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GMAT: Data sufficiency 11

51-54, pgs. 281-282. Created by Sal Khan.

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Video transcript

Problem 51. Actually, let me scroll all the way up, problem 51. They drew a little triangle here, which I assume I need, so I'll draw it as well. That side is flat and that side goes down like that, and then they draw some angles. This is being angle x, this is angle y, this is angle z. And they say, what is the value of z in the triangle above? Fair enough. Statement number one is x plus y is equal to 139. Well, as soon as you see a triangle and you have to figure out one side, you should always remember that the sum of the angles of a triangle add up to 180. So we know that x plus y plus z is equal to 180. Statement one just told us that x plus y is equal to 139. So we know from statement one that this is 139. So that would just make this equation 139 plus z is equal to 180. Which is very easy to solve. Subtract 39 from both sides which you get z is equal to 41 or something like that. It doesn'nt matter, you don't have to get the answer. You just have to know that you can get the answer. So statement one, alone, is enough. Now what do they give us in statement number two? Statement two, y plus z is equal to 108. This statement alone is useless. We don't know what y is. So we can't figure it out. I mean, one thing is true, if you had both of these statements, then you can figure out all of the angles of the triangle. Because you know that z is 41 then you could figure out y, then once you know y you could figure out x. But they're not asking us that. We need to figure out what angle z is. And this statement alone would not tell us what angle z is because we don't know what angle y is. But statement one alone works. So the answer is A. Next problem. Turn the page. 52. If x y and z are non-0-- they could have written x times y times z does not equal 0 because that's the same thing. Because if any of them were 0, it would have been equal 0. So I could have written xyz does not equal 0. Because if you multiply three non-0 numbers it's not going to equal zero. But anyway, they're asking is xz equal to 12? xz equal to 12 is the question. Statement one tells us-- and I'll do it in a different color-- e is the monotony. Statement one tells us that x squared times yz is equal to 12xy. So let's see what we can do. What if we were to divide both sides of this equation by xy? Well, let's divide both sides by x first. So if you divide both sides by x, and we can do that because we know that x does not equal 0. soon. Divide both sides by x, you get xyz is equal to 12y, right? Divided by x on both sides. Now let's divide both sides by y. You get xz is equal to 12. And we're done. Statement alone is enough. And remember, the only reason why we we're able to divide both sides by y is because we knew it didn't equal 0. Now what does statement two tell us? Statement two tells us that z/4 is equal to 3/x. And here we can cross multiply, x times z is equal to 3 times 4. And if that didn't make sense to you, you could do it one step at a time. Multiply both sides by 4, you get z is equal to 12/x, just multiplied both sides by 4. Then multiply both sides by x and you get xz is equal to 12. So each statement, independently, is enough to solve the equation. So that's D. I always have to keep looking back and looking at which letter I have to say. I should memorize that. You should at least, you have to take the GMAT. Alright, 53. A certain company currently has how many employees? So we want to know the number of emps. How many employees. OK. So statement number one: if 3 additional employees are hired by the company and all of the present employees remain, there will be at least 20 employees in the company. So let's say e is the number of employees today. So e plus 3. So the current number of employees and three additional are hired and all of them remain. There will be at least 20 employees in the company. So it at least tells us greater than or equal to 20 employees. That's what statement one is. And that by itself doesn't tell me how many employees are at the company. It tells us that there at least 17 employees at the company but it doesn't tell us anything else. I mean you can subtract 3 from both sides and you say e is greater than or equal to 17. But e could be 100. I don't know. OK. Statement two: if no additional employees are hired by the company and 3 at the present employees resign-- so e minus 3-- there will be fewer than 15 employees at the company. So fewer than 15 employees. So not 15 or lower. They say fewer than 15, so less than 15. Right here they said at least 20, so that's greater than 20, greater than or equal to. Here they said fewer than, they didn't say 15 or fewer, they said fewer than 15. So if you simplify this you get-- add 3 to both sides-- you say e is less than 18. So, let me ask you a question. First of all this by itself isn't helpful because this just tells us we could only 5 employees at the company or we could have 10. This doesn't tell us by itself. But if we use both of these in conjunction, you if we know that e is less than-- so if we say 17 is less than or equal to e. I just wrote this in a different order. Alright, 17 is less than or equal to e, which is less 18-- I'm using both statements-- what is e? It has to be greater than or equal the 17, so it could be 17. Can it be 18? Well, no, because it has to be less than 18. So e has to be 17. So both statements together are needed to solve this problem. And that is C. Both statements, together, are sufficient. Next problem. 54. Let me erase this little 5 I drew here. 54. Alright, what is the value of n in the equation minus 25 plus 19 plus n is equal to s? Well, just to simplify it, we could add up minus 25 plus 19, you get minus 6? So you get n minus 6 is equal to s, right? That's right. Actually, you don't have to do this. Remember the whole point of this is to figure out whether you can solve the problem. You don't always have to solve it but I'm solving them here just to prove it to you. To give you the intuition of when you can solve it. So if you add 6 to both sides. So anyway, this was just a simplification. Let's read the statements. I haven't read them yet. Maybe I didn't have to do any of that. Alright, what problem was I-- 54. OK. s is equal to 2. Well, clearly, if we know that s is equal to 2, we can solve for n. n would be equal to 8. This statement alone is sufficient. Now statement number two tells us n/s is equal to 4, and once again, as long as we have some relation with n and s and we can solve for s and then substitute back in, we can solve for n. And to prove it, let me do it. We have n is equal to 4s, and if we know that n is equal to 4-- what are we doing? We're trying to solve for n. We could write s is equal to n divided by 4. And then you can substitute back into that equation. So then you would get n is equal to s, which is n/4 plus 6. And then you could just solve for n. And if you want to do it, let's see, multiply both sides by 4, you get 4n is equal to n plus 24. That's an equal sign not a not-equal. I just multiplied both sides by 4. 4n is equal to n plus 24. Subtract n from both sides, you get 3n is equal to 24 and then you get n is equal to 8 again. So each statement alone is sufficient. And that is-- I should really memorize this-- that's D. Each statement alone is sufficient. OK. Let's see, do I have time for 55? Let me wait for that for the next video. See