Learn for the GMAT Math 46 Video

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Learn for the GMAT Math 46

All right, I re-read the question and now I realized what the error in my logic. I misread the question. I had misread it and I said, “Oh, there’s seven 60 siblings.” No, there are 60 sibling pairs, so that means in each class there are 60 sibling pairs it means there are 120 siblings but that tell us in each class there aren’t 30. There are 60 members of a sibling group. So let's go back through our logic again. Let’s say we have picked someone from the junior class first, what is the probability that I even picked someone from a sibling pair. That’s going to be 60/1000 which is the same thing as 6/100 which is the same thing as 3/50, right? Fair enough, so there are three in 50 chance that I picked someone who’s a member of a sibling pair. Now in order for me to have a complete sibling pair when I go to the senior class and pick someone I have to be pick this junior sibling and that junior only has one sibling in the senior class so there's only one in 800 chances that I picked their sibling. It doesn’t matter that the other 59 siblings in that are useless because they're not this guy sibling. So I have one in 800 change of doing that and you multiply them you get 3/40,000 and that is choice A. If you don’t see your choice, make sure to read the question again. We’re on problem 218, which of the following cannot be the median of the three positive integers x, y and z. So the median, the middle number they say a is x, oh no, that’s not true what if this was the order XYZ then x is will be the median so it’s not A, B, Z no reason why Z can't be the median or can be wise the x it's not B. C, x + z, well let’s see could x + z be the median. Let me think about it. If we have x, z and y, I mean by definition one of these numbers have to be the median we have three numbers one of them has to be middle number under what circumstances does x plus—I mean if x + z is the median that implies that x + z has to be that neither x nor z is the median, right? But they tell us that those are positive integers. None of these are zero. So in order for x + z to be the median that tells us that neither x nor z is the median, right and if neither x nor z is the median then y has to be the median and then that tells us that x + z has to be equal to y. But if y is the median the order is this XYZ and there's no way that I can add x and z. You get a smaller number than z because all of these numbers are positive. Yeah, they said three positive integers so I go with choice C that cannot happen the median cannot be x + z. Problem 219, what is the 25th digit to the right of the decimal point in the decimal form of 6/11? Whenever they ask you for something ridiculous there must be some type of pattern we can exploit to figure out what the 25th digit is. So let’s just start dividing. 11 goes into 6 we’re going to have some decimals there, 11 goes into 60 five times, five times 11 is 55 and remainder five and you go into 50. You get a 4, four times I already see the pattern 44. Oh no! Never mind but let me make sure that’s right, 55 you get 50 remainder 11 goes into 50 four times you get 40 so then you get 60, 11 goes into 60 five times and you repeat so on and so forth. So I just want to make sure you see the first digit to the right is 25. The second digit to the right is four, the third digit to the right is five and so you know we could keep going the fourth digit to the right is four, so every odd digit to the right of this is what? It’s five, so they want to know the 25th digit to the right and that’s an odd number 25 so it has to be five as well so that’s choice C. Next question, question 220, John and Mary were each paid x dollars in advance to do a certain job together, fair enough. John worked on the job for ten hours and Mary worked two hours less than John so Mary work eight hours. If Mary gave y dollars of her payment so that they would have received the same hourly wage, what was the dollar amount in terms of y that John was paid in advance? Okay, John and Mary were each paid x dollars in advance to do a certain job together. Okay, so John got x dollars and Mary got x dollars. They both got x dollars, right. So if you think about it let's ignore who did what, right? We had how many total hours of labor? We had 18 hours of labor and they were paid how many dollars? They were paid 2x dollars for 18 hours of labor. So the average wage should be and you can kind of view of the per hourly wage should be, and so you can divide by nine into one and you get the nine you get x/9 dollars per hour. What was x/9 dollars per hour? That’s the fare wage. Let me read again the question. If Mary gave John y dollar of a payment so that they would had the same hourly wage what was the dollar amount in terms of y that John was paid in advance. Actually let's think about it this way. So were each paid x dollar in advance to a certain job. John worked on the job for ten hours and Mary worked two hours less than John. If Mary paid John y dollars of her payment so that they would receive the same hourly wage so after Mary pays John y so that means John he got a total of y dollars and Mary has paid y dollar so now John has x + y and Mary has x – y dollars. And so if Mary paid over her payments so that they would receive the same hourly wage what was the dollar amount in terms of y that John was paid in advance? So let me think about this a little bit. So they receive the same hourly wage. So Mary should have 8/10 the money of John, right? So x – y should be equal to 0.8(x + y). Am I thinking about that right or is there an easier way to think about it. Well let's think about it this way, John worked two hours more than Mary, right. However, so Mary essentially if she pays him for one hour. Yeah, this is the right thing x – y is equal to 0.8(x + y) but I'm going to still end up with an x here so you get x – y is equal to 0.8x + 0.8y, right and all the logic here I just said is well Mary is total money is we’re going to be fair should be 0.8 of John’s total money because she worked 0.8 as much hours. And so let’s see, and actually they want to know what John was paid in advance so that’s x. Okay we’re fine so these want to know what x is in terms of y so we’re cool. So let's subtract 0.8x from both sides so we get 0.2x - y = 0.8y and then add y to both sides you get 0.2x = 1.8y and then multiply both sides by five you get x is equal to—what is that? 5 x 18 is 50 + 40 add a decimal point is 90 is equal to 9y and that is choice E. I got a little confuse with the wording of them when they say what was the dollar on in terms of y that John was paid in advance. They should have said what was x and that would be a little bit easier. Anyway, I'm all out of time, I'm starting for bumbling through that problem see you in the next video.

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All right, I re-read the question and now I realized what the error in my logic. I misread the question. I had misread it and I said, “Oh, there’s seven 60 siblings.” No, there are 60 sibling pairs, so that means in each class there are 60 sibling pairs it means there are 120 siblings but that tell us in each class there aren’t 30. There are 60 members of a sibling group. So let's go back through our logic again.

Let’s say we have picked someone from the junior class first, what is the probability that I even picked someone from a sibling pair. That’s going to be 60/1000 which is the same thing as 6/100 which is the same thing as 3/50, right? Fair enough, so there are three in 50 chance that I picked someone who’s a member of a sibling pair. Now in order for me to have a complete sibling pair when I go to the senior class and pick someone I have to be pick this junior sibling and that junior only has one sibling in the senior class so there's only one in 800 chances that I picked their sibling. It doesn’t matter that the other 59 siblings in that are useless because they're not this guy sibling. So I have one in 800 change of doing that and you multiply them you get 3/40,000 and that is choice A. If you don’t see your choice, make sure to read the question again.

We’re on problem 218, which of the following cannot be the median of the three positive integers x, y and z. So the median, the middle number they say a is x, oh no, that’s not true what if this was the order XYZ then x is will be the median so it’s not A, B, Z no reason why Z can't be the median or can be wise the x it's not B. C, x + z, well let’s see could x + z be the median. Let me think about it. If we have x, z and y, I mean by definition one of these numbers have to be the median we have three numbers one of them has to be middle number under what circumstances does x plus—I mean if x + z is the median that implies that x + z has to be that neither x nor z is the median, right?

But they tell us that those are positive integers. None of these are zero. So in order for x + z to be the median that tells us that neither x nor z is the median, right and if neither x nor z is the median then y has to be the median and then that tells us that x + z has to be equal to y. But if y is the median the order is this XYZ and there's no way that I can add x and z. You get a smaller number than z because all of these numbers are positive. Yeah, they said three positive integers so I go with choice C that cannot happen the median cannot be x + z.

Problem 219, what is the 25th digit to the right of the decimal point in the decimal form of 6/11? Whenever they ask you for something ridiculous there must be some type of pattern we can exploit to figure out what the 25th digit is. So let’s just start dividing. 11 goes into 6 we’re going to have some decimals there, 11 goes into 60 five times, five times 11 is 55 and remainder five and you go into 50. You get a 4, four times I already see the pattern 44. Oh no! Never mind but let me make sure that’s right, 55 you get 50 remainder 11 goes into 50 four times you get 40 so then you get 60, 11 goes into 60 five times and you repeat so on and so forth.

So I just want to make sure you see the first digit to the right is 25. The second digit to the right is four, the third digit to the right is five and so you know we could keep going the fourth digit to the right is four, so every odd digit to the right of this is what? It’s five, so they want to know the 25th digit to the right and that’s an odd number 25 so it has to be five as well so that’s choice C.

Next question, question 220, John and Mary were each paid x dollars in advance to do a certain job together, fair enough. John worked on the job for ten hours and Mary worked two hours less than John so Mary work eight hours. If Mary gave y dollars of her payment so that they would have received the same hourly wage, what was the dollar amount in terms of y that John was paid in advance? Okay, John and Mary were each paid x dollars in advance to do a certain job together. Okay, so John got x dollars and Mary got x dollars. They both got x dollars, right. So if you think about it let's ignore who did what, right? We had how many total hours of labor? We had 18 hours of labor and they were paid how many dollars? They were paid 2x dollars for 18 hours of labor.

So the average wage should be and you can kind of view of the per hourly wage should be, and so you can divide by nine into one and you get the nine you get x/9 dollars per hour. What was x/9 dollars per hour? That’s the fare wage. Let me read again the question. If Mary gave John y dollar of a payment so that they would had the same hourly wage what was the dollar amount in terms of y that John was paid in advance. Actually let's think about it this way.

So were each paid x dollar in advance to a certain job. John worked on the job for ten hours and Mary worked two hours less than John. If Mary paid John y dollars of her payment so that they would receive the same hourly wage so after Mary pays John y so that means John he got a total of y dollars and Mary has paid y dollar so now John has x + y and Mary has x – y dollars. And so if Mary paid over her payments so that they would receive the same hourly wage what was the dollar amount in terms of y that John was paid in advance? So let me think about this a little bit. So they receive the same hourly wage.

So Mary should have 8/10 the money of John, right? So x – y should be equal to 0.8(x + y). Am I thinking about that right or is there an easier way to think about it. Well let's think about it this way, John worked two hours more than Mary, right. However, so Mary essentially if she pays him for one hour. Yeah, this is the right thing x – y is equal to 0.8(x + y) but I'm going to still end up with an x here so you get x – y is equal to 0.8x + 0.8y, right and all the logic here I just said is well Mary is total money is we’re going to be fair should be 0.8 of John’s total money because she worked 0.8 as much hours. And so let’s see, and actually they want to know what John was paid in advance so that’s x. Okay we’re fine so these want to know what x is in terms of y so we’re cool. So let's subtract 0.8x from both sides so we get 0.2x - y = 0.8y and then add y to both sides you get 0.2x = 1.8y and then multiply both sides by five you get x is equal to—what is that? 5 x 18 is 50 + 40 add a decimal point is 90 is equal to 9y and that is choice E.

I got a little confuse with the wording of them when they say what was the dollar on in terms of y that John was paid in advance. They should have said what was x and that would be a little bit easier. Anyway, I'm all out of time, I'm starting for bumbling through that problem see you in the next video.

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