GMAT: Math 27

We're on problem 138. At a loading dock, each worker on the night crew loaded 3/4 as many boxes as each worker on the day crew. So that means that the boxes per night crew worker is equal to 3/4 the number of boxes per day crew worker. If the night crew has 4/5 as many workers as the day crew-- the number of night crew workers is going to be 4/5 times the number of day crew workers. What fraction of all the boxes loaded by the two crews did the day crew load? So, how many boxes will the day crew load? The day crew is going to load the number of day crew workers times the boxes per day crew worker. And they want to know what fraction of all of the boxes loaded is this? So that'll be the numerator, and the denominator will be all the boxes loaded. So all the boxes loaded are going to be the boxes loaded by the day crew. So that's the number of workers times the boxes per worker, plus the number of boxes loaded by the night crew. That's going to be the number of night crew workers times the number of boxes per night crew worker. And to simplify this, if we could just substitute these variables with things that look a lot more like that. And lo and behold, we have easy substitutions to tell us what b sub n is, the boxes per night crew worker. And they tell us what the number of night crew workers are in terms of the day crew workers. So let's just substitute. So this is equal to day crew workers times boxes per day crew worker, divided by day crew workers times boxes per day crew workers, plus, what is the number of night crew workers? It's w sub n, but that's the same thing as 4/5 w sub d. And then what are the number of boxes per night crew worker? That's 3/4 times the boxes per day crew worker. The 4's cancel out. Actually, we could simplify this. We can divide the top and the bottom by this w sub d times b sub d, and you get 1 over 1 plus-- all of these cancel and you're just left with 3/5. That's equal to 1 over 8/5, which is equal to 5/8. And that is choice E. Next problem, 139. A restaurant meal costs $35.50 and there is no tax. If the tip was more than 10% but less than 15% of the cost of the meal, then the total amount must have been-- So what's the range for the tip? 10% of $35.50. That's just going to be $3.55. And 15%-- there's a couple ways you can think about it. You could say it's half more than this. What's half of this? Half of this is $1.77 1/2. I think that's right. soon. Really, you can't get a half-cent. Is that right? 2 times that, you get 2. And 2 times 70 is $1.40. So this would be 5%. I just took half of this That's how people do it. Half of 10%. If where you live, the tax is 10%, but I don't want to get into that. So if you add this to this, you get 4, 5, 12, 13, and 5. So the tip is going to be between $3.55 and $5.33, I guess we could say. And so the total bill, that's what they want to know, we just add both of these. So at minimum, you're going to pay what's this plus $35? So $35.50 and $3.55. 5, 10, 9. $39.05. And at the high end, you have $35.50. And then you have $5.33. And that is equal to 3, 8, 0, 1, 4. So your total bill is going to be between $39 and $41. And that is exactly choice B. They just round up. They say $41 is here and $39 is here. If it's between these 2 numbers, it's definitely between $39 and $41. And that's choice B. Problem 140. In a weightlifting competition, the total weight of Joe's two lifts was 750. So l1, his first lift plus the second lift was 750 pounds. If twice the weight of the first lift was 300-- If 2 times the first lift was equal to 300 more than the weight of his second lift, what was the weight in pounds of his first lift? So we just want to solve for l1. So this top equation we can rewrite as l2 is equal to 750 minus l1. Then we can substitute that here. So then you get 2 times l1 is equal to 300 plus l2, which is this, plus 750 minus l1. Add l1 to both sides. You get 3 l1 is equal to 300 plus 750. That's 1,050. And 3 goes into 1,050-- 3 times 3 is 9, 15, 3 goes into 15 5 times, so it's 350. So his first lift was 350 pounds. And that's choice D. Problem 141. A club collected exactly $599 from its members. If each member contributed at least $12, what is the greatest number of members the club could have? So the more that each member contributed, the smaller you the number of people in the club. If each member contributed at least $12-- so what is the greatest number of members the club could have? So if they all contributed exactly $12-- 12 goes into 600 50 times. So if this number were $600, you could say if $600 were collected in increments of at least $12, then you could have at most 50 people. But we don't have $600. $600 would be 50 times 12. We have $599. $599 can be done by at most not 50 people, but at most 49 people. Let's think about it. Let's make sure that that's right. So my answer is 49, which is C. And let's think about how much money would be left over, so 49 times 12. This is just a reality check. 49 times 12. 2 times 9 is 18. 2 times 4 is 8 plus 1 is 9. 0, 49. 8, 18, 588. So if you have 49 people, and they all contribute $12 exactly, you'll raise $588. And then you could have had a couple of other people, you could have had 11 other people who instead of $12, they paid $13. And that's how you get to $599, because they say at least $12. You can't have 50 people, because 50 people, if they contribute at least $12, you would have to raise at least $600. So it can't be 50, so the answer is 49. And you might say why did you go immediately to $600? And a lot of times on the GMAT, where they have these numbers that are 12 and 599-- those are strange numbers. You say 599 is awfully close to 600. Let's see if I can use that information to deduce something interesting about this problem. Anyway, next problem, 142. Of the 3,600 employees of Company x, 1/3 are clerical. So clerical is equal to 1/3 times 3,600, which is equal to 1,200. If the clerical staff were to be reduced by 1/3, what percentage of the total number of remaining employees would then be clerical? We're going to reduce the clerical staff by 1/3, so how many people are we going to get rid of? So 1/3 of 1,200 is what? It's 400. So the clerical staff is now going to be 1,200 minus 1/3, minus 400, which is equal to 800. So what proportion is this of the remaining employees? So clerical is 800, and how many remaining employees are there? Are there 3,600? No, we've gotten rid of 400 employees who were clerical. So now we have 3,200 employees. 3,600 minus 400, so that is equal to 1/4. And that's A, 25%. Problem 143. Actually, I'm out of time. I'll continue this in the next video. See