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Current time:0:00Total duration:10:24

let's continue with the GMAT problem so we are on problem 16 on page 279 problem 16 is X greater than 1.8 is X greater than 1.8 that's all they're asking us and statement 1 says X is greater than 1.7 well that doesn't help us because I don't know X could be 1 point 7 1 in which case this wouldn't be true or X could be a million in which case this is true so this isn't really that helpful immediately see that statement number 2 says that X is greater than 1.9 well if you're greater than 1.9 you're definitely greater than 1.8 so this is all we need statement number two so B problem 17 problem 17 if n is an integer is n plus 1 odd n plus 1 odd well if n plus 1 is odd that's the same thing as asking is n even and I haven't looked at the statements yet but that's just something your brain might automatically connect and let's see what do they tell a statement one tells us that n plus 2 is even well if n plus 2 is even that n is definitely even then n is even if you don't believe me think about the number 4 4 is even and 4 plus 2 is 6 which is still even write it because if you add 1 you're going to go from even to odd yet to you go back to even right so this is all we need if n plus 2 is even then we know that n is even and that n plus 1 is odd and you could try it out with numbers if you don't believe me to put a statement to where did that number oh n minus 1 is odd well this is the same thing n minus 1 is odd once again this tells us that that n has to be an even number if you subtract 1 from it and you get an odd number it has to be even if you say that n is 4 4 minus 1 is 3 and try it for any even number and you know how I think it's I don't want to over explain what's a fairly simple problem so anyway the answer is that either of them alone are sufficient do try it out with numbers if you don't believe me problem 18 problem 18 is X between 1 & 2 is essentially what they're saying and it can't be 1 or 2 because these aren't equal signs they're just less than signs okay so that's what they're asking statement 1 tells us that X is essentially greater than 0 they wrote it a little different they said 0 is less than X so X is greater than 0 that doesn't help us X could still be 0.1 it could be still be 1/2 so that doesn't tell us where it is in this range and then the next and it could it could also be 100 in which case it's out of this range statement 2 tells us that X is less than 3 X is less than 3 so this alone doesn't help us we X could still be 2 point 1 or X could still be minus a million this doesn't help us and even if we took them together that would just tell us that 0 is less than X which is less than 3 which is a superset of this right if we know that X is in this range it doesn't tell us that X is definitely in this range for example if we know this is true X could still be equal to 1/2 but what ass isn't in this range X could be equal to 1.5 which is in the range or X could be equal to 2 point 5 which isn't in the range so both of these even taken together are not sufficient so the answer is e problem 19 these are going fast maybe too fast let me know if I'm going too too fast ok water is pumped into a partially filled tank at a constant rate through an inlet pipe at the same time water is pumped out of the tank at a constant rate through an outlet pipe okay so essentially we have a tank some water is let me there's a pipe here so water is going in at you know X we could say I don't know meters cubed per second or meters the unit's shouldn't matter and it's getting pumped out at Y I don't know meters cubed per second at what rate in gallons per minute okay so these aren't meter scoops for saying these are gallons per minute and these are gallons per minute at what rate in gallons per minute is the amount of water in the tank increasing so in order for the water to be increasing more has to be coming in than going out and the rate of it is going to be the difference so essentially they just want to know what X minus y gallons per minute up if X is less than Y and we get a negative number here then actually we have more coming out than going in and so the water isn't increasing so anyway they tell us that one the amount of water initially in the tank is 200 gallons that's useless why is that useless because that just tells us how much water is in the tank it doesn't tell us anything about the rates going in or out so this is that's useless to water is pumped into the tank at a rate of 10 gallons per minute so X is equal to 10 gallons per minute all right that's the rate you're pumping into it and out of the tank at a rate of 10 gallons every 2 and 1/2 minutes so Y is equal to 10 gallons per 2.5 minutes which is equal to what that's 4 gallons per minute so that second statement was a little bit with that second part of statement 2 is a little bit shady but you do that you get a Y it's 4 gallons per minute and so you actually don't have to figure it out but if you wanted to you could say that the rate at which water is increasing is the rate which is coming in at 10 minus 3 is going out so it's 6 gallons per minute is actually the answer of the question but all you have to know is that you just needed statement 2 which gave us this information to figure it out and statement 1 was useless so that's B statement two alone is sufficient let's do another one okay so we have problem number 20 problem number 20 is X negative x negative negative number okay the first statement they tell us that 9 X is greater than 10 X so this is this is this is an interesting situation so let's let's try to solve this equation let's subtract 10x from both sides of this equation and what if you're adding and subtracting on both sides of an equation inequality the inequality stays the same so let's subtract 10x from both sides of this so you get 9x minus 10 X is greater than 10x minus 10x and then you get minus X is greater than 0 or you can multiply both sides by negative 1 you get X and when you multiply or divide by a negative number with an inequality you switch the inequality X is less than 0 so we know that X is definitely negative you the other way you can done you can subtracted 9x from both sides and you're gotten 0 is greater than X which is a faster way of doing it but either way statement 1 lets us know that X is definitely negative let's see what statement 2 does for us statement 2 X plus 3 is positive x plus 3 is positive well I mean X could be a hundred if X is 100 then 103 is definitely positive or X could be negative 1 right because negative 1 plus 3 is positive 2 so this doesn't tell us any information about whether X is negative so this is useless so the answer is a statement 1 alone is sufficient statement 2 alone is useless see how much time do I have all I'm doing well on time it's clear I'm on problem 21 21 does 2m minus 3 n 2m minus 3 n equal 0 equals 0 and then the first and let's just think about they're also asking that's the same thing as asking this to M equal 3 n if you just add 3 into both sides these are equivalent questions so if you can answer one you can answer the other so statement 1 statement 1 says M does not equal 0 well that seems fairly useless to me I mean M does not equal 0 so M is is still you know I could pick a random n not equal to 0 and you'd get different you know depending on what n is this may or may not be true so I so far that seems kind of useless for me but maybe it's useful in conjunction with two the next thing they say is 6 m is equal to 9 n 6 M this one's interesting is equal to 9 n so what does this tell us so 6 M is equal to 9 n so if we do if we let's say let's divide both sides by let's divide both sides by 3 we get two M is equal to 3 N and then we can subtract 3 n from both sides and you get 2 m minus 3 n is equal to 0 so statement 2 I mean you essentially just do a little bit of algebra and you get what we're trying to prove so statement true 2 is good statement 1 do we need it at all well no because you know I mean that is kind of one solution that if m and n are both equal to 0 that this thing is is true but it doesn't it doesn't really do it much in the way of anything else and we don't need it for to come up with this so the answer is B statement two alone is sufficient and oh I'm already past 10 minutes so that's it I'll stop do 22 in the next video see you soon