how do you do these QR word problems??

[Tina324]

Advertisement - Members don't see this ad

1. It takes 5 painters 12 days to paint a certain office. How long would it take 6 painters to paint an office with 50 percent more wall space?

2. If N is any positive integer, how many consecutive integers following N are needed to insure that at least one of the integers is divisible by another positive integer m?

m-1, m, m+1, 2m, or m^2

3. Mrs. Parson's gross salary in 250 dollars per week. If her employer deducts 15% from the 1st $10,000 earned in a year, and 20% from the earnings between $10,000 and $15,000 in a year, how much moey does Mrs. Parson take home in one year (52 weeks)?

$21,000; $10,900; $11,050; $11,540; or $12,650

4.How many of the three-digit numbers containing no digits other than 2,3, or 4 are divisibe by 3? (what is quick way of doing this??)

5. Suzanne picks 60 percent more apples than Sam in the same amount of time, and Bert picks 5% more than Suzanne in the same amount of time. If Bert picks apples for one hour and Same picks apples fo 1.5 hours, what is Bert's output expressed as a percentage of Sam's?

6. A manufacturer decreses the price of its washing machines from $600 to $400. If the cost if 1/2 of the original sellign price, by what percentage must the number of machines sold increase so that the company's profits will remain the same?


THese are from subject test 1 (kaplan) just in case ya wanna kno ;-)
better explanations would be veryyy verry appreciated🙂

 

[Streetwolf]

1. It takes 5 painters 12 days to paint a certain office. How long would it take 6 painters to paint an office with 50 percent more wall space?

6 painters is 6/5 the amount of help which means it takes 5/6 the time which would be 10 days. With 50% more space, that's 3/2 the space which means it would take 3/2 the time. That's 15 days.

2. If N is any positive integer, how many consecutive integers following N are needed to insure that at least one of the integers is divisible by another positive integer m?

m-1, m, m+1, 2m, or m^2

Sorry but this one will be a long explanation.

Answer is m-1. You have a positive integer N and I give you another positive integer m. Now I ask you, can you do N/m and get an integer? If not, can you do it with N+1? If not, how about N+2? And so on until you hit something that works. The question is asking you to consider the "worst case scenario" in a sense - find the greatest possible distance between N and the number that can divide by m evenly. Think about m. What happens when you divide a number by m? What can the remainders be? It can go in evenly and be 0. There can be remainder 1, 2, 3, etc up until m-1. Need an example? Consider m = 5. You can have remainder 0, 1, 2, 3, or 4.

Now think about N and m. You want to GUARANTEE that one of the numbers above N will divide by m evenly. Think of an example. Let's say N = 101 and m = 10. Does 101/10 work? No. Remainder is 1. How about 102/10? Remainder 2. Go all the way up to 109/10 and you get remainder 9. Using 110/10, you get remainder 0 - it goes in evenly. The best case scenario here is if N/m gives you an integer (remainder 0). The WORST case scenario is if N/m gives you remainder 1. Then every number after it adds on to the remainder until it finally divides evenly again. In our example with 101 and 10, you can see that we started with remainder = 1 and we went up to 2, 3, 4, etc until we hit 9. At that point we cycle back around to remainder = 0.

Notice that the remainder only goes up to m-1. If we start with remainder 1, we need to add m-2 numbers to get up to remainder m-1. Then by adding 1 more number, you cycle back to remainder = 0. That's a total of m-1 numbers. For our example, with m = 10, you need to consider the next 9 numbers. One of them will DEFINITELY divide by 10. Remember that we also consider the starting number of N, so this is a total of 'm' numbers we are considering. That's why it works. Given 'm' consecutive numbers, one of them will ALWAYS divide evenly by 'm'.

3. Mrs. Parson's gross salary in 250 dollars per week. If her employer deducts 15% from the 1st $10,000 earned in a year, and 20% from the earnings between $10,000 and $15,000 in a year, how much moey does Mrs. Parson take home in one year (52 weeks)?

$21,000; $10,900; $11,050; $11,540; or $12,650

To start off, you make 250/week with a 15% deduction. It takes 40 weeks to hit $10,000 at which point you only earn 85% which is 8500. There are 12 more weeks in the year at 80% of your salary which ends up being 2400. In total you make $10,900. Unless I misinterpreted this problem.

4.How many of the three-digit numbers containing no digits other than 2,3, or 4 are divisibe by 3? (what is quick way of doing this??)

The only options are numbers with one of each digit (ie 234, 423, etc) or numbers with 3 of the same digit. Nothing else works. You just need to see this quickly or write down every option. The numbers are 222, 333, 444, and the 6 combos using 1 of each number. Total is 9 possibilities.

Some answers in bold. I need to run out of the house now so if no one gets to these in the next couple hours I'll come back for the rest.

 

[Streetwolf]

5. Suzanne picks 60 percent more apples than Sam in the same amount of time, and Bert picks 5% more than Suzanne in the same amount of time. If Bert picks apples for one hour and Same picks apples fo 1.5 hours, what is Bert's output expressed as a percentage of Sam's?

Let s = Suzanne, a = Sam, and b = Bert.

s = 1.6a
b = 1.05s

Compare Bert to Sam (b to a): b = 1.05(1.6a) = 1.68a.

Bert picks 68% more apples than Sam in the same amount of time. But the question says Sam picks apples for 3/2 the amount of time as Bert. If Sam picked 100 apples then Bert picked 168 apples in the same time. Since Sam goes for 3/2 the time, Sam ends up picking 150 apples. To make things simple you can bring that back to 100 by multiplying by 2/3 on both of them. Sam would be at 100 and Bert at 2/3(168) = 112. Remember that these are just relative numbers. The question asks for percentage. So Bert would pick 12% more than Sam if Bert picks for 1 hour and Sam for 1.5 hours.

I put Sam's back at 100 to make the percentage part simple. Otherwise you'd have had to figure out what percentage of 150 is 18 (168-150).

6. A manufacturer decreses the price of its washing machines from $600 to $400. If the cost if 1/2 of the original sellign price, by what percentage must the number of machines sold increase so that the company's profits will remain the same?

Okay so the cost was 1/2 of 600 = 300 so the original profit was 300. The new profit is only 100. So you'd need 3 machines sold instead of 1 to match the original profit. That's a 200% increase ( [ (3-1) / 1 ] * 100% ).

THese are from subject test 1 (kaplan) just in case ya wanna kno ;-)
better explanations would be veryyy verry appreciated🙂

Answers in bold.

 

[Tina324]

dude u are absolutely amazing..thanks so much..ok imm need time to let this all sink in lol