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Current time:0:00Total duration:10:03

all right problem 42 let's say for the system of equations given and this is a system of equations they give they say X minus 4 is equal to Z they say Y minus X is equal to 8 and that eight minus Z is equal to T eight minus Z is equal to T so they say for the system equation what is the value of Z so we're trying to figure out Z and then statement number one they tell us that X is equal to 7 X is equal to 7 well if we know X is equal to 7 we can solve for Z right here because X is 7 then 7 minus 4 is Z so then that so 7 minus 4 is 3 so Z is equal to 3 that was pretty straightforward so one alone is sufficient just using this first equation in the system so let's see if 2 is of any use T is equal to 5 T is equal to 5 well this is easy one two you put T is equal to five right here and then you could easily solve for Z right you get 8 minus the Z is equal to 5 and you can solve for but I'm not going to do it you just have to know that you can so this alone is sufficient as well so the answer is d each statement alone is sufficient problem 43 43 is X equal to 5 is x equal to 5 and statement number one they say x is greater than or equal to 5 well that doesn't tell me whether X is equal to 5 and just as it's greater than 5 statement number two tells us X is less than or equal to 5 once again that does not tell me whether X is 5 but if I told you that both of these are true X is greater than or equal to 5 and not or and X is less than or equal to 5 well actually that's still well the only the only the only X that satisfies that equation that satisfies both of these is five right I mean you put three in three will not satisfy this one if you put seven in seven will not satisfy this one so the only thing that satisfies it is is both this is five I'm sorry I'm my brain's malfunction a little bit so you need both of these so the answer is both statements together are sufficient see that one's confusing because it's so simple on some level 44:44 the table above shows that this let me see if I can draw this table oh and they write they write they write r s t u r s t and you have a bunch of things let me just I don't even know what these are yet I haven't read the question but let's see 0y x 62 y 0 56 75 x 56 0 69 and then 62 that's a six sixty to seventy five sixty nine and zero and what are they going to ask if they're saying the table above shows the distance in kilometers by the most direct route between any two of the four cities for example the distance between city are between city are and city u is 62 or if you said between you and are it's gonna be 62 as well right that's the same thing fair enough what is the value of x so the value of x is the distance between T and R let me circle then they want to know what the value of x is the difference the distance between T and R so it's that one and another way to look at the distance between TNR that's this one so these are both x fair enough okay so statement number one tells us by the most direct route the distance between SN T you could say the distance between s and T I'll just say its line segment s T is equal to twice the distance between s and R is equal to 2 times 2 times s R let's see do we know what s r is SR is equal to Y right and Esty Esty is equal to 56 we figured that so s T is 56 let me do this s T is 56 Union s and T is 56 so 56 is equal to 2 times SR the distri s and r is y or s and r is y so it equals 2y and so we can solve for y y is equal to 28 we actually didn't have to solve it but let's see I'm just trying to see what this goes but that still doesn't help me figure out the distance between what did we have between R and T that just helps me solve for y y is 28 y is 28 statement number two see where this is going by the most direct route the distance between T and u so the distance between T and u is 1.5 times the distance between R and T R and T so the distance between R and T this is the interesting thing because this is our R and T is is is X right so they're saying the distance between T and U is equal to 1.5 times X and what's the distance between T and U the distance between T and u is 69 all right this is U T and U is 69 so you have 1.5 X is equal to 69 you only have to solve it you just know that you can easily solve for X if you know statement number two so statement number two alone helps you figure out what X is statement number one is fairly useless so the answer is B statement two alone is sufficient draw a line here I don't want to problem number 45 45 what is the value of the two digit integer X so two didge integer x equals who knows all right statement number one the sum of the two digits is three so let's say that X is equal to the number a B where this is the tens digit and this is the ones digit so statement number one says the sum of the two digits is three so a plus B is equal to three well that doesn't help us there's a lot of well you know that these are going to be positive numbers but we don't know whether they're two different numbers two X is divisible by three X is divisible by three well I don't know if you learned that trick in in school but any number that's divisible by three the sum of their the sum of their digits add up the sum of the digits are also divisible by three so once again that just means that a plus B is equal to some some multiple of three well if you keep adding them they eventually add up so if you had a two-digit number so this is a C let's think just a plus B is equal to three this could be a couple of different things you could be see a two-digit number I mean it could be 3 0 3 0 it could be 1 it could be 12 it could be 21 I think those are all of the the possibilities that we can have just off of statement number one an X is divisible through we'll all of these are divisible by 3 so really both statements give you no information so the answer is e that both statements combined still give me nothing but all of these are possibilities and actually this one leads to a lot many many more possibilities that X is divisible by 3 because then you could have things like I don't know this would have been a valid a valid number as well so this would actually give a lot more this is a little bit more strict but anyway either way we can't figure out what X is it could be 30 it could be 12 could be 21 could be anything all right problem 46 what is the tenth digit in the decimal representation of a certain number so the tenths that's the number right behind the decimal point so the number let's just call it X so statement number one says X is less than one-third and two says that X is greater than 1/4 so is this enough to figure out what the tenths digit is so what's the number that's less than one-third let me just think of a couple of them well one-third is like point three three two three repeating so if I just write 0.32 that satisfies one and it satisfies to write 0.32 is barely one fourth but what's another and then in this case a tenths digit would be a three well let me try to find if another one that would satisfy these both well let's see greater than one fourth what about 0.26 0.26 is definitely greater than 1/4 and is definitely less than one-third but both of these have different tens ones as two one has a three there so even both statements combined still do not allow me to solve the problem there's not enough information given so once again e together I'm still not getting enough information oh I'm almost at ten minutes anyway I'll see you in the next video