Annoying maths question

[Trader]

WTF? The answer is 21 days. If he's got enough money to pay both of them, then you go with the lowest common denominator which is the carpenter, and he's got some cash left over to go buy beer.

...unless the wording of the question is incorrect.

Did that, and this is what I read in the original post:

He has enough to pay a plumber for 28 days and a carpenter for 21 day.

After re-examining that question, yes it is worded rather ambiguously.

It could be read in the same manner you read it as: 'He has enough to (pay a plumber for 28 days and a carpenter for 21 days)'

Or it could be read in this manner: 'He has enough to pay plumber for 28 days, and (implied: enough to pay) a carpenter for 21 days'

It's like in real life when your friend says: 'I have enough money to buy a Lexus and a BMW.'

Usually you would interpret that to be: 'My money is enough so that it allows me to afford a Lexus or a BMW.' You wouldn't think: 'Your friend has enough money to buy BOTH the Lexus and BMW.'


But I agree, the wording is very suspect

 

[search1ng]

In my haste to get the question up i may have worded it incorrectly. It's what Trader initially though. Enough to pay a plumber for 28 days OR a carpenter for 21 days. But BOTH must be working together.

 

[cordoncordon]

Think of 28P = 21C as a relationship. P and C can't be any old numbers in the sky, P & C have to follow this stringent relationship, which acts as a constraint to the number of possibilities. Once you have the that constraint, PLUS the additional fact that you only have enough money to hire a plumber for 28 days, no more, no less, is enough information to figure out how how long you can hire both the plumber AND the carpenter for.

It's like me telling you: 'I want to ask out one of the girls in this room, can you guess who she is? And there are 100 girls in the room.'

Then I tell you a constraint: 'Well, she is between 5'2 and 5'5, has blond hair, she is wearing a white dress.' then that really does reduce the number of girls that it could be.

Then I give you one more key fact: 'Her hair is long, past her shoulders.'

Well that's enough information for you to figure out the right girl.

For those of you that aren't algebra freaks, like me, there is a MUCH easier way to figure this out than with formulas. I was put ahead in my math classes in school, but always struggled with the formulas. Adding, subtracting, dividing, multiplying, figuring out answers to questions like this? All easy for me and I can do it faster than anyone I know (which might be why I love the stock market), but start laying these formulas on me? My eyes glaze over.

Anyway, OP, go into questions like this.....using common sense. This literally took me about 10 seconds to figure out. Since the question tells you how many days the guy has enough money for to pay either the carpenter or the plumber for their work, you just assign a random number to how much money the guys has to pay them, doesnt matter what it is. Let's say he has $100 to pay either one for their work in total.

So you simply take $100 and divide that by the plumbers 28 days, which means he can pay the plumber $3.57 a day. Then take $100 and divide it by the carpenters 21 days, which means he can pay him $4.76 per day. Add $3.57 and $4.76 together and you come up with $8.33, which is the average cost of paying both together on the same day. Since he only has $100 to spend, you then divide $100 by the $8.33, and you come up with the answer....12 days.

The thing is, you could give the guy ANY number for a value in which he could spend on the tradesmen, lets say $1,000,000,000, and the answer still will be 12...everytime.

 

[Trader]

For those of you that aren't algebra freaks, like me, there is a MUCH easier way to figure this out than with formulas. I was put ahead in my math classes in school, but always struggled with the formulas. Adding, subtracting, dividing, multiplying, figuring out answers to questions like this? All easy for me and I can do it faster than anyone I know (which might be why I love the stock market), but start laying these formulas on me? My eyes glaze over.

Anyway, OP, go into questions like this.....using common sense. This literally took me about 10 seconds to figure out. Since the question tells you how many days the guy has enough money for to pay either the carpenter or the plumber for their work, you just assign a random number to how much money the guys has to pay them, doesnt matter what it is. Let's say he has $100 to pay either one for their work in total.

So you simply take $100 and divide that by the plumbers 28 days, which means he can pay the plumber $3.57 a day. Then take $100 and divide it by the carpenters 21 days, which means he can pay him $4.76 per day. Add $3.57 and $4.76 together and you come up with $8.33, which is the average cost of paying both together on the same day. Since he only has $100 to spend, you then divide $100 by the $8.33, and you come up with the answer....12 days.

The thing is, you could give the guy ANY number for a value in which he could spend on the tradesmen, lets say $1,000,000,000, and the answer still will be 12...everytime.

Agreed, that is one way to do it, you simply substitute any number for T and use concrete values instead of variables.

But the downside is that this method is computation heavy and on timed exams such as the GMAT where you are not even allowed to use a calculator, trying to plow through 100 divided by 28, and 100 divided by 21 might not be so wise.

To each his own.

 

[SmoothTalker]

This has already be solved but I figured I'd throw mine in, maybe somebody that didn't understand the other solution can follow mine.

First, it isn't worked too clearly because it says you have enough money to pay a plumber for 28 days and a carpenter for 21 days. If we take AND to mean you can pay both like this, then this I think this is unsolvable because you have only one equation and 3 unknowns. I mean what if the plumber costs the exact same amount as the carpenter (possible under this interpretation) then the ratio is meaningless, it could just as easily be 25 and 24 or 20 and 29 days, etc.

If however it means that we can pay a plumber for 28 days OR a carpenter for 21, it's fairly straightforward to solve.

First, let m be the total amount of money we have, p the daily wage of the plumber, and c the daily wage of the carpenter.

Then we know m =28 p and m = 21c, so 28 p must equal 21c. Dividing both sides by 28 we get 1p = 21/28 c, or p = 3/4 c. So a plumber costs 3/4 of a carpenter.

Then to pay both of them you would have to pay the carpenters wage and the plumber's wage, which is 1c + 3/4 c = 4/4 c + 3/4 c = 7/4 c.

But we know our total money m = 21 c, so just divide total money by the daily rate, 21c /( (7/4) *c) = 12 days.