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we're on problem 116 what is the value of a plus B squared statement one statement one tells us that a times B is equal to zero that to me seems fairly fairly useless let me see look what if we expand that out that's equal to a squared plus 2 a B plus B squared right this is the same thing I just expanded out a plus B squared and so they're giving us a piece of telling us that this right here this term right here is going to be equal to zero right if a B is equal to zero this term right here is going to be equal to zero but we still don't know what a squared + B squared are so statement 1 by itself not so useful statement 2 a minus B squared is equal to 36 this is interesting so let's expand let's expand this out a little bit so this says this tells us so you might want to say oh that means that a minus B is plus or minus 6 but actually I don't think that is going to help you as much well actually that could help you as well but the way I'm thinking about it is let's expand this out we get a squared minus 2 a B minus 2 a B plus B squared right is equal to 36 so by itself the statement isn't that useful I mean even here the statement says that if you would take the square root of both sides it tells us that the difference between a and B is either positive 6 or negative 6 if you took the square root of both sides so statement 2 by itself is kind of useless but if you use them together you expand out statement 2 you get this now if we also take in statement 1 and we say oh a B is equal to 0 so then that is equal to 0 and we're left with a squared plus B squared is equal to 36 and if a squared plus B squared is equal to 36 then we know that this a squared and plus B squared is also equal to 30 six right so that tells us that a plus B a plus B squared is equal to 36 as well so both statements together are sufficient and this is interesting because if you think about it makes a lot of sense this statement tells us that the difference between a and B and this is all a waste of time but I just want to give you some intuition this tells us that a minus B is equal to plus or minus six all right so tells you that the difference between a and B is either positive six or minus six so that one is six bigger than the other but we don't know which way it goes this statement tells us that one of them is equal to zero right both of them aren't going to be equal to zero because there's a six difference right so one of them if one of them is equal to zero then the other one is either going to be plus or minus six right and if only if we look at here if we look at this statement one of these numbers is zero the other one is plus or minus six but it doesn't matter if one is zero and one is plus six when you square it you get 36 if one is zero and the other it's not minus six you square it you get 36 so I just want to give you that little intuition but the correct answer is that both statements together are necessary to solve this problem 117 the more connections you can make while doing these math problems the better you'll be really better off you'll be in life I think and I'll start making sense all right they've drawn this thing this okay and then they draw this down like that now let's see this is l m n and k and the figure above what is the ratio of K n to M n so they want to know the ratio of this side KN to MN k and to M and fair enough okay statement number one tells us the perimeter of rectangle k l m n the perimeter of rectangle kam is 30 meters so perimeter is equal to 30 meters so this is a rectangle right so what does this tell that tells us that you know let's put it in terms of the things we care about that two times MN all right because MN & KL are going to be the same length since rectangle so this tells us that two times M n plus 2 times K n because KN and L M are the same length so this just put in the terms of the things we care about plus two times K n so 2 times KN is equal to 30 that's the perimeter twice this plus twice this is the perimeter you could say that Plus that Plus that Plus that but this keeps it in terms of that so what I think well I think we can sort let's divide both sides by the divide both sides by 2 you get m n plus K n is equal to equal to 30 and actually yes you still can't figure out the ratio between the two you just have you just know it that the sum of the two are equal to 30 let's look at statement two right you can't figure out the ratio from this statement two tells us the three small rectangles have the same dimensions the three small rectangles have the same dimensions this is interesting so that's telling us well this this that's interesting because that tells us that whatever that tells us that this distance and this distance have to be the same that tells us that that tells us that and if this distance and this distance is the same then this distance right there is twice this distance how did I get that well this distance is twice each of this these distances right this longer side of this horizontal rectangle is twice this and this is the same thing as this so for all of these rectangles their ratio of their sides is kind of is one to two is the ratio of the sides so let's create a unit called the short side of this rectangle right so how many units long is MN well MN is going to be this side right here it's going to be two of those units long so one two and then three right and we figured that out because the long side of this is twice as long as a short side so if we were measuring these in terms of the short sides of the rectangle and men is three of them and then KN is two of them one two right one two so the ratio of of KN to MN we just it doesn't matter what units you measure and you just want to get the ratio so the ratio is going to be equal to two to three so statement two alone is sufficient to solve this problem next question 118 if N is a positive integer is 150 over n an integer so it's essentially asking us is n divisible into 150 that's the only way that 150 over N is going to be an integer statement number one tells us that n is less than seven now if every number less than 7 is divisible into 150 then we're all set because we know it's positive as well we know it's positive so and one works right to work seventy-five three works fifty-four let's see you go for into this four goes into 100 and then does it go into fifty four goes into 50 no it doesn't go into fifty so four does not work so just by telling us that n is less than seven does not solve the problem because if n was four four does not go into 150 evenly it goes into it well I'm not gonna figure it out four goes into it what 19 it goes into twenty five twenty five plus twelve thirty seven point five times so that doesn't do us any good so statement 1 by itself doesn't isn't that useful statement two and is a prime number n is prime so this statement by itself is not useful because I mean n could be a prime number larger than 150 so that by itself doesn't tell us that we we definitely can get an integer and and could easily be Y or it could be three which would allow it so n doesn't tell you one way or another whether this is an integer but if you combine this do statements if you say that N is a prime number that has to be less than seven then we can take four out of the picture because four isn't prime and then you put five there five definitely does go into 150 and then six six does go into 150 it goes into 120 and leave 30 left over so six goes into 120 so all of the prime numbers less than seven are divisible into 150 so both statements combined are sufficient to answer this question see in the next video