solve the problem so two alone is also sufficient so they are each independently sufficient to solve the problem that problems confusing just with the language company employee manager passenger guests it was very confusing 85 in the XY plane does the point 4 comma 12 lie on line K okay this is interesting so let's let me draw a line okay and I'll worry about the point 4 comma 12 later so let's see they say let me look at the points that they do say is line K so they let me so if this is the x-axis that's the y-axis statement 1 tells us that the point 1 7 lies on case of the point 1 comma 7 lies on K 1 comma 7 and then they also tell us that the point well you know that alone isn't going to let me know if the point 4 comma 12 lies on it so 1 2 3 4 4 comma 12 it might be up here right this is the point that we care about if you can see that let me scroll down 4 comma 12 so if the line looks like that maybe we'd go goes through but the line could be like that's the statement number 1 alone isn't enough statement number 2 says the point minus 2 comma 2 so minus 2 minus 2 comma minus 2 X is minus 2 y is positive 2 you so they're saying that lies on it eyeballing it it seems - - comma - eyeballing this line K it seems like 4 comma 12 could very well lie on it but we have to do a little bit of math to figure it out so first of all just statement or two by itself doesn't help us cuz this line could go anywhere you need two points to just know what the line is and so how do we figure out if the point 4 comma 12 is on this line well the easiest way to do it is to figure out the slope well I don't know if it's the easiest way but it's the way I would think about doing it is to figure out the slope of the line and then extend that slope here and see if the point 4 comma 12 lies on it so let's see what's the slope of this line so when we went up 7 - 2 so the rise is 5 when you go up 5 we went over how much 1 minus -2 we went over 3 right so for every 3 that you move over you go up 5 that's the easiest way to think about it so when we go from we're going from X is equal to 1 to X is equal to 4 so we're going to the right by 3 and so we should be going up 5 so 5 + 7 sure enough is equal to 12 so these so if you just extend the slope it does hit the point 4 comma 12 so both statements combined are well actually you know what I just wasted a lot of your time because we just have to know whether the data is sufficient to answer the question we don't have to prove that the question is true I've just proven to you that that 4 comma 12 does lie on the line but you could have just said oh well you know what statement number 1 gives me a point on the line that alone isn't enough to solve the problem statement number 2 gives me another point and then at this point if you're really you know taking the GMAT and time matters you just say hey I got two points for this line two points is everything I need to know about a line once I know two points online I can figure out if any other point is on that line I'm done both statements combined are sufficient you wouldn't have to do all of this stuff that I did which would waste your time but if you just to prove to you that you could figure it out I did that but anyway I have to admit I did waste your time a little bit you should just immediately say oh I got two points on the line once I have two points it's I can completely figure out if I can if I if any other point lies on that line 86 the length of the edging that surrounds circular garden kay is okay so we have two Gardens it looks like so we have circular garden kay and then we have circular garden let's see what does it say is 1/2 the length of the edge that's around circular garden G so this is circular garden G this is K this is G so they're saying the length of the edging that's around circular garden K is 1/2 the length of the edging that surrounds circular garden G so we could say circumference of K right that's the edging that surrounds it is equal to 1/2 the circumference of G fair enough what is the area of garden K assume that the edging has negligible width well a couple of things if we know the circumference we know the area right because the circumference is 2 PI R and once we know our area is PI R squared so if we can figure out the circumference of of K then we know its area and if what likewise if we know anything about the radius or the diameter or the area of C of G we can figure out a circumference if we know its area we can use a formula area equals PI R squared right PI R squared to figure out what R is and then once you figure out R is you could figure out that circumference is equal to 2 PI R so if you have any of this information you're able to figure out any of the rest of it so statement number one says the area of G is equal to 25 PI square meters so let me write it area of G is equal to 25 pi so immediately should say hey if I know the area of G I can figure out the radius of G and if I know the radius of G I can figure out the circumference of G if I know the circumference of G I can figure out the circumference of K if I know the circumference of can figure out the radius of K and if I know the radius of K I know area of K you shouldn't have to calculate any of that so this is enough this is sufficient statement to and maybe I'll do that for you just to show you that it can be done but I hopefully making is making some sense the edging around G is 10 PI meters long so they're actually giving us there's telling us that the circumference of G is equal to 10 pi so this is even easier they're giving us this that means the circumference of K is 5 pi which means that we can figure out the radius of of K and we could figure out the area so this is also sufficient to solve the problem and just so you know you don't take a word for let me just show you how quickly you could figure it out if the area of G is 25 pi that means that pi times the radius squared of G is equal to 25 pi that means that the radius is equal to 5 right cancel out the PI on both side R squared equal to 5 these are radius is 5 that means the circumference is 2 pi times this so that means that the circumference of G is equal to 2 pi times 5 which is 10 PI which is exactly what statement 2 told us and then from there we could forget the circumference of K which is half of that so circumference of K is equal to 5 pi and then we know that 2 pi times the radius of K is equal to 5 pi divided both sides by pi we know that the radius is equal to 5 halves and then the area of K would be pi times this squared so it would be pi times 25 over 4 and we'd be done but all of this is a waste of time I just wanted to show you that you once you have the radius or the circumference or the area of either of these you're able to figure out everything else and I'm out of time see in the next video