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alright we're on problem 59 59 on page 282 if a real estate agent received a commission of 6% of the selling price of a certain house what was the selling price of house of the house so the price of the house price of house and they just told us that the real estate agent received 6% but that alone doesn't tell us much so statement number one they tell us the selling price - the real estate agents Commission was eighty four thousand six hundred dollars so let's see if we can write that algebraically the selling price let's say P for price - the real estate agents Commission well they told us was beginning the real estate received a 6% of the selling price so that's 0.06 6% of the price so they're telling us that that is equal to eighty four thousand six hundred dollars well we're done that's that's a linear equation with one unknown this is Algebra one you can solve for this let's see this is you could say this is I mean if you had to if you wanted this point nine four P is equal to 80 four thousand six hundred and then you to F P is equal to 84 six hundred divided by point two nine four whatever that is you get here calculator but we don't care which we just have to know that we could solve it well since we got so close let's just solve it eighty-four six hundred divided by point now this is a bad habit when you're taking the GMAT you want to just know that you could solve it so the selling price of the house is ninety thousand dollars we didn't have to solve that that would be a waste of time on the real GMAT but I just wanted to show you how easy it was to solve statement number two statement over to let's see if this is in the independently useful the selling price was two hundred fifty percent of the original purchase price of thirty six thousand dollars well this is okay so the price we we chose P is the selling price right the selling price - right everything we talked about before was the selling price and now they're introducing this thing called the purchase price so the price selling is equal to and that's what we want to figure out is equal to two hundred fifty percent so that's 2.5 times the purchase price of $36,000 so times $36,000 36,000 actually we didn't have to write this so the price is 2.5 times 36,000 which is I'm guessing and c72 yep it's $90,000 again we didn't have to do that but once again this is just a very this is not this is actually not even algebra you just multiply 2.5 times 36,000 you get the answer so each of these independently are enough to solve this problem so that's D next problem 60 this yellow is a little bit over the top let me do a more muted color so they write if the square root of x over Y is equal to what does that say D right is that what they write is equal to D I know that's equal to n I think all right is equal to n what is the value of x so statement number 1 they tell us that yn is equal to 10 well this is pretty useful because this first equation they give us we just multiply both sides by Y we get square root of x is equal to Y n right Y times both sides gets us this and if yn is equal to 10 and then we know that the square root of x is equal to 10 so X is equal to 100 so statement a 1 alone is enough now what a statement to do for us they tell us y is equal to 40 and N is equal to 1/4 so once again this this I mean they substituted everything else so we just have to solve for X so both of these individually are enough so the answer is d but we could you know solve for it just for fun we get square root of x over 40 is equal to 1/4 and then you get essentially solving this you get square root of x is equal to 10 and you get the same thing X is equal to 100 and you are all done right and you might say oh but isn't there plus or minus no because we're taking the square root of something is equal to 10 we're not saying the square root of hundred is what if you the weather is the square root of 100 you'd say oh it's plus or minus ten but if we said the square root of something is ten that something has to be a hundred anyway next problem don't want a dilly dally dilly dally 61 I want to imbue you with a sense of urgency for the GMAT how many integers are there between but not including R and s fair enough so essentially we have to figure out what R and s are how far apart there are so statement number one so integers between R and s but not including remember not including so statement number one tells us that R minus s is equal to 10 now this is it this is an interesting this is an interesting question because if we knew that R and s were integers then this could be you know we could just pick R minus s is maybe R is equal to 11 and s is equal to 1 and then if you if you actually just want me to write it out you could say well 1 2 3 4 5 6 7 8 9 10 11 how many integers are between the two and not equaling the 2 1 2 3 4 5 6 7 8 9 right but that's if we assume that R and s are integers and and this would work for any two sets of integers that are 10 apart but what happens if we do it a little bit differently what happens if we say that this is one point 12.13.12 sorry what if it's between one point one and eleven point one so if it's one point two one is R let me write it this way what if R was eleven point one and s was equal to one point one then what are the integers between them but not equal so you start at one point one you would have two three four five six seven eight nine ten and now eleven would be included because 11 would still be less than R 10 11 so now you one two three four five six seven eight nine ten so statement number one is actually not enough because they didn't tell us that RNs are interns if R and s were integers then the answer would be nine in this case but if R and s are not integers then the answer could be ten so statement number one alone is not enough the answer could be nine or ten okay let a statement number two do for us let me do a different color statement number two is interesting problem there are nine integers between but not including R plus 1 R plus 1 and s plus 1 ok so this is interesting so they're telling us that there are 9 integers between R plus 1 and s plus 1 so I mean actually just looking at it inspection you could say oh well then there are 9 integers between R and s and they say but not including so this is enough this alone is sufficient and you don't need statement number one statement one one actually doesn't get you anywhere so let me prove to you that if if there are nine integers between R plus 1 and S plus 1 well think of it this way the if there are nine integers between R plus 1 and s plus 1 if you subtract 1 so s is one of the ones that are between I want to make sure I I do this I do this right so if let me let me think of a good way for me to prove it to you well I'll just do it with an example so let's say let's say that the example is well the only example let's say it's 11 and 1 right this isn't a proof but I just want to give you the intuition right so if R is 11 and s is 1 so then you would have 12 well I don't wanna do it that way the easiest way to think about it is it doesn't matter how much you are adding if you add the same amount to both the bottom rate of the range and the top of the range it should not change the total number of integers that are between them so if you were to say so there would also be 9 integers between R minus 1 and s minus 1 you're just shifting the range along the number line but you're not going to actually change the number of integers in between them so if there are nine integers between our plus 1 and s plus 1 there's going to be 9 integers between R and s so 2 is all you need hopefully that that's a satisfactory explanation I didn't want to go into something rigorous when we're trying to imbue you with a sense of urgency see if I have time for the next problem okay 60 - 60 - what is the number of members of Club X who are at least 35 years of age so age so number whose age is at least 35 so it's greater than equal to 35 the number whose age is true okay they tell us statement number one exactly three-fourths of the members of Club X are under 35 years of age so 3/4 are less than 35 that is fair enough but that doesn't tell us that doesn't tell us the number that are at least 35 this tells us the percentage they tell us this tells us that one fourth above or we could say one fourth greater than or equal to 35 one third fourth of total members total members greater than or equal to 35 but it doesn't so tells it's proportion but it doesn't tell us the total amount and I just got the 1/4 from you know three fourths are less than 35 1/4 are going to be greater than or equal to 35 years of age so one by itself doesn't help us let's see what 2 does for us the 64 women am i reading the same problem okay the 64 women in Club X constitute 40% of the club's membership ok so 64 is equal to 40 percent of the total membership now we're set right because we can use this equation to figure out the total membership call it t for total T is going to be equal to 64 divided by 0.4 right they just told us that statement essentially that 64 is 40% of the total they just they said it's the women and all of that but they they could have just told us that 64 is 40% of the total so then you can solve for the total and then you substitute that here and you say one-fourth of the total our 35 years or older and you get what we were trying to solve for and so the answer is one-fourth times 64 over 0.4 and whatever that is you could put it in your calculator but all we have to care is that when you use both of these equations combined you are able to solve for the number that are greater than or equal to 35 years old and each statement alone isn't sufficient so you need both statements and that is see both statements together are sufficient see in the next video