GMAT: Math 18

We're on problem 96. It says 1/2 plus, open brackets, 2/3 times 3/8 divided by 4 minus 9/16. Do you know order of operations, and can you deal with fractions? 2/3 times 3/8, the 3's cancel out, and the 2 and the 8 become 1/4. 1/4 divided by 4, let me write this, 1/2 plus 1/4 divided by 4, that's the same thing as times 1/4, minus 9 over 16. So that is equal to 1/2 plus 1/16 minus 9/16. And now it doesn't matter what order we do it in, but since everything's in 1/16ths, so let me write this in 1/16ths. So this is 8/16 plus 1/16 minus 9/16. So that's equal to 8 plus 1 minus 9 all over that 16. That's 9 minus 9, that equals 0. Choice E, all that work to get to 0. Next problem, 97. Water consists of hydrogen and oxygen, and the approximate ratio by mass of hydrogen to oxygen is equal to 2:16. Approximately how many grams of oxygen are there in 144 grams of water? OK, 144 grams of water, that means that the oxygen and hydrogen is equal to 144. They say 144 grams of water, not when you have 144 grams of hydrogen. So when you add these together, you have 144. And then they tell us that the ratio of hydrogen to oxygen is 2:16. Or another way to write it, you can say hydrogen over oxygen is equal to 2/16, which is another way of saying 1/8. And they want to know how many grams of oxygen, so we want to solve for oxygen, so we want to substitute for hydrogen. So we could say hydrogen is equal to 1/8th the oxygen. I just multiplied both sides times oxygen. So if hydrogen is equal to 1/8 oxygen, you have oxygen plus 1/8 oxygen, let me make sure that's right. Yeah, hydrogen to oxygen is equal to 144. And if you view this as 8/8, 1 oxygen is the same thing as 8/8, so you get 9/8 oxygen is equal to 144. So you get oxygen is equal to 144 times 8 over 9. Does 9 go into 144? I think it should, let me see how many times does 9-- 3 definitely does. This is 12 times 12, so 3 will go into 144 48 times. 9 goes into 144 1, 9, 54, 16 times. So this is equal to 16 times 8 over 1, which is what? That's equal to 250-- no, that can't be right. No, you can't have more grams of oxygen than you do-- let me see, I've made a mistake someplace. Hydrogen to oxygen is equal to 2:16, which is 1:8. Oxygen plus hydrogen is equal to 144, you get 9/8. Oh, I see my mistake. That's good. I've been making a lot of careless mistakes, maybe I need to take a rest. 9/8 oxygen is equal to 144, so oxygen is equal to 144 times 9 over 8-- sorry, times 8 over 9. I was doing it right, so where was my mistake? So 144 times 8 over 9, that's equal to-- oh, I just made a mistake at the very last step. 9 goes into 144 16 times. 16 times 8 isn't 256, it's 128. That was my mistake. So there's 128 grams of oxygen. I just made a mistake right at that last step. All right. And that's choice D. Question 98. If x times 2x plus 1 is equal to 0, and they also tell us that x plus 1/2 times 2x minus 3 is equal to 0, then x is equal to what? So this is interesting. x times 2x plus 1 is equal to 0, that means that either x or 2x plus 1 has to be equal to 0. So one of these has to be equal to 0. But then x plus 1/2 times 2x plus 3, this tell us that one of these have to be equal to 0. So if x is equal to 0, then this has to be the one that's equal to 0. So either this and that is equal to zero, or-- do you see that? Well I guess both of these could be equal to 0. Let me multiply them out. Maybe I'm going down the wrong path. If I multiply these out, I get 2x squared plus 2 is equal to 0. If I multiply these out, I get x times 2x, which is 2x squared, x times minus 3 minus 3x, 1/2 times 2x, so it's plus x. And then 1/2 times minus 3 minus 3/2 is equal to 0, so I get what? 2x squared minus 2x. 3x plus x is minus 2x, minus 3/2 is equal to 0. Actually I think I made a mistake, x times 2x plus 1, that's not right. That's 2x squared plus x is equal to 0. Fair enough. We know 2x squared, so we can just write that 2x squared is equal to minus x, and then substitute this information in here. So we get minus x, 2x squared is equal to minus x. Minus x minus 2x minus 3/2 is equal to 0. So you get minus 3x, let's add 3/2 to both sides, is equal to 3/2. And then divide both sides by minus 3, you get x is equal to 3/2 times minus 1/3, so that equal to minus 1/2. And that is choice B. Next problem, 99. On a scale that measures the intensity of a certain phenomenon, a reading of n plus 1 corresponds to an intensity that is 10 times the intensity corresponding to a reading of n. So n plus 1 is equal to 10 times the reading of just an n. On that scale, the intensity corresponding to a reading of 8 is how many times as great as the intensity corresponding to reading of 3? So if you call a reading of 3, I don't know, let's call that a 1. A reading of 4 is going to be 10 times the reading of 3. A reading of 5 is going to be 10 times that, so 100. A reading of 6 is going to be 10 times that, or 1,000. A reading of 7 is going to be 10 times that, or 10,000. And then a reading of 8 would be 10 times that, so it would be 100,000. Which is not one of the choices. Let me make sure I'm reading that. On a scale that measures the intensity of certain phenomenon, a reading of n plus 1 corresponds to an intensity that is 10 times the intensity corresponding to a reading of n. So a reading of 4 is 10 times the intensity of a reading of 3, and a reading of 5 is 10 times that. Fine. On that scale, the intensity corresponding to a reading of 8 is how many times as great as the intensity corresponding to a reading of 3? A reading of 4 would be 10 times as great, a reading of 5 would be 100 times as great, a reading of 6 would be 1,000 times as great. Oh yeah, 100,000, which is 10 to the fifth. 10 to the fifth power. Five 0's, so that is choice C. Confusing myself unnecessarily, and I'm out of time. See you in the next video. Let me stop this one.