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GMAT: Data sufficiency 4

16-21, pg. 279. Created by Sal Khan.

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Video transcript

Let's continue with the GMAT problems. We're on problem 16 on page 279. Problem 16. Is x greater than 1.8? That's all they're asking us. And statement one says, x is greater than 1.7. Well that doesn't help us because I don't know, x could be 1.71, 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. We immediately see that. Statement two 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? 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 us? Statement one tells us that n plus 2 is even. Well if n plus 2 is even, then n is definitely 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. Right? Because if you add 1, you're going to go from even to odd. You add 2, 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 n plus 1 is odd. And you could try it out with numbers if you don't believe me. Two. What is statement two? n minus 1 is odd. Well this is the same thing. n minus 1 is odd. Once again this tells us that n has to be an even number. If you subtract 1 from it and you get an odd number, then it has to be even. If you say that n is 4, 4 minus 1 is 3. And try it for any even number. I don't want to over-explain with a fairly simple problem. So anyway, the answer is either of them alone are sufficient, D. And try it out with numbers if you don't believe me. Problem 18. Is x between 1 and 2? Is essentially what they're saying. It can't be 1 or 2, because these aren't equal signs, they're less than signs. OK. So that's what they're asking. Statement one 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. It could also be 100, in which case it's out of this range. Statement two tells us that x is less than 3. So this alone doesn't help us. x could still be 2.1. 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 1/2 isn't in this range. x could be equal to 1.5, which is in the range. Or x could be equal to 2.5, 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 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. OK. So essentially we have a tank. There's a pipe here. So water is going in at, x-- we could say, I don't know-- meters cubed per second or-- units shouldn't matter. And it's getting pumped out at y meters cubed per second. At what rate in gallons per minute-- OK, so these aren't meters cubed per second, 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 are. 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 it just tells us how much water is in the tank. It doesn't tell us anything about the rates going in or out. So that's useless. Two. Water is pumped into the tank at a rate of 10 gallons per minute. So x is equal to 10 gallons per minute. That's the rate you're pumping into it. And out of the tank at a rate of 10 gallons every 2 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, that second part of statement two is a little bit shady, but you get a y. It's 4 gallons per minute. So you actually don't have to figure it. But if you wanted to, you could say that the rate at which water is increasing is-- the rate at which it's coming in at 10, minus the rate it's going out. So 6 gallons per minute is actually the answer to the question. But all you have to know is that you just needed statement two, which gives us this information to figure it out. And statement one was useless. So that's b, statement two alone is sufficient. Let's do another one. OK. So we have problem number 20. Is x negative? OK. The first statement, they tell us that 9x is greater than 10x. So this is an interesting situation. So let's try to solve this equation. Let's subtract 10x from both sides of this equation. And if you're adding or subtracting on both sides of an equation or inequality, the inequality stays the same. So let's subtract 10x from both sides of this. So you get 9x minus 10x is greater than 10 minus 10x. And then you get minus x is greater than 0. Or you can multiply both sides by negative 1. 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. The other way you could have done it, you could have subtracted 9x from both sides, and you would have gotten 0 is greater than x. Which is a faster way of doing it. But either way, statement one lets us know that x is definitely negative. Let's see what statement two does for us. Statement two. x plus 3 is positive. Well I mean, x could be 100. 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 one alone is sufficient. Statement two alone is useless. Let's see how much time I have. I'm doing well on time. I'm on problem 21. Does 2m minus 3n equal 0? And let's just think about this. That's the same thing as asking, does 2m equal 3n? If you just add 3n into both sides, these are equivalent questions. If you can answer one, you can answer the other. So statement one says, m does not equal 0. Well that seems fairly useless to me. I mean, m does not equal 0, so m is still-- I could pick a random m, not equal to 0, and depending on what n is, this may or may not be true. So far that seems kind of useless for me, but maybe it's useful in conjunction with two. The next thing they say, 6m is equal to 9n. This one's interesting. So what does this tell us? So 6m is equal to 9n. So let's divide both sides by 3. We get 2m is equal to 3n. And then we can subtract 3n from both sides. And you get 2m minus 3n is equal to 0. So statement two-- I mean, you essentially just do a little bit of algebra, and you get what we're trying to prove. So statement two is good. Statement one, do we need it at all? Well no, because-- I mean, that is one solution, that if m and n are both equal to 0, that this thing is true. But it doesn't really do as much in the way of anything else. And we don't need it, to come up with this. So the answer is b. Statement two alone is sufficient. I'm already past 10 minutes. So that's it. I'll do 22 in the next video. See you soon.