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problem 33 asks what distance did Jane travel Jane travel what distance does she travel so one bill traveled 40 miles in 40 minutes bill 40 miles in 40 minutes are essentially a mile a minute which 60 miles an hour whatever a 1 mile a minute right that's what we could figure out one mile per minute per minute that has no information about how far did Jane travel it's useless to Jane traveled at the same average rate as Bill so that tells us that Jane also if she'd go into the average rate of bill that means that she also went one mile per minute but we're not asking for how fast did Jane travel or what was her average rate we're asking for how far did she travel so with statements 1 & 2 combined all we know is Jane's rate but we don't know how long she traveled for so we don't know the distance so the answer is e that both statements together are not sufficient if if statement 2 told us that Jane traveled at the same rate as Bill and she traveled at that rate for 10 minutes then we would we would be able to solve this problem but it didn't so even with both pieces information we still don't know how far Jane traveled me now how fast she traveled 34 what number is 15 percent of X so what we want to know is 0.15 X that's what we're trying to solve for statement 1 tells us 18 is 6 percent of X 18 is 6 percent of X so you normally wouldn't even have to solve for it you all you know is by looking at this statement you couldn't solve for X and if you can solve for X then you can just multiply that times 0.15 and you'll have the answer to the original statement so you immediately know that statement 1 is if you don't believe me you can just write this out of this equation 18 is equal to 6% of X and then you just solve for X so 18 divided by 0.06 and then multiply it times 0.15 and you get your answer problem number two our statement number two 2/3 of X is 200 2/3 of X is equal to 200 once again all you you look at this you say this is a simple equation I can solve for X here if I solve for X here then I just substitute it back here and I will know what 15% of X is and I would be done so each of these statements individually are sufficient to answer our question what is 15% of X 35 now if I have to go through the exercise of actually solving for that because I think you understand what I'm talking about 35 oh I like these so they say 30 3.2 rectangle rectangle triangle or Delta 6 and they say if rectangle and Delta or triangle each represent single digits in the decimal above okay so this is a decimal I thought that it might be operation so this is a decimal so it's four digits behind the decimal spot what does rectangle represent so we want to know what does this decimal what what's the digit right here so the statements statement number one tells us when the decimal is rounded to the nearest tenth 3.2 is the result the nearest tenth so when you round what you do is you look at if we're rounding to the nearest tenth we look at this number right we look at the rectangle and if the rectangle is 5 or greater we would round up so we would get to three point three if the rectangle is less than five is then we would round down to two so we know this statement number one tells us that rectangle is less than five and we know it's it's greater than or equal to zero because it's a digit so it's zero one two three or four right so because it's zero two three or four that's rectangle but that by itself does not allow us to figure out what rectangle is now statement number two statement number two tells us when the decimal is rounded to the nearest hundredths to the nearest hundredth three point two four is the result three point two four is the result when you round to the nearest hundredth okay so this is this is interesting now okay so this number here is either going to be so when you're rounding to something it's either going to be either rounding down or rounding up so this tells us so this number right here can either be three so we already know it can be zero one two or three or four but which of these numbers when you round them could be rounded up or down to four well if if we have if the triangle you know this could be two three five right one let me give you one scenario we could have two three point let me three point two three five six right where this is the rectangle and this is triangle so this would round to three point two four you could also have three point two four one six where this is the rectangle and this is the triangle and either of these would round to three point two four so this tells us essentially that the rectangle has to be either three or four has to be three or four but and and this tells us that it's either 0 1 2 3 or 4 but even when you use them individually they don't tell you exactly what the rectangle is and we use them together you can just narrow down to three or four which just statement two alone tells you so this actually turns out that when you use both statements together you still can't get the answer you'd either need a third term there or we would have to have a little bit more information about what the triangle is if they told us that the triangle is it is you know rounds upward you know is greater than five or less than five or something like that then we could figure out what the rectangle is so the answer here is e if I haven't missed something that they're together both statements are not sufficient to answer the question thirty-six the profit from the sale of a certain appliance increases though not proportionally with the number of units sold the profit it increases but not proportionally with the number so it's not you know the profits do not equal just some constant times units it equals you know maybe some constant times units squared or something like that did the profit exceed four million on sales of 380,000 units so is profit greater than four million this one's interesting when units when units is equal to 380 okay let's see if we can figure this out so they say that the profit exceeds two million on sales of two hundred thousand so statement one says profit is greater than two million when units is equal to two hundred okay now if if they told us that the profit was proportional to units then we could say oh well if if we increase units from two hundred to 380 then we're not doubling the units so then we can't be well it still would be ambiguous because not saying it profit equals two they're saying that profit is greater than two so this actually still doesn't give me a lot of information statement number two I'm doing a different color statement number two says the profit exceeds five million on sales of so this isn't profit exceeds five million on sales of 350,000 units or 350,000 units okay so this is interesting so this tells us that when units are 350 up profit has already in there greater than five million so they're definitely greater than four million and noticed that that they told us that the profit from the sale of certain appliance increases though not proportionally with the number of units sold so if when we if we made more than five million dollars when there's 350 thousand units we know that when you go from 350 thousand to three hundred eighty thousand we know from the statement of the problem that the profit has to increase we don't know by how much but it's going to increase so the profit was already greater than five million it's going to increase above five million so statement two tells us that the profit is definitely gonna be above five million so it's definitely gonna be above four million so statement two alone is enough and statement one is actually tells us very little information because we don't know you know how there's a profit change as you incremental II add units maybe every every other you maybe every unit above two hundred thousand that you add you get like you know a millionth of a penny and then it you know it doesn't tell you anything or maybe you get a million pennies so it's very hard to tell problem number thirty actually let me see I'm already at ten minutes let me do that in the next video see you soon