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or on problem 73 73 how much did a certain telephone call cost all right no you know nothing so far statement 1 the call lasted 53 minutes 53 minutes well unless they tell us how much it cost per minute that still doesn't tell us how much the call cost statement 2 tells us the cost for the first three minutes was five times the cost for each additional minute so first three minutes five times additional minute well that still doesn't help us I mean the cost for the first three minutes might have been five cents a minute and then we might have been one cent a minute after that or it could have been 10 cents a minute and then or let me make it multiple through 12 cents a minute and then four cents after that so tells us nothing about the actual both of these satisfy that statement and actually if I have to be honest the statement is slightly ambiguous because they're saying the cost for the first three minutes do they mean that the total cost for the first three minutes was five times each additional minute or was it the cost per minute of the first three minutes was five times additional minutes well either way both statements combined don't help us because we're not able to figure out the cost per minute and then we could that so we can apply it to this so they are both useless 74 74 in a certain office 50% of the employees are college graduates so let's say 50 percent college I'll call that C 50 percent well I could say 50% of the employees are college graduate right 60 percent of the employees are over 40 years old so it's a 60 percent of the employees equal we'll call it oh for over 40 over 40 I don't know where this is going I'm just making up numbers and I said if 30 percent of those over 40 have mastered degrees how many of the employees over 40 have master degrees okay so thirty percent of the over 40 have have master's degrees I don't know I'm just trying to make up some notation how many of the employees over 40 have master's degree so we're actually trying to come up with this number so if we knew how many employees over 40 there were we would be set because we just went by 30 percent times that if we knew how many employees there were we would be all set because we could figure out the number over 40 and then multiply 34 times that so let's see what they give us statement 1 exactly 100 of the employees are college graduate 100 of so essentially C is equal to 100 right 100 of the employees are college graduates and they told us that 50 percent of the employees are college graduates so that means how many total employees are there that means that there are 200 employees right hundred is 50 percent of 200 so that told us there are 200 employees if there are 200 employees how many employees over over 40 are there well that's oh right oh for over 40 well that's just 60 percent of 200 that's 120 and then how many over 40 with master's degrees let's call that OMD that's band one way how many of these are there over 40 with master's degrees well that's 30 percent of over 40 so that's 30 percent this isn't oh this is 30 percent of this which is equal to so over 40 with master's degrees is equal to 36 and we would be done so statement one alone is sufficient this is old as you call it over 40 instead of a zero don't get confused over 40 with master's degrees so statement two of the employees 40 years old or less 25 percent have master's degrees so that doesn't tell us anything really I mean doesn't tell us how many employees there are over 40 which was one of the things that we realize we have to figure out it doesn't help us how many total employees there are so we really can't do this type of logic so it seems fairly useless so yeah employees forty forty years old or last 25% imagine you know this is this is a useless piece of information so the answer is what is that I always forget a statement alone is sufficient and statement two is useless seventy-five seventy-five they asked is are s T equal to one statement one tells us that RS is equal to 1 and statement - I mean this by itself doesn't help us right if RS is equal to one the only way that this whole thing is going to be equal to 1 is if T is also equal to 1 but they don't we don't know that so I mean T could be equal to 10 so easily the statement 1 alone doesn't help us statement 2 tells us s T is equal to 1 well I can show that even if we have both of these statements that we still can't prove this for example I can come up with a scenario that meets both statements where this is true because I can say what if R is equal to 1 s is equal to 1 and T is equal to 1 then we can then we can make both of these statements true so then then then definitely our s T is equal to 1 but let me see if I can construct something where this doesn't hold up so what if R is equal to 6 s is equal to 1/6 and then T is equal to 6 so then R times s would still be equal to 1 right s times T would still be equal to 1 but what is RS T now it's 6 times 1/6 times 6 which is equal to 6 so I can satisfy both of these but still end up not knowing whether it evil 's 1 or something different and I just pick this arbitrary you can actually kind of pick an arbitrary number here and set this up so anyway this is e I think that's C right both statements combined are useless right they're not sufficient next problem next problem turn the page it's a problem 76 and they've drawn a nice pie chart for us which I'll reproduce 76 total expenses for the five divisions of company H let me draw this pie chart that's my okay and then they have a bunch of see how many pies are there five five I'll try to draw it the way they do it so that's one one two three that looks pretty close to what they've drawn and then they write this is q r s t and p o is the center they call this angle x all right fair enough so this is the total expenses for the five divisions so each of these are divisions for company age 76 the figure above represents a circle graph of the company H's total of company HS total expenses broken down by the expenses for each of its five divisions if o is the center of the circle fair enough so this is the center although I didn't draw it quite the center o is the center of the circle and if company H is total expenses are five point four million dollars what are the expenses for division R so the whole thing is five point four so the whole pie is five point four million dollars and we need to figure out what R is equal to so if we know what angle X is whatever so the whole expenses are 360 degrees so whatever fraction X is of 360 degrees that's going to be the fraction that r is of the total expenses so let's see if they give us that if we can figure out what angle X is 1 X is equal to 94 well we're done because x over the total degrees in the circle so 94 over 360 degrees that's going to be equal to the expenses of division are divided by the total expenses 5.4 million and this is a trivial equation to solve so one alone is sufficient let's see what they give us for statement number two the total expenses for divisions s and T are twice as much as the expenses for division R so they're saying that this this right here is twice as much of what as what we're trying to figure out is this right here well that doesn't help us much because you know P and Q could be arbitrarily small or large I mean you know these two combined could be two dollars and this could be one dollar right in which case pmq are the bulk of the expenses for the company or maybe these two are four dollars and r is two dollars which are all possible and these would be represented for the rest of the you know whatever it gets you to five point four million dollars so statement two is useless so statement one alone is sufficient and statement two does us no good and I am out of time I'll see in the next video