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let's keep going one problem number six on page 278 in the data sufficiency sample questions so let's see they've drawn a little figure they say in the figure above lines K and M are parallel I guess I better draw lines K M let's see they have line let's line K let's line em and then they have a transversal line and we've gone over all of this in the geometry playlist if you might want to review it and if this looks completely foreign to you and so this is line K this is line m and they calling this angle right here x degrees this line here is Z degrees and then this angle here that's a line that's an angle this angle here is y degrees Y degrees and the question is question number 6 and the figure above if lines K and M are parallel so they're both parallel what is the value of X okay and statement number one they tell us that Y is equal to 120 degrees so if Y is equal to 120 let me do that in let me do this one in magenta so we're this is based on this is equal to 120 what can we figure out well this Y is y is supplementary to Z right so when they you know they kind of you add these two angles together there's 180 degrees right because you're completing kind of a whole half arc or half circle so Z would be 60 degrees right Z would be 60 degrees and then you could say that I you know there's all these words that people use in geometry class but if you have two parallel lines and a transversal then these opposite inside angles are going to be the same so you know that X is equal to 60 degrees another way you could have done it you could have said okay if Y is equal to 120 degrees then this angle then Y and this angle right here are also supplementary right because they complete this whole arc so Y Plus this angle have to be equal to 180 so this angle would also be 60 and then you use what you learned in geometry class that you know corresponding angles on on a transversal intersecting two parallel lines that they're also equal so you'd also get to the same conclusion that X is equal to 60 so either way statement number one alone is enough to figure out X now what did they give us for statement number two and I'll do that in a different color statement number two Z is equal to 60 well this actually gives us the same information as that because if we know that Z is equal to 60 then we know that Y is going to be equal to 120 even if I never even if the book never told us this the first time so Z equal to 60 is the same information as Y is equal to 120 and so you can make the exact same argument as you did for the first one so actually point number two alone is also enough to figure out that X is equal to 60 you actually didn't even have to figure it out and an important skill eventually when you're when you're taking the GMAT is to be able to just look at it and say oh I can figure that out and then move on instead of actually having to figure out that X is equal to 60 but anyway so this one is either of them alone are sufficient so that's D okay problem number seven problem number seven what percentage of a group of people are women with red hair so women we want women with red hair percentage okay so statement number one tells us of the women in the group five percent have red hair five percent of women have red hair that alone doesn't tell me what percentage of the entire group have are women with red hair because I don't know how large the whole group is there could be um you know there could be I don't know 20 women and there could be ten million men so you know the percentage or there could be 20 women and no men so that still doesn't help me with you know what percentage of women what percentage of the group are women with red hair see statement number two statement number two tells us where was that of the men in the group ten percent have red hair so 10 percent of men have red hair that's really useless have red hair once again I don't know how big the group is right I mean you you think about it if I have 20 women then that tells me that there's one woman with red hair and I don't know I have 20 women right but I still don't know how many men there are right if there are 20 women and one has red hair there could be a million men there could be no men in which case this answer would turn out very different what percentage of the group are women with red hair so both of these combined are fairly useless questions and actually let me let me draw a little Venn diagram because I think it's it's useful so the entire group is both women and men let me I'll draw a vent of a Venn rectangle instead of a so that's women and men so some percentage of you know we don't know how many women there are and how many men so this this area right here is women this is women that's the number of women and this is the number of men and this first point tells us a five percent of the women have red hair so it just tells us that five percent of this area is red right which is maybe I don't know how I ball it's like that and then this says that ten percent of the men have red hair so maybe that area looks something like that all right so we know the ratio of this to this box and we know the ratio of this to this box is 10 percent but we don't know the ratio of this to the entire universe because we don't know how many we don't know what the total we don't know the total population sizes so we'll never be able to figure it out anyway so that is that is e all right problem number 8 maybe maybe I missed something but that's problem 8 if R and s are positive integers are is what percent of s so R s positive integers and we want to know R is what percent of s so essentially we just want to figure out what R over s is equal to right this will give us some decimal and then you multiply by 100 and you know the percentage so if you can figure out this you can figure out the percentage of what what press R is what percentage of s ok so statement number one statement number one they tell us that R is equal to 3/4 s well let's just do a little algebraic manipulation we're just trying to get R over s so let's divide both sides by s so you get R over s is equal to 3 over 4 so there we got it we got the answer this is what that was a helpful data point all we needed was that data point actually let's see what the second data point gives us data point 2 R divided by s well they they wrote it like this they wrote it the way you did in second grade R divided by s is equal to 75 over 100 well that's just another way of just writing R over s is equal to 75 over 100 which is exactly the same thing as this so these are actually you know equivalent statements almost so each of them independently are enough to figure out R / s or what percentage are is of s all right problem number 9 problem number 9 let me draw a line you don't to get too messy 9 in magenta is it true that a is greater than B sometimes find these statements kind I don't know slightly humorous is it true that a is greater than B anyway okay all right the first statement is 2 a is greater than 2 B so I don't know if you remember from algebra but you can operate on inequalities the exact same way you can operate on equality Zoar are young as you call them equations and you just have to remember that if you multiply or divide by a negative number that you have to swap the inequality sign well luckily in this case we're we are we are we could divide both sides by a positive number so if you're doing if you're multiplying or dividing by 2 positive on both sides you don't have to change the inequality so just divide both sides by two and you could test that with numbers just to see why that makes sense so you divide both sides by two and you get a is greater than B so that's all we needed we just need a statement one now let's see what statement two does for us statement two tells us that a plus C is greater than B plus C well once again this is a we can subtract C from both sides of this equation or from both sides of this inequality without changing the inequality sign right so you subtract C from both sides and once again you get a is greater than B so each of these statements independently are enough for us to figure out that it is true that a is greater than B let's do one more actually I've run out of chalkboard space so I might as well just wait until the next video see you soon