Learn for the GMAT: Math 17 Video

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Learn for the GMAT: Math 17

Problem 92, in the certain furniture store each week Nancy earns a salary of $240.00 plus 5% of the amount of her total sales that exceeds 800 for the week, plus 5% of whatever is greater than 800 for the week. If Nancy under total of $450.00 in a week what were her total sales that week. So she earns $450.00 right, so what was her kind of her 5% bonus parts. So 450 minus 240 so she got $210.00 bonus. So, $210.00 represents 5% of her sales above 800. So 2% to 5% of what number, all right so let divide, so you could say 210 is equal to .05 times x right and x will be her sales above 800. So x is equal to 210 divided by .05 so .05 goes into 210 add some decimal points so that’s the same thing a five going into the decimal point there 21,000. So five goes into 21 four times four times five is 20 bring down one to two, five goes into 10 two times, two times minus 10 were done. So her sales were 4200 but that’s not her total sales remember she only gets 5% on her sales above 800 so she sold $4,200.00 more than $800.00 that week. So her total sales are going to be 4,200 plus 800 which is $5,000.00. All right, 4,200 plus 800 and that’s choice E. Next question 93, okay this goes little two list. So that’s list one and they give it let's three, six, eight, 19 and this goes list two and they say it's x, three, six, eight, 19 so it's actually the same list except for they have an x here. If the median of the number is in list one above is equal to the median of the numbers in list two above, what is the value of x. So what's the median of this list? Well it's, since we have an even number of numbers it's going to be the average of the middle two numbers. So, what is the middle two numbers right here? The middle two numbers are six and eight, the average you could be on six plus eight divided by two and seven. So the median is seven, the median is equal to seven. So they're telling us the median of this list is also equal to seven. So where can I put x so that the median doesn’t change but what if x is seven? Right, if x is seven and this must becomes three, six, seven, eight, 19 and now the middle number since we have odd numbers is actually the middle the number. We don’t do this averaging business, so now the median is actually seven. If you place seven there, so x equals seven, choice B. 94, in a certain city 60% of the registered voters are democrat and the rest are republican. So democrat is equal to 60% of voters and republican is equal to the rest. So 40% of the voters, in a mayor, in a mayoral race if 75% of the registered voters who are democrats and 20% of the registered voters who are republicans expected to vote for candidate a what percentage of the registered voters are expected to vote for candidate a. Okay, the mayor is at 75% of democrat so .75 democrats are voting for candidate a and 20% of republicans, so plus .2 time the republicans are expected to vote for candidate a what percentage of the of the voters are voting for candidate a. So let's just express this in terms of the total voters. And the republicans the democrats are 60% of the voters republicans are 40% of the not the republicans of the voters, right. So .75 times the democrats, so democrats are 60% of the voters so they’ll just substitute .6 voters for d so we get .75 times .6 of all the voters that’s the number of democrats there are. Plus .2 times the republicans, republicans are .4 times all of the voters. And so let's see, what is 75 times six? 75 times six let me just do the whole decimal .75 times .6, six times five is 30, six times seven is 42 plus three is 45. And we have one, two, three numbers behind the decimal point. So it's .45 of the voters plus, it's a two times four is eight and we have two numbers behind the decimal so it's plus .08 times the voters. .45 Plus .08 that’s .53 right, your have 45 plus eight is .53 or 53% of the voters are going to vote for candidate a and that’s choice B. Problem 95, a certain company retirement plan has a rule of 70 provisions that allows an employee to retire when the employee’s age. So they're employee’s age plus years of employment, plus years of employment within the company total at least 70, so greater than or equal to 70. In what year could a female employee hired in 1986, so 1986 is interesting, 1986 on her 32 birthday first to be eligible to retire under this provision. Okay, so what is, so let's say that y is equal to the year, right? Her age, her age is going to be the years minus 1986 right plus 32, that’s her age. Because that’s how much she is you know she starts at 32 so 1980 if years is 1986, were just going to get her age is 32, right. If year’s 1987 were going to get 1987 minus 1986 which is one year plus 32 her age will be 33 so that’s her age. Her experience at the—plus her years of employment are going to be the years minus 1986, right. So a plus e is going to be equal to this and so that is equal to what? 2y minus two times 1986 plus 32 it have to be greater than or equal to 70 just to have to multiply two times 1986 let's divide both sides of this equation by two and I don’t have a change in the quality because that’s positive. So I get y minus 1986 plus 32 is greater than or equal to 70 and then let's see. So y is greater than or equal to 70, let me add 1986 to both sides plus 1986 minus 32, minus 32. So it's 1986, minus 32 that’s 1954 right, eight minus three is five, six minus two is four, right. It was 70 plus 1954 plus 70, four, is five plus seven is 12, one plus nine is 10, so 2024 is an acceptable year for her. 2024 and that is not one of the choices, so I clearly made a mistake. Let me see where I might have made a mistake. So a certain employee retirement has a rule of 70 provisions that allows an employee before retiring. When employees age, age plus years of employment within the company to let at least 70, right age plus years of employment to at least 70 in what year could a female employee, in fact that she’s female it shouldn’t matter. Female employee hired in 1986 on her 32 birthday, first be eligible to retire under this provision. Okay, her age is going to be the year that she would, whatever you were talking about minus 1986 plus 32 and then her years of employment are going to be whatever you were talking about minus 1986 fair enough. Fair enough and then two times, so of the year plus the year and I have two subtractions of my 1986 plus 32 is greater than or equal to 70, I divided both sides by, oh, I see my mistake. Here this stuff right here where I decided to divided both sides by two I divide only the left side by two, right. That by two, that by two, oh, I didn’t even do that, so two times 1986 divided by two is 1986 32 divided by two is 16, 70 divided two is 35, okay. So let me rewrite it here. So essentially I have, so that’s what happens when you try to do too much at ones. So I have y, is greater than or equal to 35 plus 1986 minus 16 right. I just added 1986 to both sides subtracted 16 from both sides. So this is equal to 1970, 1970 all right and then we have 35 plus 1970, so y has to be greater than to equal to 2005 which is choice C and I'm out of time sorry for that careless error. And I’ll see you in the next video.

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Problem 92, in the certain furniture store each week Nancy earns a salary of $240.00 plus 5% of the amount of her total sales that exceeds 800 for the week, plus 5% of whatever is greater than 800 for the week. If Nancy under total of $450.00 in a week what were her total sales that week. So she earns $450.00 right, so what was her kind of her 5% bonus parts. So 450 minus 240 so she got $210.00 bonus.

So, $210.00 represents 5% of her sales above 800. So 2% to 5% of what number, all right so let divide, so you could say 210 is equal to .05 times x right and x will be her sales above 800. So x is equal to 210 divided by .05 so .05 goes into 210 add some decimal points so that’s the same thing a five going into the decimal point there 21,000. So five goes into 21 four times four times five is 20 bring down one to two, five goes into 10 two times, two times minus 10 were done. So her sales were 4200 but that’s not her total sales remember she only gets 5% on her sales above 800 so she sold $4,200.00 more than $800.00 that week. So her total sales are going to be 4,200 plus 800 which is $5,000.00. All right, 4,200 plus 800 and that’s choice E.

Next question 93, okay this goes little two list. So that’s list one and they give it let's three, six, eight, 19 and this goes list two and they say it's x, three, six, eight, 19 so it's actually the same list except for they have an x here. If the median of the number is in list one above is equal to the median of the numbers in list two above, what is the value of x. So what's the median of this list? Well it's, since we have an even number of numbers it's going to be the average of the middle two numbers. So, what is the middle two numbers right here?

The middle two numbers are six and eight, the average you could be on six plus eight divided by two and seven. So the median is seven, the median is equal to seven. So they're telling us the median of this list is also equal to seven. So where can I put x so that the median doesn’t change but what if x is seven? Right, if x is seven and this must becomes three, six, seven, eight, 19 and now the middle number since we have odd numbers is actually the middle the number. We don’t do this averaging business, so now the median is actually seven. If you place seven there, so x equals seven, choice B.

94, in a certain city 60% of the registered voters are democrat and the rest are republican. So democrat is equal to 60% of voters and republican is equal to the rest. So 40% of the voters, in a mayor, in a mayoral race if 75% of the registered voters who are democrats and 20% of the registered voters who are republicans expected to vote for candidate a what percentage of the registered voters are expected to vote for candidate a. Okay, the mayor is at 75% of democrat so .75 democrats are voting for candidate a and 20% of republicans, so plus .2 time the republicans are expected to vote for candidate a what percentage of the of the voters are voting for candidate a.

So let's just express this in terms of the total voters. And the republicans the democrats are 60% of the voters republicans are 40% of the not the republicans of the voters, right. So .75 times the democrats, so democrats are 60% of the voters so they’ll just substitute .6 voters for d so we get .75 times .6 of all the voters that’s the number of democrats there are. Plus .2 times the republicans, republicans are .4 times all of the voters. And so let's see, what is 75 times six? 75 times six let me just do the whole decimal .75 times .6, six times five is 30, six times seven is 42 plus three is 45. And we have one, two, three numbers behind the decimal point. So it's .45 of the voters plus, it's a two times four is eight and we have two numbers behind the decimal so it's plus .08 times the voters. .45 Plus .08 that’s .53 right, your have 45 plus eight is .53 or 53% of the voters are going to vote for candidate a and that’s choice B.

Problem 95, a certain company retirement plan has a rule of 70 provisions that allows an employee to retire when the employee’s age. So they're employee’s age plus years of employment, plus years of employment within the company total at least 70, so greater than or equal to 70. In what year could a female employee hired in 1986, so 1986 is interesting, 1986 on her 32 birthday first to be eligible to retire under this provision. Okay, so what is, so let's say that y is equal to the year, right?

Her age, her age is going to be the years minus 1986 right plus 32, that’s her age. Because that’s how much she is you know she starts at 32 so 1980 if years is 1986, were just going to get her age is 32, right. If year’s 1987 were going to get 1987 minus 1986 which is one year plus 32 her age will be 33 so that’s her age. Her experience at the—plus her years of employment are going to be the years minus 1986, right.

So a plus e is going to be equal to this and so that is equal to what? 2y minus two times 1986 plus 32 it have to be greater than or equal to 70 just to have to multiply two times 1986 let's divide both sides of this equation by two and I don’t have a change in the quality because that’s positive. So I get y minus 1986 plus 32 is greater than or equal to 70 and then let's see. So y is greater than or equal to 70, let me add 1986 to both sides plus 1986 minus 32, minus 32. So it's 1986, minus 32 that’s 1954 right, eight minus three is five, six minus two is four, right.

It was 70 plus 1954 plus 70, four, is five plus seven is 12, one plus nine is 10, so 2024 is an acceptable year for her. 2024 and that is not one of the choices, so I clearly made a mistake. Let me see where I might have made a mistake. So a certain employee retirement has a rule of 70 provisions that allows an employee before retiring. When employees age, age plus years of employment within the company to let at least 70, right age plus years of employment to at least 70 in what year could a female employee, in fact that she’s female it shouldn’t matter.

Female employee hired in 1986 on her 32 birthday, first be eligible to retire under this provision. Okay, her age is going to be the year that she would, whatever you were talking about minus 1986 plus 32 and then her years of employment are going to be whatever you were talking about minus 1986 fair enough. Fair enough and then two times, so of the year plus the year and I have two subtractions of my 1986 plus 32 is greater than or equal to 70, I divided both sides by, oh, I see my mistake. Here this stuff right here where I decided to divided both sides by two I divide only the left side by two, right. That by two, that by two, oh, I didn’t even do that, so two times 1986 divided by two is 1986 32 divided by two is 16, 70 divided two is 35, okay. So let me rewrite it here.

So essentially I have, so that’s what happens when you try to do too much at ones. So I have y, is greater than or equal to 35 plus 1986 minus 16 right. I just added 1986 to both sides subtracted 16 from both sides. So this is equal to 1970, 1970 all right and then we have 35 plus 1970, so y has to be greater than to equal to 2005 which is choice C and I'm out of time sorry for that careless error. And I’ll see you in the next video.

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