Math Questions

M

mud duck

New member
1. If a baseball bat an a ball cost $1.10 total and the bat is 1 (one) dollar more then the ball. How much does the ball cost?

2. If a patch of lillypads doubles in size every day, and after 48 days will cover 100% of the lake. How many days would it take to cover 50% of the lake?

3. If it takes 5 machines, 5 minutes to make 5 widgets. How long does it take 100 machines to make 100 widgets.

If I understand it right, something like 3500 college students where ask to solve these questions, and only something like 17% got all three correct. Lets see how the CMon'ers do!
 
R

Ritual

New member
The answer to question 1 is $0.05. I agree with the other answers though...

(ball costs x, bat costs x + 1. Total is x + (x + 1) = 1.10, 2x + 1 = 1.10, 2x = 0.10, x = 0.05).
 
BPI

BPI

New member
Hi Mud Duck, the baseball question I encountered recently in a book called...

drat, lent it out, will try to remember to edit in later, Risk something,...

...aren't Search Engines great :) http://www.amazon.co.uk/Risk-Science-Politics-Dan-Gardner/dp/1905264151

a book about how human beings work & have developed & how those hunter gatherer instincts don't always serve us well in the modern world. I had to spend a few minutes to get the answer right (actually work it out rather than confidently pronounce "10c") & then tried it out on people at work. A couple got it straight away, most were happy once I revealed the answer & they worked it back themselves & the last couple got very upset! I used to get a lot of mileage out of laterel thinking puzzles with my teammates when I did 12hr line work shifts :)

It's a fascinating piece of work written at quality magazine rather than academic level (I can't do the academic stuff, 3 dictionary lookups per sentence is more than I can handle). Many interesting anecdotes & scientific studies, which if you enjoy having something more interesting to talk about at work than the last episode of X-Factor is a real boon! The last third that deals with media & recent war was treading old ground for me but I recommend it heartily nevertheless.

Cheers, B.


EDIT:

One from memory to flesh it out (please correct me if you know better!), marketing related so you may have heard it before...

End of a supermarket aisle, promo display, tins of beans, only 8p each!!!
Average customer picks up how many tins?

End of a supermarket aisle, promo display, tins of beans, only 8p each!!! Maximum 10 per customer.
Average customer picks up how many tins?

The point is to try and "know thyself" so that you aren't manipulated into action that doesn't benefit you. Make a rational desicion rather than a gut one. 2 & 8 by the way.

Cheers, B.
 
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C

cfwheeler58

Member
Try this one

Your bank has an ATM in a location that you frequent.

The machine is routinely loaded with $5 and $20 bills.
The system will allow you to select any denomination of 5 dollars for withdrawal.
i.e. $5, $10, $15, $20, etc.

The maximum you can request for one visit is $500.

The machine will always calculate the most efficient mix of bills for a request.
That means the minimum raw count of bills, regardless of denomination.
YOU CAN NOT REQUEST SPECIFIC MIXES OF BILLS.

One day, the machine is accidentally loaded with the denominations reversed.
IOW, the machine dispenses $20 bills when $5 bills are requested and vice versa.

Imagine:
1) You are aware of this
2) You can visit the ATM once and request a single withdrawal
3) You have no scruples
4) The bank will debit your account for the amount you REQUEST
5) You won't get caught. Period. The bank eats the mistake.
6) The machine is fully loaded.

A) What amount do you select to maximize your gain and how much is that gain ?
B) What would be the worst possible request and how much would it cost you ?

Extra Credit....Same scenario but the machine is loaded with ALL $20 bills.
i.e. The 20 bin has $20 bills and the 5 bin has $20 bills.

C) What amount do you select to maximize your gain and how much is that gain ?
D) What would be the worst possible request and how much would it cost you ?

So that many can answer.....please PM me your response and I will publish
after I receive 10 responses.

Good luck....and apologies for the distinctly American context of the quiz.

CFW
 
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M

mud duck

New member
thanks BPI, Im going to have to see if i can find it around here.

Great, thanks CF, now Im going to be working on that problem for days. :curse!::snicker::snicker::snicker:
 
H

Hoblit

New member
You know, when solving the maths problem is more interesting than work, it's time to find a new job.
 
C

cfwheeler58

Member
ATM Solution

Congrats to Scherdy, Exilesjjb, Ritual, Hoblit
All of whom correctly solved the problem.
Three of you also did a good job explaining the solution as well.

The critical issue to understand and apply is that the machine
will make the most efficient combination of bills given a request.

A) To optimize your gain, you want to request the maximal number
of $5s ( receiving $20s) and minimize the number of $20s ( receiving
$5s ). The most $5s the machine will opt to give is 3. Therefore
you should request $15 and you will get $60....for a gain of $45.

B) Conversely, every $20 you request will yield a $5 bill, costing you
$15 per. The only upper bound on this is the maximum withdrawal.
So...if you want the whole $500 consider yourself screwed.
That will yield a $500 debit and $125 in your hand....loss of $375.

The second half is actually easier than the first.

C) The logic works the same as A, except that there is no "penalty"
for selecting $20s. So your maximum dollar gain is still $45, but that
can be achieved by requesting any amount which is a denomination
of $20 minus $5 from the total....see it as (20 x N)-5. The upper
bound would be $495.

D) There is no worst case scenario, in a sense. The worst you can do
is to fail to gain. Any request which is a denomination of $20 will
yield the requested amount.

In the first scenario, wherein the 20s and 5s are switched, there are
3 requests which will yield the requested amount. In each case, the
customer requests an equal number of 5s and 20s. That would be
$25, $50 or $75.

CFW
 
E

exilesjjb

New member
cfwheeler58 said:
Congrats to Scherdy, Exilesjjb, Ritual, Hoblit
All of whom correctly solved the problem.
Three of you also did a good job explaining the solution as well.


Did not know you wanted to see our working out, should have listerned to my math teacher and always put working out. :bashful:
Click to expand...
 
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