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we're on problem 68 and they want to know what is the average arithmetic or arithmetic mean of J&K so average of J and K so essentially if we knew what they were you could take J plus K and divide by two and you'd know their average what is statement one statement one tells us the average of J plus 2 and K plus 4 is 11 so this is interesting so the average of J plus 2 in k plus 4 is 11 so that means that J plus 2 plus K plus 4 over 2 I'm just averaging the two numbers so they're telling us that that is equal to that is equal to 11 and remember the question they're asking is the average of J and K so if we could just figure out what J plus K over 2 is equal to we're done or if we just knew what J plus K is we were done so I've maybe we could figure that out from this let's see if we can simplify so you get this simplifies to J plus K plus 6 over 2 is equal to 11 this simplifies to J plus K over 2 plus 3 right it's plus 6 over 2 I'm just taking this 6 over 2 out so plus 6 over 2 right is equal to 11 so then we get J plus K over 2 is equal to 8 and we're done the average of J plus K of J and K is 8 we're done statement 1 alone is sufficient let's see what statement number two does for us statement number two says the average of JK and 14 is 10 I suspect we're gonna be able to do the exact same thing so the average of J plus K plus 14 so now we're averaging three numbers is equal to 10 right and here we should be able figure out what J plus K is again let's multiply boats we don't have a convenient two in the denominator anymore so let's just solve for J plus K so you get J plus K plus 14 multiply both sides by 3 is equal to 30 and then you get J plus K is equal to what subtract 14 from both sides is equal to 16 and then if you wanted to figure out the average of the two you just divide both sides by 2 and you get J plus K over 2 is equal to 8 so each statement alone was sufficient to solve this problem next problem I feel the sneeze coming on this is not happening all right where was I problem 69 we need to move the scroll bar up all the way 60-69 Paula and Sandy were among those people who sold raffle tickets to raise money for Club X if Paula and sandy told sold a total of a hundred of hundred of the tickets how many of the tickets did Paula sell okay so essentially they're telling us Paula Plus sandy sold 100 tickets and they want us to figure out how many did Paula sell where P is the number Paula sold and s is the number Sandee sold problem number one Sandee sold 2/3 as many of the raffle tickets as Politan so sandy is equal to 2/3 times Paula well this alone is sufficient we have won one equation of two unknowns and now we have another equation of the same two unknowns these are both linear equations so we have two equations of two unknowns we can easily now solve for s and P and maybe I'll do it but you should just already recognize that this is sufficient if you're on the GMAT and we will solve it just to do it after this sandy sold 8% of all the raffle tickets sold for Club X all right now this is a little different this says sandy is equal to 8 percent of not not all that all the tickets that sandy and polish told she sold 8 percent of the total that Club X sold so this is a different number than because we know there could have been I might have been in Club X selling raffle tickets so we don't know how many I sold so we know what this total number is so this is actually there's not much we can do with it because there's no way for us to figure out this total number so this is not that useful so statement one alone is sufficient and just to prove the point to you right we're trying to figure out what Paulo Sol so let's just substitute this back in so you have P plus 4 s I'll write 2/3 P is equal to 100 and so this is what this is 5/3 P is equal to 100 just added 1 plus 2/3 or 3/3 plus 2/3 and then the F P is equal to 3/5 times 100 which is equal to 60 so that's how many she sold so we were definitely able to figure it out but this would have been a waste of time if you were taking the GMAT for real you should have just recognized two linear equations and two unknowns I'm done next problem 70 is ax equal to 3 minus BX so a X equal to 3 minus BX who knows prob statement number one let me scroll down a little bit statement number one tells us x times a plus B is equal to 3 well that's essentially the same thing as this top equation right let me show you let's just multiply the C that says that x times a that's ax plus BX is equal to 3 and then subtract B X from both sides you get ax is equal to 3 minus BX which is exactly what we were trying to prove so if this is true then this is definitely true statement 1 alone is sufficient statement 2 tells us a equals B equals 1 point 5 and X is equal to 1 well let's see if this is true so it is you have 1 point 5 times 1 so you have 1 point 5 is equal to 3 minus 1 point 5 times 1 so 3 minus 1 point 5 well this is true 11.5 is equal to three minus 1.5 is 1.5 so two alone is also sufficient so the answer is d each statement alone is sufficient to solve this problem 71 let me switch colors 71 a number of people each wrote down one of the first 30 positive integers where any of the integers written down by more than one of the people all right that's interesting so are any repeats any repeats a number of people so clearly if we had more than 30 people and they all had to pick a number but one of the first 30 integers and you're gonna have repeats but let's see what they tell us the number of people who wrote down an integer was greater than 40 with a number of people greater than 40 so 40 people each have to pick a number between the right one of the first 30 positive integers right so they only have a pool of 30 to pick from so 40 people have to pick numbers from a pool of 30 numbers there's definitely going to be repeat right so even if the first 30 people all pick different numbers which we cannot guarantee by any means the next ten are going to have to repeat with somebody because all the first 30 would have already been picked and we you could very easily have even more repeats so statement number one is very very sufficient statement number two the number of people who wrote down an integer was less than 70 number of people well that's useless less than 70 I mean this this statement by this statement maybe only one person wrote down an integer right and if only one person wrote down an integer we definitely don't have any repeats because there's no one to repeat with so this is a useless statement so statement one alone is sufficient and statement two is useless 73 I think there should be a third option where you can rate the degree of uselessness of a statement some of them borderline on almost being useful some of them are ridiculous like this one okay seventy-three I know what am i oh that no one 72 72 and the figure above is C D greater than BC so they drew us a number line or whatever you want to call it some type of a line do another color this end we have a and we have B then we have C and then we have D and the figure above is C D so this is C D greater than BC so they want to know is this greater than this so C D greater than BC all right so number one they tell us that ad ad is equal to 20 so this whole thing whole thing is equal to 20 so that doesn't help me much right statement number one statement one tells a D is equal to 20 and it tells me the whole length maybe I can get some more information statement number two a B is equal to C D a B is equal to C D so this is interesting their shape they're telling us that this is equal to this but this still doesn't help us right I mean I can imagine a situation where both of these are let's say that both of these are 5 that could be 5 that could be 5 and then this would be 10 right 5 plus 10 plus 5 in which case C D would not be greater than BC right so this would this would be a situation that meets all of the conditions where C D would not be greater than BC but then I can construct one where it is greater than BC I can make C D equal to what if that was 8 and then this one was also has to be 8 and then we would only have 4 left where C D is greater than BC so in this case both statements together are still not sufficient so the answer is e and I have run out of time I'll see you in the next video