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we're on problem 80 problem 80 if a B and C are integers is a minus b plus c grader okay so they want to know is a minus b plus c greater than a plus B minus C fair enough and if you think about it there's an a on both sides of this equation so they're really wanting to know is minus b plus c greater than B minus C or another way they're just trying to say great i just took a from both sides of this inequality so it doesn't change anything or not really what they're asking if you just rearrange this is is c minus b greater than B minus C which is another way of saying well as one of them greater than the other one right if c is greater than B this is going to be greater than this one if B is greater than C this is going to be greater than this one so let's look at our statements now statement number one B is negative B is negative well that by itself doesn't help us much because be could be negative but see could be even more negative so C could still be smaller than be right if be could be minus five so you could be minus six or so you could be plus six so it really tells us nothing about see relative to be statement to says C is positive C is positive so this statement by itself once again it tells us nothing about the value of B relative to see if C is positive maybe B is positive as well maybe B is more positive or maybe B is negative who knows but this by itself doesn't help us but if we use both of these together if C is positive and B is negative then we know if this is positive this is negative we know this is going to be positive and we know that this is going to be negative right essentially we know that C is larger than B so this will be positive this will be negative and we can answer our question if C is larger than b if c is larger than B this is true the left hand side is greater than the right-hand side or this holds good so we need both of the statements together both statements together are sufficient to answer this question to which colors 81 if a certain animated cartoon consists of a total of seventeen thousand two hundred and eighty frames frames on film how many minutes will it take to run the cartoon so they want to know how many minutes so such if we knew how fast the frames have to go through if it's you know X frames per second if we knew that number we'd be able to figure out how long the the cartoon runs so statement one is the cartoon runs without interruption at a at a rate of 24 frames per second well that's exactly what I just asked for 24 frames per second so using just that information how many seconds does it run what runs 17 thousand two hundred eighty frames / 24 frames per second this will give you seconds and then if you divide this number by 60 you'll get minutes times 60 or divided by 60 is equal to minutes divided seconds by 68 minutes so this is the answer so one alone was enough to answer the question what a statement to give us I'll write it here statement two it takes six times as long to run the cartoon as it takes to rewind the film and it takes a total of 14 minutes to do both six times as long to run the cartoon as it takes to rewind so six times the minutes let's say to run let me have to let's say six times to play I want different letters 6 times 10 so the play the cartoon takes six times as long as to rewind the cartoon and they say it takes a total of 14 minutes to do both so they say play plus rewind is equal to 14 and what we want to know is how long does it take to play the movie and we don't even have to use that information alone but the 17,200 b-but just looking at this we have two linear equations and two unknowns so we can just solve for P P is the playtime of this movie and if you wanted to figure it out not that you would have to because we would be done at this point we would say oh 1 & 2 are each independently sufficient to answer this question but just to show you that we could figure it out say r is equal to 14 minus P and you substitute that into that right this is that substitute in you get p is equal to 6 times are so 6 times 14 is 60-plus 2480 4-6 p you get 7 p is equal to 84 p is equal to 12 minutes and we'd be done but actually don't have to do all that's a waste of time just want to prove it to you 8282 a box contains only red chips white chips and blue chips if a chip is randomly selected from the box what is the probability the chip will either be white white or blue so essentially to answer this we just have to know what proportion of the chips in the bag are white or blue all right so statement says one says the probability that the chip will be blue is one-fifth so probability of blue is equal to one fifth that also tells us that one-fifth of the chips in the bag are blue but we don't know what what what proportion are white so we still can't answer that top question statement two tells us the probability the chip will be red is one-third probability of red is equal to one-third so once again just this alone we don't know what the well actually just this alone is fine right because it I cracked myself the chips are only the probability of getting white or blue right that's probability of white we could write do set notation white or blue that is just equal to what it's 1 minus the probability that we get a red right think about that I'm either going to either this is going to be true i'm going to pick a white or blue or i'm going to pick a red because there's only red white and blue in the bag so the probability of white or blue is equal to 1 minus the probability of red which is equal to 1 minus one-third which is equal to two-thirds so statement two alone is sufficient and then if we have statement number two statement one alone is not sufficient 83 see this is this is tricky because i think you know at least when i first read it I was like oh I could use this and this to figure out the probability of getting a white so I need both statements but we don't even need to know the probability of we just need a little probability of a white or blue which is just 1 minus the probability of red so statement two alone gets us there we do the next problem a d3 if the successive tick mark shown on the number line are equally spaced and if x and y are the numbers designated designating the endpoints of the interval is shown what is the value of y okay so let me see if I can draw what they have drawn so they have a number line and I probably have to draw the exact same number of tix as they did so they have zero and then let's see this one tick two ticks and then they have a third tick and they say this is X and then they have three more one two three and then they have Y and then they have one more this keeps going on and on and they ask us gave this if they're the tix are equally spaced and if x and y are the numbers designated the endpoints of intervals as shown what is the value of y so they're equally spaced but they're not telling us that these are integers we don't we don't know that you know this is 1 this is 2 this is 3 we don't know that but what we do know is we do know that Y is how much further than X so see X is X is 1 2 3 spaces so we could say x is equal to three times let's say s right where s is the length of each interval or each tick and y is 1 2 3 4 or five six seven so y is equal to 7 s and so we could use this to come up with a relation with x and y this is before they've done anything this is just looking at the diagram so if we want to we could say that s is equal to Y over seven or if we substitute this back here we could say that x is equal to sorry x is equal to 3 over 7 y and actually you didn't have to even do this s stuff you could have just said oh well X is three sevens as far as why is from zero because these are equally spaced so just the problem set up just looking at it gives us that information but we want to know what the value of y is and that by itself isn't enough what a statement one tell us x is equal to one half x is equal to one half well that's enough to figure out y if x is equal to one-half you just substitute there one half is equal to three sevens why multiply both sides by 7 thirds you get y is equal to what 7 over 6 and you're done you don't have to solve that you just know that i have this i have that i can solve it so one alone is sufficient statement two tells us y minus x is equal to two-thirds so once again we have one two equations two linear equations with two unknowns we can just substitute and solve them and just to prove it to you x is equal to 3 7th y can substitute that right there so I have Y minus three sevens y is equal to two-thirds so 77 s minus three sevens so that's just to go here 77 why so it's 47 y is equal to two-thirds y is equal to two-thirds times 7 over 4 which is it's 1 this is 2 which is seven over 6 once again 7 over 6 see you in the next video so once again each of these are independently sufficient to answer the question see you soon