GMAT: Math 3

We're on problem 12. 0.1 plus 0.1 squared plus 0.1 to the third. So that's the same thing as 0.1. What's 0.1 squared? It's 1 times 1 with 2 numbers to the right of the decimal, so it's 0.01. And then to the third power. You're just going to end up 1/10 of that, right? 0.01 times 0.1. Well that's 1 with 3 numbers to the right of the decimal point. If I'm going to add them all up, I get 1, 1, 1. And that is answer B. They're making sure you can multiply your decimals. Problem 13. If you have trouble with decimals, you might want to get on the Kahn Academy-- the actual application, it's free-- and just work through the basic arithmetic, because we have actually a bunch of things on multiplying decimals and stuff. You have to start at 1 plus 1, but it makes sure you don't have any holes in your knowledge. It eventually gets to algebra and trigonometry and calculus. You might find that useful. Anyway, question 13. A carpenter constructed a rectangular sandbox with a capacity of 10 cubic feet. If the carpenter were to make a similar box twice as long-- 2 times length-- twice as wide-- 2 times width-- and twice as high as the first sandbox, what would be the capacity in cubic feet of the second sandbox? So you might want to visualize it, right? The best way to visualize it is probably how many of the old ones could fit? So if this was one of the old ones, and now I'm going to make a new one that's 2 times the size in every dimension, right? That's 2 times the height. So essentially, I could increase the width by 2. Increase the depth by 2, or whatever you want to call it. Right? And then I'm going to increase the height by 2. And I'm going to have trouble drawing. So how many of the original sandboxes-- that's what they want to know-- how many of the original sandboxes essentially could fit into the new one? Well, 2 in 1 direction times 2 times 2. So 2 times 2 times 2 is equal to 8. So another way to think of it, you could view the old sandbox as almost a unit, like one cubic unit sandbox. And now we're going to go 2 in every direction. So we could fit 8 of the old sandboxes into the new one. And the old one had a capacity of 10. So 8 times that is equal to 80 cubic feet, which is choice D. Question 14. And these, at least so far, I think these are on the easier end. They'll probably get harder, but so far they're a lot faster than the data sufficiency ones. Which of the following cannot be a value of 1 over x minus 1? And I think this is one of the ones where we have to look at the choices. 1. Negative 1. So can we pick x so this is negative 1? Well sure, if x is equal to 0, 1 divided by negative 1 is negative 1. So it's not negative 1 because that can be a value for that. 0. Well, this is interesting. How can we ever make this equal to 0? The only way we can get this close to 0 is if the denominator becomes a really huge number, right? But it'll never be equal to 0. It'll just be a really, really, really small fraction. This approaches 0 as x approaches infinity. But this will never equal 0. So the answer is B. All of the other things are completely possible. You just have to realize, you should just see choice B, and is like, how could this ever equal 0? Because the numerator is never equaling 0. This can only approach 0 if the denominator gets really, really, really big. It will just become a really small fraction. But it'll never, ever equal 0. And you could even try. 1 over x minus 1 is equal to 0. You can try to solve it. If you multiply both sides by x minus 1, you get 1 is equal to 0. It's impossible. Undefined. 15. A bakery opened yesterday with a daily supply of 40 dozen rolls. Half of the rolls were sold by noon. 1/2 by noon. And 80% of the remaining rolls were sold between noon and closing time. 80% remaining, noon and closing. How many dozen rolls had not been sold when the bakery closed yesterday? OK, half sold by noon. So 20 sold by noon. And 20 left. Right? And they said 80% of the remaining rolls were sold between noon and closing time. So we could view it two ways. If you wanted to do it really fast, you're like, OK, 20% of the remaining rolls will not be sold. Right? So you could say 20% of the remaining rolls-- so times 20-- don't get sold, right? If 80% get sold, 20% don't get sold. And that equals what? We could say 20 times 20 is 400. Two spaces behind the decimal point. And that makes sense. 20% is 1/5. So 1/5 of 20 is 4. So 4 rolls don't get sold when it closed. You could do it the other way around. You could say, OK, how many sold between, at this time, 80% of 20 is 16 more sell. 16 sell. And then you can say, OK, how many total were sold? Well, 20 plus 16, 36. And then 40 minus 36 is also 4. It takes a little bit more time, but it gets you the same answer. Eventually time is what you'll have to focus on. Once you are confident that you can get every problem right. What is the combined area in square inches of the front and back of a rectangular sheet of paper measuring 8.5 by 11? So it's essentially going to be 2 times 8.5 times 11. If you just multiplied 8.5 times 11, that would give you the area of one side. So we want the area of both sides. It's going to be 2 times that. And I want to do this first, just so I can get rid of this mixed number. So 8.5 times 2. That's 17, times 11, which is going to be what? 17 times 11 is 170. Because that's 17 times 10, plus 17. So that's 187. That's choice E. Let's do problem 17. 150 is what percent of 30? So 150 is equal to x percent of 30 times 30. Or another way we could write that is-- well, let me just write it as a variable. Let's figure it out as a decimal. And then once you know a decmial, it's easy to convert that. So 150 is equal to x of 36 or 36x. This is some number times 36. Divide both sides by 36. You get x is equal to 150/36. Let's see, I think we can divide the top and the bottom. Definitely we can divide them by 6. 6 goes into 150 25 times. And it goes into 36 6 times. Right? Oh wait, what am I doing? It's 30. My own handwriting got me caught up. This is a much easier problem than what I was doing. They're saying 150 is what percent of 30, right? So it's x times 30. This is easy. You divide both sides by 30. I mistakenly wrote 36 there. Divide both sides by 30, you get 5 is equal to x, right? If you wanted to write 5 as a percentage, you just multiply both sides by 100. So you could say x is equal to 500%. And that makes sense. 150 is 5 times 30. 100% of 30 is 30. 200% of 30 is 60. And so forth. So 500% of 30 is 150. That took me too long I think. E. Got to make sure your handwriting is good. Next question. 18. The ratio 2:1/3 is equal to-- Well, 2 divided by 1/3 is equal to 2 times 3/1, which is equal to 6/1. So 2:1/3 is the same thing as the ratio of 6:1, which is choice A. Right? 2:1/3 is equal to 6:1. Another way to think about it is 2 is 6 times 1/3. And 6 is 6 times 1. Same thing. So 18 is A. Next question. 19. Running at the same constant rate, 6 identical machines can produce a total of 270 bottles per minute. At this rate, how many bottles could 10 such machines produce in 4 minutes? OK, so how much does each produce per minute? So 1 machine will produce 270 divided by 6 bottles per minute. Right? That's one machine. I just divided both sides by 6. 6 machines produce that. So 10 machines would produce 10 times as many per minute. So 10 times this is 2,700 divided by 6 bottles per minute. And if they want to know how much 10 machines are going to produce in 4 minutes, you just multiply this times 4. So this is how much they produce in 1 minute, so the answer's going to be 2,700 times 4 divided by 6. So let me see if I can do this math fast. So 6 is equal to 2 times 3. If you divide 2,700 by 3, that's 900. And 3 divided by 3 is 1. And then 4 divided by 2 is 2. So 900 times 2 is equal to 1,800. And that is choice B. And I'm all out of time. See you in the next video.