If you're seeing this message, it means we're having trouble loading external resources on our website.

If you're behind a web filter, please make sure that the domains ***.kastatic.org** and ***.kasandbox.org** are unblocked.

Main content

Current time:0:00Total duration:10:18

or on problem 47 47 on page 281 if the two floors in a certain building are nine feet apart how many steps are there in a set of stairs that extends from the first floor to the second floor of the building so I think I can draw that so this is this is the second floor this is the first floor they want to know how many there's they're 9 feet apart that's what they tell us already now if you we need to figure out how many steps there are to go from the first to the second floor so a piece of information one they give us each step is 3/4 foot high foot high well this by itself should give us enough information right because each of this these distances I'll do it in green each of these are 3/4 foot high so to figure out how many total steps to get to the top you just say 3/4 times the number of steps is going to be equal to 9 and then you could just solve this by multiplying both sides by 4/3 but we don't have to solve it we just have to know that we can solve for it so one alone is enough right and you could what if you multiply both sides of this you get 12 that you need 12 steps but anyway we don't we want to avoid having to actually do math we just want to figure out whether we can do the math piece of information to each step is one foot wide one foot wide well that's clearly useless because it doesn't tell us how how how much I guess altitude we're making on each step and that's what you have to figure out to say how many steps you need to go up 9 feet in the air so this is useless so the answer is a statement one alone is sufficient next problem 48 48 if XY is equal to 0 XY o does not equal 0 so that tells us that neither X nor Y is 0 right is X Y going to be less is x / y going to be less than 0 x / y it's going to be less than zero in order for this to be true one of these numbers so I mean if x / y is negative that means that either X or Y but not both of them are negative right that's the only way you can get a negative number when you're dividing if both of them were negative this would be a positive number so let's see what we can do it there with their information number 1 X is equal to and this is the question is X y less than 0 and 1 says X is equal to minus y well immediately let's let's just substitute that back in if X is equal to minus y then what's x / y X is equal to minus y so you have minus Y over Y and that will equal and we know Y doesn't equal 0 so for any other value other than 0 if this was 0 this would be undefined but then this is equal to negative 1 so in this case this is X X divided by Y is equal to negative 1 which is definitely less than 0 so that proves our statement so statement 1 alone is all we need now let's see what statement 2 gives us I'll do it here statement 2 minus X is equal to minus minus y so that tells us that minus X is equal to Y and then we can just substitute the same thing in again we could say well now we could substitute for our X well or we could just multiply both sides by negative get X is equal to minus y which is the same thing as this year so statement 2 alone is also sufficient to solve this problem and so the answer is d each statement alone is sufficient switch colors problem 49 problem 49 how many people are directors of both company K and company are okay directors of K and R statement number one there were seventeen directors present at a joint meeting of the directors of companies K and R and no directors were absent at a joint meeting of the directors so that's all the directors of K and R so let that let me draw a vent some Venn diagrams so if that is K and then that is R so they're saying that when you add both of these together because this is a joint meeting of all the directors of both we got 17 so there's 17 in this entire universe of directors that's what statement 1 tells us that this circle that if you take this whole circle and then you add up the the extra don't double count the intersection you add up the extra you get 17 but that alone doesn't tell us how many joint directors are joint directors are these people people who are on the board of both K and R so this is K and this is R so statement 1 alone doesn't help us although I'm suspecting maybe in conjunction with something else that could statement number two is company K has 12 directors and company are has eight directors okay K is equal to twelve directors twelve directors that's an i and r is equal to eight directors okay so everything in this let me in this in the case urkel combined is eight right everything I'm sorry everything in the case circle is twelve right K directors everything in the our circle is eight now if we wanted to get the the total of the K and the R so if I might buy itself that doesn't tell me how many overlaps so when you take statement one or statement two independently that doesn't help us but what if we were to figure out if we would use them together so how many total directors are there going to be there's going to be the total directors in K so Kay's directors plus the directors in R but if you were to just add those two up you would double count the people who are in both K and R right you would count them twice you would count them when they're in K and you would count them when they're in R so if you wanted to figure out how many total directors there are you then subtract out the people who are in K and R right you don't want to subtract them twice you just don't want to double count them right because when you when you do capable sorry you're counting them for K and then you're counting them for R so let's subtract them out once so that I don't know you only count them for K or that you only count the far you only count them once so minus K R so this notation that's people who are in K and R and what does that equal well statement one told us that it told us that their total of 17 directors and so statement two told us there are 12 Directors in K + 8 directors in R - the joint directors is equal to 17 and by the way we don't even have to do this we could have just recognized that if we know the total number of Directors and we know how many are in each of the groups that we can figure it out and we would just answer the question that both statements together are needed to answer this - are sufficient but I'll just show you that we can figure it out just so that you're happy with it let's say we get 20 minus kr is equal to 17 and so you get kr is equal to 3 so there are three directors that overlap with both and we were only able to answer that question by using statements 1 and statement 2 next problem 50 if x and y are positive so x y are both positive is x y greater than one x y greater than one is a question statement number one tells us x y is greater than one so let's see does that help us at all and it's not obvious that just tells us that X is greater than one over Y or Y is greater than one over X so let's just think about this statement is equivalent if we multiply both sides by Y and we can do that without changing the inequality because we know y is greater than zero so if we do that we get X is greater than Y this is if we can show this we can show that and remember the reason why I could I didn't have to change the inequalities because I knew that when I'm multiplying both sides by Y then Y is greater than zero if Y was less than zero I'd have to switch the sign right here when I multiply both sides by but anyway if I can prove X is greater than Y we're all set this doesn't help me let's see statement number two is X minus y is greater than zero well if I add Y to both side of this equation what do I get I get X is greater than Y so this proves exactly what I need to prove it if you want to go all the way to what originally they asked divide both sides by Y and we don't have to change the sign because Y is positive you get X divided by y is greater than one which is exactly what we needed to prove so a statement two alone is sufficient see you in the next video