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now on problem 37 37 and they say what is the value of XY minus y Z minus y Z statement 1 says y is equal to 2 well that by itself doesn't help us that just tells us 2 X minus 2 Z so if you don't know what x and z are you can't figure out what this whole thing is if you just know Y is equal to so that alone doesn't help statement 2 is X minus Z is equal to 5x minus Z is equal to 5 now this is interesting because this expression we can factor out the Y what happens if we take if we divide if we factor out of Y of these both of these expressions let me just rewrite it XY minus zy I just switched the Y in the Z that equals X minus Z times y well we can figure out X minus C from statement number 2 X minus C this is equal to 5 and we know what Y is equal from statement 1 so Y is equal to 2 so we can definitely figure out as long as we have both statements and we can show that the answer is well Y is equal to 2 so the answer is 2 times 5 is 10 but we didn't have to figure it out we just had to know that we could figure it out if we had both of these data points 1 by themselves you you wouldn't be able to solve it so the answer is C both statements together are sufficient but neither alone is problem 38 ok they drew us a picture let me see if I can draw that same picture looks like some type of device so it looks like that and they have the other end yes the other end looks like that there's these handles or something it looks like antal haven't read the problem yet so they say with the first 10 volumes of a 20 volume encyclopedia fit up right in the book rack shown above this is a book rack so I guess the books get stacked that way and they label this right here this dimension is X and they're saying we'll the first 10 volumes of a 20 volume encyclopedia fit up right in the book rack shown above so essentially I am I gonna put the first ten in there so the first statement they say is that X is equal to 50 centimeters well that doesn't help me because I don't know how big the first ten volumes of the Encyclopedia are if each of them are at least the first ten are less than 5 centimeters each are on average less than 5 centimeters and I maybe I could fit them but one by itself doesn't help me to twelve of the volumes twelve of the volumes have an average thickness of five centimeters twelve have average of five well that doesn't help me either because remember they're saying well the first 10 volumes of a 20 volume encyclopedia may be the twelve that have an average thickness of five centimeters maybe those are the you know volumes 8 through 20 and volume maybe volumes 1 through 7 have an average thickness of 50 centimeters each or five million centimeters each so even both of these conditions combined don't help me know if I can definitely fit the first ten volumes of the 20 volume encyclopedia so that is e both statements together are still not sufficient problem 39 a circular tub okay so they've drawn this circular looking tub so the top looks like that and then there's two sides you know well I can construct what they've drawn and the bottom something like that and then they shade in a little area a strip of this like that and they say a circular tub has a painted band has a band painted around its circumference is shown above so this is the painted band around its circumference what is the surface area of the painted band and they tell us that the height of the painted band is X so in order to essentially know the surface area you would have to know the height which is X x times the circumference of the circle right which would be the length so if you knew the height times the circumference of circle you'll be able to know the surface area so they tell us the first statement X is equal to 0.5 0.5 whatever meters so this is in meters 0.5 meters so that's that alone doesn't help us we have to be able to figure out the circumference of this tub in order to really be able to figure out the surface area because the circumference times its height will be the surface area point - they say the height of the tub is 1 meter so they are telling us that this is 1 meter well that doesn't help us that still doesn't tell us how far around to the tub goes if they had given us the diameter or the radius or the circumference then we could have used our basic geometry to figure out the circumference but they didn't so either way so one meter height both of these combined still do not allow us to figure out the surface area of this green band II again problem 40 what is the value of integer N and n is an integer so statement number one they tell us that n times n plus 1 is equal to 6 now I we should already be able to figure this out because n is an integer and one is an integer so let's just so what are the the factorizations of six you could have one times six but that doesn't fit n in n plus one right this is N and n plus five you have two times three which work right if two is n n plus one is three and they equals six let me circle that and then what other factorizations you don't have any other four times so these are these are all of the factors of six and so just looking at the first statement you know that n has to be equal to two this is the only integer where this is true actually let me let me take that let me take a step back no what if n is negative because I was assuming it's a positive integer but they didn't say it's a positive integer so let me think about that if I did minus 3 times minus 2 that also equals 6 and these are both integers huh ok so this isn't enough because in this case and could because this would be N and this would be n plus 1 so n is either equal to 2 or n is equal to minus 3 that's a little tricky yet the intuition is to just assume that n is positive but it doesn't have to be positive so n could be 2 or minus 3 here that's a tricky one so that one by itself does not help us solve the problem the second part of it point to it says 2 to the 2n is equal to 16 and whenever you have these and whether you're doing the SAT or the GMAT or anything whenever you have a variable in the exponent your goal really is to just get everything in the same base so we could write the left-hand side the same so that's 2 to the 2n and how do we write 16 as a as a with the base 2 well 16 is just 2 to the fourth right 2 to the fourth and so we get 2 n is equal to 4 n is equal to 2 so this this statement alone is enough to figure it out this statement alone is not so the answer is B our review for what the state B statement two alone is sufficient already is B and this was tricky because one you you think that one is aloneness efficient but it is ambiguous because n could be -3 41 41 okay they've drawn a bunch of if I see this right they've drawn a bunch two lines I can draw this so line and then they have a bunch of circles one circle two circles they have and then they keep going see three circles and then one more like right there or a circles I think that's about right and then they keep they say essentially that the circles just keep going on and on that's what I think the drawing implies and they say the inside of a rectangular carton is 48 centimeters long so the inside of a rectangular carton is 48 centimeters long 32 centimeters wide so 32 centimeters wide this is an 8 32 centimeters wide and 15 centimeters high 15 centimeters high okay so that's the inside kind of reviewing from the other from the other wall this is the floor of the inside of the container and then there would be another up here but I think you get the idea the carton is filled to capacity with K identical cylindrical cans of fruit that stand up rights in rows and columns as indicated in the figure above okay so this is like a top view of it so you can we could say that this side up here this is the top this is 48 and then this is 32 so we don't care so much about the height I think so let's see the carton is full to capacity with K identical cylindrical cans are furthest and upright in rows and columns indicate in the figure above if the hands are 15 centimeters high okay so each of the cans are exactly 15 centimeters high so they're they literally are as exactly high as the carton if the cans are 15 centimeters high what is the value of K so we have to figure out how many will fit how many of these cans will fit in this in this area essentially and they tell us point number one each of the cans have a radius of 4 centimeters radius is 4 centimeters well if we know that each of them have a radius of 4 centimeters then we know exactly how much Square area each of these circles will take up assuming that they're packed exactly like this right because if you think about it what is this area right here well this is well there's a bunch of different ways you could think about it well the easiest is that if the radius is 4 centimeters the diameter right here is 8 centimeters so if this is 8 and you have a 48 length you can only do six of these all right 6 times 8 is 48 so you can only do 6 that way and then if the diameter is 8 this way and this length is 32 you can only do four this way so statement number one alone is enough to figure out how many you can put it would actually be 4 times 6 you could put 24 K would be 24 cans and you could fit in so statement 1 alone is enough now what a statement to tell us 6 of the cans fit exactly along the length of the carton 6 of the cans fit exactly along the length of the carton so they're telling us that these cans that there's 6 cans that fit right along the length which we figured out from statement number 1 but that also gives you the same information as statement number 1 because you know that these are cylindrical cans I guess we can assume I think it's a safe assumption to say that these are that these are circles although they haven't you know a cylinder yeah a cylinder you're assuming that the tops are circles so if you say that six can fit that way then you know that the diameter of each of them is 8 centimeters and then you can make the same argument to the diameter is 8 centimeters to say that 4 can fit the other way down so 2 alone is also 2 also is sufficient by itself so the answer is what is that see both statements no no D each statement alone is sufficient see in the next video