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# GMAT: Math 4

## Video transcript

We're on problem 20. Of the 5 coordinates associated with points A, B, C, D and E on the number line above, which has the greatest absolute value? OK. Let me just draw the number line that they drew. And they say from 0 to 1. 0, 1, 2. And then they say minus 1, minus 2. And then they say these are choices A, B, C, D, and E. Of the 5 coordinates associated with the points A, B, C, D, and E on the number line above, which has the greatest absolute value? So you can view absolute value as the distance from zero So the greatest distance from zero is going to happen in two places. It's going to happen here at A. It's also going to happen here at E. Can you have more than one right answer? Because both of those are choices. Let's see. Indicate the best of the answer choices given. I'm looking up the thing. Is it possible to have more than one right answer? Because this doesn't seem quite right that I can have two possible answers for this one. The answer is A. The coordinate A is the farthest from zero. This has the greatest absolute value. I disagree with that. It could be choice E as well. The absolute value of the number x is the distance between x and 0 on the number line. The coordinate of point A is the farthest from 0, and thus has the greatest absolute value. That's false. I mean, that's true, but E is just as far. I don't know, I think they made a mistake. I think this could be choices A or E, because the absolute value of either of those is 2. I think they made a mistake. And they say the choice is A, which I agree with, but it could just as easily be choice E. So I don't know. Write a letter to GMAT. I mean, this seems pretty straightforward. Of the 5 coordinates associated with choices A, B, C, D, and E on the number line, which has the greatest absolute value? The absolute value of this point is 2. The absolute value of this point is 2. They're equal. Anyway. Next problem. I think it should be A or E. It's surprising that they would let a question like that get through their screen. Or at least they should get rid of choice E. If x and y are prime numbers, which of the following cannot be the sum of x and y? x plus y cannot equal what? So statement 1: 5. Well, I can immediately say 2 plus 3 is equal to 5. So that doesn't work. Cannot equal, so B. 9, I could do 2 plus 7 is equal to 9. This was A. This is B. Let's see what C is. So it's not B. C is 13. So let me think. What could it be? 11 plus 2 is equal to 13, so it's not choice C. D. 16. The sum. So let me see, 16. 9 and 7. No. 11 and 5. 11 plus 5 is equal to 16. So without even looking at E, it's probably going to be E. E , 23. Let me see if I can come up with two prime numbers that add up to 23. 19 and 4. No. Let's see. 2 and 21. No. First of all, we found examples for all of these, so if you don't want to waste time on the GMAT, you should already have chosen E and moved on by this point, but we could just look through a bunch of prime numbers and think if they can add up to 23, but I can't think of any right at the moment. And I feel pretty good that E is the answer, because I was able to find prime numbers that added up to all of the other four choices. Next question. 22. I'll switch colors just to ease the monotony. If each of the following fractions were written as a repeating decimal, which would have the longest sequence of different digits? Are they going to sit here and make us-- so let me write all the choices down. Maybe we can do some cancellation from the get-go. 2/11. B is 1/3. And we already know that that's just going to be 0.33 repeating. Longest sequence of different digits. So it's not going to be choice B because choice B doesn't have different digits. It just keeps being a 3, so it's not going to be choice B, so we don't have to worry about that. Choice C. 41/99. Choice D is 2/3. We know that that's 0.666. It just keeps going. So it's not going to be that. It's the same digit that just keeps repeating. And choice E is 23 divided by 37. So 2 divided by 11 repeats. Let's just try it, though. 11 goes into 2.000 one time. 1 times 11 is 11. You get a 90. 11 goes into 90 eight times. 88. It's 20. I already see the pattern. 11 goes into 20 two times. Sorry, it goes into 20 one time. 1 times 11 is 11. Then you get a 90. It goes into it eight times, so it's just 0.181818. It's just going to keep repeating 0.18. So that's 2/11. 41/99. Let me do it in a different color just so I don't get too messy. 99 goes into 41.0000. So 99 goes into 410 four times. 4 times 99 is what? 396. 4 times 9 is 6. 3. 4 times 9 is 36. Yep, 396. This is equal to 140. 99 goes into 140 one time. 1 times 99 is 99. This becomes 41. Already started repeating, right? 99 goes into 410. That's just like that. So it's going to be 0.41 repeating over and over again because we got the same number again. We're going 99 into 41 four times. We're going to get 396 and it's just going to keep happening. Then we're going to get 396. And then we're going to get 140 again. It's 41, 41. So it's 41 repeating. So if I had to guess, it's already going to be choice E, without having to do any work because these just have the same numbers repeating from the get-go. Choices A and C have the same two numbers repeating from the get-go. So I'm guessing that this one has a lot more. So if you just wanted to worry about time, you could just pick E and move on. But let's do it just to prove to ourselves. So 37 goes into 23. I don't remember when I took the GMAT having to do this much decimal division or decimal multiplication. So 37 goes into 230. I don't know. Does it go into it six times? No, probably five times. 5 times 7 is 35. 5 times 3 is 15, so it's 18, plus 3. OK. 30. 85. Actually, this would have gone six times. Let me change that to 6. Let me to it in a different color. I don't want to make it too messy. 6 times 7 is 42. 6 times 3 is 18, plus 4 is 22. 80. 37 goes into 80 two times. 2 times 37 is what? 74, right? 60 plus 14. 74. You get a 60. 30 is going to go into 60. So already we haven't even started repeating and we're already three digits into it. So this is going to have the longest sequence of different digits. We don't have to keep going. We've answered our question. The choice is definitely E. Next question. They've drawn something there. In the figure above the coordinates of point V are-- well, this is just kind of a reading the graph type of problem. I'm just going to draw this 4th quadrant just so that I can show you how I think about it. OK, so let me just count: one, two, three, four, five; one, two, three, four, five. They tell us that each of those slashes are 1, because they do it in a couple of places. They go one, two, three, four, five, and then they say this is negative 5. So that's information that you actually need. You have to know that each of those slashes are definitely 1. But then on this, they go one, two, three, four, five, six, seven. So they go one, two, three, four, five, six, seven, so this is point 7. And you have to just count it on your paper. So this is one, two, three, four, five. And this is point one, two, three, four, five. This is minus 5. And this is where V is. So they're just testing to see if you know how to graph a point. So this is x is 7. And y is minus 5. So it's 7 minus 5. And actually, that's interesting. You don't even have to count the points, because you say, you know what? This is in the 4th quadrant. x is positive. y is negative. And if you look at all the choices, there's only one choice where x is positive and y is negative, and that's choice E. So you really didn't even have to count it, although I think this wouldn't have taken much time to count it, so that's not like a huge shortcut. Anyway, see you in the next video.