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Current time:0:00Total duration:11:05

we're on problem 103 103 and it says if N and K are greater than zero so both N and K are greater than zero is n over K an integer and over K an integer so essentially they're asking is K divisible into n so let's see statement one says N and K are both integers N and K both integers and that's good that they told me that because I was assuming it incorrectly so they're saying N and K are both integers well that still doesn't help me much and could be 2 and K could be a hundred and two over hundred is 1 over 50 that's not an integer although and could be four and K could be 2 and that would be an integer 4 over 2 is 2 so statement 1 by itself doesn't help me statement 2 says N squared and K squared are both integers N squared and K squared both integers well once again I don't see this is helping me much right if N and K are both integers of course when you square them they're going to be integers you take any integer and you square it you get an integer you take any other integer and you squared you get an integer so this is actually this gives me no no new information relative to one so I'm just trying to see if I'm missing something but as far as I can tell it's e both statements together are not sufficient to answer this question all right I mean I can give you a case it n could be 4 and could be 4 K could be 2 and then n over K would be an integer but then and both of these would satisfy both of these conditions or it could be 2 and 4 in which case and over K could aren't integers they don't actually differentiate between N and K at all yeah so it's e next problem 104 if the average arithmetic mean of 6 numbers is 75 how many the numbers are equal to 75 excuse me okay so six numbers are equal to 75 how many of them are equal to 75 okay equal to 75 is the question let me go scroll down a little bit the first statement says none of the six numbers is less than 75 so none less than 75 so this is interesting if I have six numbers and their average is 75 and none of them are less than 75 well they essentially all have to be 75 and less list well let me let me write down and eat I mean it's it will let me write down if I let's say the first number is 75 now let's just say that I had some number above 75 in the list let's just say for argument that there was a 76 in the list it doesn't have to be an integer they're not assuming that but let's say I had 76 in the list in order for it the average to be 75 I would have to offset this number that's one more than 75 with another number that's one less than 75 but they told us that none of the numbers are less than 75 so I can't so if I have a number greater than 75 I have to have a corresponding number less than 75 or several of them to weight to balance off that number or you could have several balancing several it can get complicated but the general idea is is that if no numbers are less than 75 you can't have any numbers greater than 75 either so this actually tells you that all six all six are 75 so statement one alone is sufficient statement two says none of the six numbers is greater than 75 so none greater than 75 well it's the same argument if I have a number if if I have some number let's call it a let's say it's one of the numbers that's in my list and it's greater than 75 in order to average down to 75 I'm gonna have to have or I'll say a is a is less than 75 right because we're using statement number two if a is less than 75 let's say 75 is here in the number line I'm just doing ad hoc diagrams so a is less than 75 in order for the whole group to average to 75 I have to have some number that's bigger than 75 to balance off the ACE and we call that B but they're saying that we have no numbers greater than 75 so we have no numbers greater than 75 we can't have any numbers less than 75 either and all the numbers have to be equal to 75 all six of them so once again two is also sufficient so each of these statements independently are sufficient to answer this question actually they both answer the question that all six are equal to 75 that was interesting 7t what am i doing I am on problem 105 105 is the absolute value of x equal to y minus Z okay absolute value of x equal to Y minus Z all right so statement number one they tell us that X plus y is equal to Z X plus y is equal to Z so let's see if we can do some substitution Z is equal to X plus y so if we substitute Z into this top equation we get the absolute value of X is equal to Y minus X plus y minus X plus y so that means that the absolute value of x is equal to y minus X minus y and that says that the absolute value of x is equal to minus X because the Y's cancel out well I don't know if this is true still this would this would apply to any negative number right if I have a negative 1 here negative one absolute value is 1 and negative negative 1 is 1 as well so this would apply if X is 0 or some negative number but they don't tell us that so we don't know if this is true statement 2 tells us well there you go statement 2 tells us that X is less than 0 so if this tells us X is definitely a negative number and if you put any negative number into this which we got from this condition and this condition if you put this into that you know this is true for any negative number right the absolute value of any negative number is the opposite of that number so you need both of these team it's an obviously statement two alone is useless because if you just say X is less than zero you don't know anything about Y or Z without this condition right here so both statements together are sufficient but individually they're reasonably useless 106 we're getting up there 106 what was the total amount of revenue that a theater received from the sale of 400 tickets some of which were sold at X percent of full price and the rest of which were sold at full price so sale of for 400 tickets so let's say we have the reduced priced tickets and the full price so R is a number of reduced priced tickets and F is the number of full priced tickets so R plus F so the total number six tickets was 400 what was the total amount of revenue and then the total amount of revenue generated is going to be equal to is going to be equal to the price of full price times the full priced tickets so P times F where P is the price of full priced plus the number of reduced tickets and that's sold at X percent of the full price tickets okay so whatever X is X percent will convert it to a decimal at the appropriate time so this is what did the the initial problem description tells us that the total number of tickets is four hundred and then whatever now it's X percentage of P so whatever the full price is times the full price tickets Plus this would be the reduced price times the reduced price tickets equals a total revenue now let's see if we can figure this one out X is equal to 50 X is equal to 50 well this by itself just tells us that this is P over two right here this X is 0.5 right it's 50% remember its they said X percent so this just makes this equation it turns it into 0.5 times P times R plus P times F is equal to the revenue and we still have one two three unknowns and two equations so that by itself isn't enough alright we have that P we're actually four unknowns are P F and revenue four unknowns two equations not good enough to full price tickets sold for $20 each so the price of a full price ticket is $20 so now this is interesting now we could take this and substitute it into this equation because we now know what the price is the P variable and so if we use both of these conditions we have 50% of a full price well that's ten dollars times the number of reduced priced tickets plus $20 times the number of full priced tickets is equal to is equal to the revenue generated and then they and then we know that a total of 400 tickets are sold our sorry our plus F is equal to 400 well even now we still just don't have enough information if they had just told us they would have to tell us you know either R or F or they would have to tell us the total amount of revenue generated in order for us well actually that's what they want to figure out they want to know the total amount of revenue so in order to figure that out we would have to yeah we'd have to have at least one more condition to solve for R and then be able to solve for F we have to know our F to figure out the revenue let me just make sure I'm not missing something here yeah there's no other way to just you can't just separate out an R plus F so I'm gonna say that e both statements together are not sufficient if I have to go back and yes I think I'm pretty sure I'm right I don't think I'm missing anything right here some of which were sold at X percent of full price of the rest was sold at full price which is 20 dollars yeah so R plus F is 40 and then we have 10 our bust is equal to revenue yeah we don't we have three unknowns and two equations two linear equations not good enough next problem oh I'm overtime see in the next video