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we're on problem 87 it says an employee is paid one point write that down 87 an employee is paid 1.5 times the regular hourly rate for each hour worked in excess of 40 hours per week okay so after 40 they get overtime one and a half times excluding Sunday and two times the regular hourly rate for each hour worked on Sunday how much so each hour worked on Sunday regardless of whether or not they're above 40 hours how much was the employee paid last week so how much paid okay so let's see statement 1 tells us the employees regular regular hourly rate is $10 $10 per hour is normal now if they just so based on that we know what their overtime is that means that overtime overtime is one and a half times so it's $15 an hour and that tells us that Sunday is double that $20 an hour all that was said in the problem description I guess you could call it but we still don't know how much they were paid because we don't know how many hours they worked and when those hours happen to be so it's still not enough information statement number two says last week the employee worked a total of 54 hours 54 hours total but did not work more than 8 hours on any day no more than 8 hours in a day okay so let's think about that if you worked no more than 8 hours in a day how many days would you have to work you would have to work well you would have to work 6 you would have to work 6 you'd I guess at minimum you would have to work six days for eight hours and one day you would work for six hours right or I mean there's other ways you could say it you could have seven days all seven days you could be working for how many times does 7 go into you could be working seven and six seven hours seven and six seven hours a day now this still doesn't neither of these help us because we don't know where the hours were allocated we don't know how many of these hours ended up on Sunday because that's a critical question and we know that there was some overtime in some form right but we don't know if that was Sunday overtime or if that was regular overtime and both of these cases would imagine working seven in six seven hours every day then you would have 7 + 6 7s for Monday through Friday then you'd get some overtime for Saturday as soon as you got above 40 hours and then it's Sunday you'd get paid double but then you have this situation maybe sunday is the day you work six hours or maybe Sunday is one of the days you work eight hours so we don't know so this problem there's not enough information to solve this problem 8888 what was the revenue that a theater received from the sale of 400 tickets 400 tickets some of which were sold at the full price and the remainder which were sold at reduced price okay fair enough the number of tickets sold at full prices is a statement number one so let's say so immediately we know that there are 400 tickets sold and that is the number of full priced tickets plus reduced priced tickets is equal to 400 right statement number one tells us oh and they want us to know some of which were sold at full price and the remainder of which or they want to know the revenue okay they want another revenue so we have to know how much we got for each of these tickets in order to be able to figure it out so number one the number of tickets sold at full price full price or one-fourth the total number of tickets sold so 1/4 times what was the total number of tickets sold well they already told us at 400 so it equals 100 and then you could just look at that and that tells us that the reduced price were equal to 300 tickets were sold at the reduced price but I still doesn't tell us the total revenue because we don't know how much full price was or how much reduced priced was so that's not enough information just yet problem 2 says the full price of a ticket was $25 25 for price but they still don't know we still don't know what the reduced price is we know that 25 times 100 or 2500 dollars were generated from the sale of a full price ticket but the reduced price they don't tell us that what how much did they reduce the price right some of which were sold at full price and the remainder of which were sold at a reduced price we don't know what that is it was 25% off 50% off we don't know so unless we know the price of the reduced price ticket we can't figure this out so once again not enough information to solve the problem problem 89 if what is that a circle circle represents one of the operations plus minus and times and okay this is interesting so they say in circle represents one of the operations plus minus and times is K Circle L plus M equal to K circle L plus K Circle M for all numbers K L and M well essentially what are they doing they're doing the distributive property right they're saying that K whatever this operation times L plus n is the same thing as K times whatever this operation is with L plus K whatever this operation is with M and the only places where the distributive property works is either with multiplication or division and division isn't one of these ease properties so essentially if circle this doesn't work with addition or subtraction so if essentially we're able to prove or disprove that multiplication is this operator then we have enough information so statement one is so another way of saying is that this circle could that this this question could be rephrased as is circle equal to multiplication so if we can answer this with the statements that we can answer this top one because only multiplication or with this or division but division is one of the options statement one says k circle one is not equal to one Circle K for some numbers K for some numbers K well this immediately tells me that this is not multiplication right in fact this tells me that this is subtraction alright because the only time where you know K minus 1 is different than 1 minus K with addition that's always going they'd always be equal to each other with multiplication they'd always equal each other so this has to be if you believe statement 1 then circle is subtraction which tells you that this statement up here is not true so statement 1 alone is sufficient to determine whether this statement is true or another way to phrase the problem whether circle is equal to multiplication so statement one is sufficient statement 1 actually tells us that the circle is subtraction problem number 2 or statement number 2 circle represents subtraction ok well they just told it out right there well so this and this are equivalent information and so they're enough to determine that this up here is not true remember we're not they're not saying is the statement true that are saying you have enough information to figure it out and we know that this isn't true because circle the subtraction and this statement only holds true if the circle is equal to multiplication so each statement alone is sufficient to solve that problem problem 90 how many of the 60 cars sold last month by a certain dealer had neither power windows nor a stereo ok so it tells us 60 sold and we want to know how many had neither power windows nor a stereo statement 1 tells us of the 60 sold 20 had a stereo but not power windows 20 had stereo no power windows fair enough but that still doesn't tell us how many had neither so let's let me draw a little circle Bend Grahame here okay so that's all sixty cars that were sold that that pool right there that set twenty had stereos with no power windows so let me draw some Venn diagram excuse me all right no that's knees that I was talking about a couple of videos ago finally happened I feel excuse me alright back to the problem twenty head stereos with no power in this so let's say that this is the pool and then had stereos this is the pool that had power windows and what we care actually is what had neither stereo nor power window so we care about we care about this outside row that looks tacky that's a little garish but anyway so this is stereos this is power windows this would be stereos and power windows they're saying 20 has stereos but no power windows so that's this right here so I'll do another fill that's you know it's not pleasant to look at but this is this is 20 stereo no power window and then but that alone doesn't tell us what this green area is so what's the second statement that's too dark statement 2 tells us of the 60 cars sold 30 had both power windows and a stereo 30 had both so that tells us that this range right here let me do it another in another tacky color that tells us that that right that's how many had power windows and stereos that's how many had power windows and stereos so that is third let me make sure I have a good color here so that's 30 I know that you can't see that 30 okay so I mean we could answer a couple of questions we can answer how many cars sold had stereos in general well 50 right fit 20 had a stereo no power windows 30 had a stereo with power windows so a total of 50 stereos we know that 50 had stereos but that still doesn't answer our question of the ten that remained of the ten you know 60 were total and there's ten left within this space and this space we don't know how those ten fall out maybe five had neither and five had only power windows with no stereo or maybe there maybe there were no cars with only power windows and no stereos and all ten were had neither so you don't know even using both statements so at least for this one they haven't given us enough information to to figure out how many had neither they did give us enough information to figure out how many stereos got sold or how many cars with stereos got sold anyway see you in the next video