Annoying maths question

[search1ng]

Hey, I've been looking over some prepared questions for an upcoming exam similar to the LSAT.

Anyway, my brain doesn't seem to want to help with this question and I know i know this answer!

Anyway, please help shine a light on this question and share your reasoning behind it.

Mike needs to have his house renovated. He has enough to pay a plumber for 28 days and a carpenter for 21 day. for how many days can he hire the tradesmen if it is required that both the carpenter and plumber are working at the same time.

a. 10 days
b. 12 days
c. 15 days
d. cannot be determined.

 

[Rogue]

[edit: never mind]

 

[synergy1]

I tried doing this and I think there are too many unknowns to solve for the knowns. I tried to solve for a fraction of the time required to pay a plumber and carpenter but ended up with variables in the solution. Maybe one of my assumptions is wrong?

you can solve for the plumber rate as a function of carpenter rate, but since you don't know the total, you are left with the day fraction required to pay both and the total sum, so the former is a function of the later.

 

[Trader]

Hey, I've been looking over some prepared questions for an upcoming exam similar to the LSAT.

Anyway, my brain doesn't seem to want to help with this question and I know i know this answer!

Anyway, please help shine a light on this question and share your reasoning behind it.

Mike needs to have his house renovated. He has enough to pay a plumber for 28 days and a carpenter for 21 day. for how many days can he hire the tradesmen if it is required that both the carpenter and plumber are working at the same time.

a. 10 days
b. 12 days
c. 15 days
d. cannot be determined.

You have a plumber and a carpenter but the key is you want to convert everything into plumbers OR carpenters.

It's like algebra 101 where you try to convert everything in TERMS of X

Mike has enough to pay a plumber for 28 days. Algebraically: 28P = Cash, where P is the plumber's daily wage, and Cash is Mike's total cash.

Likewise, 21C = Cash.

Set both equations equal to each other.

28P = 21C.

P/C = 21/28

P/C = 3/4

So Mike wants to hire 1 plumber and 1 carpenter. Let's convert everything into plumbers.

1 plumber is, obviously 1 plumber.

To convert carpenters into plumbers

P/C = 3/4
C/P = 4/3
C= 4/3P

So when Mike hires 1 plumber and 1 carpenter, he really is hiring 1 + 4/3 = 7/3 plumbers, when you look at it in terms of how much wages he is paying out.

Well he can hire 1 plumber for 28 days before his money runs out. Obviously if he is hiring 7/3 plumbers, he can only hire them for SHORTER than 28 days. So for how many days exactly?

28 x (3/7) = 12 days

The answer is B.


To connect this with sexual attraction, girls find guys who think very logically to be attractive. Examine couples in a relationship, a girl will feel very frustrated if she is smarter than her bf.

 

[search1ng]

You have a plumber and a carpenter but the key is you want to convert everything into plumbers OR carpenters.

It's like algebra 101 where you try to convert everything in TERMS of X

Mike has enough to pay a plumber for 28 days. Algebraically: 28P = Cash, where P is the plumber's daily wage, and Cash is Mike's total cash.

Likewise, 21C = Cash.

Set both equations equal to each other.

28P = 21C.

P/C = 21/28

P/C = 3/4

So Mike wants to hire 1 plumber and 1 carpenter. Let's convert everything into plumbers.

1 plumber is, obviously 1 plumber.

To convert carpenters into plumbers

P/C = 3/4
C/P = 4/3
C= 4/3P

So when Mike hires 1 plumber and 1 carpenter, he really is hiring 1 + 4/3 = 7/3 plumbers, when you look at it in terms of how much wages he is paying out.

Well he can hire 1 plumber for 28 days before his money runs out. Obviously if he is hiring 7/3 plumbers, he can only hire them for SHORTER than 28 days. So for how many days exactly?

28 x (3/7) = 12 days

The answer is B.

Thank you so much to the guys that answered and especially to Trader! I got to the 3/4 by myself but then got confused. You answer is indeed what the answer says it is, and i see how you got there, but i just got a little confused over the bold part.

from 7/3 why was it flipped to 3/7 in the 'solving for number of days'?

 

[Trader]

Thank you so much to the guys that answers and to Trader! I got to the 3/4 by myself but then got confused. You answer is indeed what the answer says it is, and i see how you got there, but i just got a little confused over the bold part.

from 7/3 why was it flipped to 3/7 in the 'solving for number of days'?

Think of it as an inverse relationship.

If you have just enough money to hire a plumber for 28 days, how long could you hire double the plumbers (i.e. 2 plumbers) for? It is 14 days.

In other words, the reciprocal of 2, which is 1/2. 1/2 x 28 days = 14 days.

So how long could you hire 7/3 times the plumbers for?

28 days x (3/7) = 12 days.

The more plumbers you hire, the shorter amount of time you can employ them for given a certain wallet size.

 

[search1ng]

AH! bloody Ace.

Thanks Trader. Saved me from a night of tossing and turning in my bed.

EDIT: Btw, if you don't mind me asking, what do you do for a living?

Your mind seemed to grasp the problem fairy easily and I want to be able to do the same thing as i grow older.

 

[handle]

I had fun figuring that one out, cool, thanks for sharing

 

[taiyuu_otoko]

To connect this with sexual attraction, girls find guys who think very logically to be attractive. Examine couples in a relationship, a girl will feel very frustrated if she is smarter than her bf.

Then how come Spock only ever got laid when he lost his "logic-ness" due to some drug emitting flower?

Nice work on the problem, saved me from getting out pen and paper and trying it myself.

 

[Trader]

AH! bloody Ace.

Thanks Trader. Saved me from a night of tossing and turning in my bed.

EDIT: Btw, if you don't mind me asking, what do you do for a living?

Your mind seemed to grasp the problem fairy easily and I want to be able to do the same thing as i grow older.

I'm in accounting/finance.

What's really fascinating is that being smart gives you depth and adds paradox to you, that girls cannot resist.

Dressing trendy + muscle + alpha attitude is already awesome, but then you ADD a quick mind & name brand school and you drive girls crazy

They think: 'He is stylish, has muscles and is dominant? Nice. Wait, he is ALSO ridiculously smart? I want!'

The combination is very alluring cause so few guys have it

Keep working on your intelligence, knowing that it provides you with fun, and money, but also an extra layer of attractiveness

 

[Desdinova]

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.

 

[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.

The question states, if your wallet is *just* big enough to hire a plumber for 28 days, OR a carpenter for 21 days

'OR'

not 'both'


Besides, you can check to make sure you have no reading errors by appealing to common sense. If the answer is that trivial, why would this question be on an upcoming exam?

No top 25 university would bother testing this.

 

[JustLurk]

I'm in accounting/finance.

What's really fascinating is that being smart gives you depth and adds paradox to you, that girls cannot resist.

Dressing trendy + muscle + alpha attitude is already awesome, but then you ADD a quick mind & name brand school and you drive girls crazy

They think: 'He is stylish, has muscles and is dominant? Nice. Wait, he is ALSO ridiculously smart? I want!'

The combination is very alluring cause so few guys have it

Keep working on your intelligence, knowing that it provides you with fun, and money, but also an extra layer of attractiveness

Smarts all by itself doesn't seem to do the trick.
BTW, at ^, there are at least one or two cake "free points" questions on just about every x-sat test.

 

[Trader]

Smarts all by itself doesn't seem to do the trick.
BTW, at ^, there are at least one or two cake "free points" questions on just about every x-sat test.

I never said smarts all by itself can attract girls. Re-read my post.

Smarts + looks + dominance TRUMPS looks + dominance

 

[Aazman]

Trader, what I never seem to get in these questions is WHY

do you set

28P= 21C?

it doesn't make sense to make it P/C. What does P/C actually give?

 

[Just a Shot Away]

They think: 'He is stylish, has muscles and is dominant? Nice. Wait, he is ALSO ridiculously smart? I want!'

You don't need to be anywhere NEAR "ridiculously smart" to solve a question like that. The trick is just knowing how to convert words into an equation...it's a learned skill.

Smarts + looks + dominance TRUMPS looks + dominance

Yeah, and confidence trumps all three (although it sort of goes hand in hand with dominance.) I don't even know why you threw "looks" in there.

 

[Trader]

Trader, what I never seem to get in these questions is WHY

do you set

28P= 21C?

it doesn't make sense to make it P/C. What does P/C actually give?

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.

 

[Desdinova]

Besides, you can check to make sure you have no reading errors by appealing to common sense.

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.

 

[Aazman]

thanks man, much appreciated. I've forgotten most of my maths in a year... bad times.

i laughed at the girl analogy!

 

[ArcBound]

This is on a LSAT type test?