Three easy math problems. Can SMP do better than MIT?

[maurile]

Take this quiz

(1) A bat and a ball cost $1.10 in total. The bat costs a dollar more than the ball. How much does the ball cost?

(2) If it takes 5 machines 5 minutes to make 5 widgets, how long would it take 100 machines to make 100 widgets?

(3) In a lake, there is a patch of lily pads. Every day, the patch doubles in size. If it takes 48 days for the patch to cover the entire lake, how long would it take for the patch to cover half of the lake?

Did you get them all right?

Undergrads at elite universities really struggled with them. The percentage of students quizzed at each university who got all three answers right were as follows:

MIT: 48%
Princeton: 26%
Carnegie Mellon: 25%
Harvard: 20%
U.Michigan (Ann Arbor): 14%
Bowling Green: 13%
U.Michigan (Dearborn): 6%
Michigan State: 6%
U.Toledo: 5%

LINK

[madnak]

My answers:

<font color="white">1 - 0.05
2 - 5 minutes
3 - 47 days</font>

How did I do?

[Borodog]

<font color="white">1. $0.05
2. 5 minutes
3. 47 days
</font>

[lufbradolly]

Grunch

1, ball cost $0.05
2, 100 machines takes 5 minutes to make 100 widgets.
3, 47 days

Now to check the answers!

Edit - I'm an undergrad at Loughborough uni England

[maurile]

By the way, this quiz was not the point of the paper I got it from. The actual point was much more interesting.

The quiz was given so the correctness of those answers could be correlated with the answers to questions about risk-aversion and discount rates.

Would you rather have a) $1000 for sure, or b) a 90% chance of $5000?

The people who got 3 out of 3 correct on the quiz were much more likely to take the 90% chance of $5000 than were the people who got 0 out of 3 correct on the quiz.

In general, the paper concludes that intelligence of the sort required to do well on the quiz is positively correlated with a willingness to take +EV gambles, and also with lower future discount rates (e.g., people who aced the quiz were more likely to take $140 next year instead of $100 now).

That's kind of interesting.

[Zoelef]

<font color="white">

(1) A bat and a ball cost $1.10 in total. The bat costs a dollar more than the ball. How much does the ball cost?

x + y = 1.1
y = x + 1
x + x + 1 = 1.1
2x + 1 = .1
2x = .1
x = .05

.05 + y = 1.1
y = 1.05

(2) If it takes 5 machines 5 minutes to make 5 widgets, how long would it take 100 machines to make 100 widgets?

5 machines / 5 minutes = 5 widgets

1 machine / 5 minutes = 1 widget

1 machine / 1 widget = 5 minutes

1 machine 100 widgets
--------- * ------------ = 1 * X = X
1 widget 100 machines

X = 5 minutes

(3) In a lake, there is a patch of lily pads. Every day, the patch doubles in size. If it takes 48 days for the patch to cover the entire lake, how long would it take for the patch to cover half of the lake?

On the 48th day, the patch covers the entire lake. Since the previous day has half as much covered as the current (problem posed in reverse), the 47th day has half the lake covered.

</font>

Edit: Math Major, Undergrad Liberal Arts College

Also, I gamble it up for 5k since the expected EV's are $4,500 vs. $1,000 - that's too big a differential to ignore.

[Nottom]

My answers: <font color="white">
1) The bat costs $1.05
2) 5 min
3) 47 days
</font>

Seemed easy enough, hopefully I'm not stupid.

Edit: GDI I am stupid ... I checked the first one twice and still put the wrong one.

[garion888]

<font color="white"> 5 cents
5 minutes
47 days </font>

[ChromePony]

<font color="white">
1).05
2)5 min
3)47
</font>

did we at least beat Toledo?

[soon2bepro]

(not reading the rest of the thread, just responding the original test)

(1) The ball costs $0.05

(2) What the hell is a widget?! j/k [img]/images/graemlins/smile.gif[/img]. 5 minutes is the answer.

(3) 47 days.



It's really amazing that these people couldn't get at least 99% on these easy questions