Wednesday, June 03, 2009

A FUN math problem from L!



I am studying for the SAT right now and in my practice book, there is an INSANELY HARD(at least for me) problem that I CANNOT figure out. My book overs no explanation on it as it is in one of the practice tests, just the answer. I thought I'd post it here to see if anyone knew how to figure it out. It's probably not as hard as I think it is, but it's just been bugging me so much and as it is summer, there is no teacher in sight to ask for help.
Here we go:



On the disk shown above, a player spins the arrow twice. The fraction a/b is formed, where a is the number of the sector where the arrow stops after the first spin and b is the number of the sector where the arrow stops after the second spin. on every spin, each of the numbered sectors has an equal probability of being the sector on which the arrow stops. What is the probability that the fraction a/b is greater than 1?

(A) 15/36

(B) 16/36

(C) 18/36

(D) 20/36

(E) 21/36

(the sections are supposed to all be equal by the way...)

and the book says that the answer is A. If anyone knows how to do this and wishes to enlighten me, I would greatly appreciate it!

--L

20 comments:

Reya Mellicker said...

OMG. Is there really anyone on earth who can figure it out? Makes my eyes cross just to think about it!

Good luck!

Kurt said...

If you roll 1 first, there are zero possible rolls that result in a fraction greater than 1.

If you roll 2 first, there is one possible roll that result in a fraction greater than 1. (2/1)

If you roll 3 first, there are two possible rolls that result in a fraction greater than 1 (3/1, 3/2).

If you roll 4 first, there are three possible rolls that result in a fraction greater than 1 (4/1, 4/2, 4/3).

If you roll 5 first, there are four possible rolls that result in a fraction greater than 1. (5/1, 5/2, 5/3, 5/4)

If you roll 6 first, there are five possible rolls that result in a fraction greater than 1 (6/1, 6/2, 6/3, 6/4, 6/5).

Total: 15 out of 36 possible combinations.

Baino said...

Sorry toots, numbers, fractions, maths generally make my head spin!

subtorp77 said...

GAH! I never did well in math( except geometry )...my head hurts...sorry, I'm no bloody help here, am I?

kmkat said...

Someone smarter than I am could read that problem, think about it, and figure it out theoretically. That may be what the SAT expects you to do, since it is a timed test. But I am a do-er, so here is how I solved it.

1. I opened up an Excel spreadsheet, and in the cells of the first column I entered all the values of all the possible combinations -- 1/1, 1/2, 1/3, ... 4/6, 5/6 6/6. That told me there were 36 possible combinations. (I should have been able to know that before I started, but my math education was woefully weak in the area of permutations.)

2. The problem asks for the probability of any given pair of spins yielding a number greater than one. So I sorted the column of numbers into increasing order; the lowest is .17 (1/6) and the largest is 6 (6/6).

3. The first 21 numbers in the sorted column are 1 or less; the last 15 are greater than 1. Therefore, the answer is 15/36, or A.

4. I heaved a huge sigh of relief because when I figure out something like this, it is a total crap shoot as to whether I get the right answer the first time.

karen said...

I'm so lazy, I couldn't even apply my mind to this.. interesting to see others' responses, though! Suddenly it all makes perfect sense! good luck with the exam! :)

PG said...

My artistic, non-math brain has just flip flopped and twisted itself into a Moebius strip.

Merle Sneed said...

Kurt and Kmkat beat me to it.

Megan said...

i'm glad somebody already figured it out. whew!

have a great weekend!

Candie Bracci said...

WHAT???I can't normally solved anything like that but even less having an hangover,lol.Good luck!:D

lettuce said...

nope, means nothing to me

nuffink at all


enjoying the telemann tho!
have a good weekend

mouse (aka kimy) said...

I still have nightmares about taking standardized tests....they mainly concern oversleeping and getting there when half the time has passed!

best of luck I'm sure you'll blow the top off the sat!!

Shammickite said...

I think all that figuring just when WHOOSH! over my head.

Kurt said...

I'm available for online tutoring, $20/hour.

Barbara said...

It's really easy:

2/1
3/1
3/2
4/1
4/2
4/3
5/1
5/2
5/3
5/4
6/1
6/2
6/3
6/4
6/5

There may be a more mathematical solution, but I always found the quickest solution to be preferable for timed problems like this one!

Barbara said...

I'll try this again in case you didn't get me comment yesterday. The answer is really quite simple:

15/36 consists of

2/1
3/1
3/2
4/1
4/2
4/3
5/1
5/2
5/3
5/4
6/1
6/2
6/3
6/4
6/5

Thus, there are a total of 15 our of the 36 possibilities that satisfy the requirement that the ratio be greater than 1.

I often find the SAT math problems are most easily solved quickly by a common sense approach instead of an equation.

Betty said...

Umm. No. Mind is a complete blank (a fairly normal state of affairs, actually, but always made worse by math.) :D

croneandbearit said...

I'm sorry but that test is just wrong -- there needs to be an F. None of the above coz that's what I'd pick. If it hadn't been for Devoted Spouse I never would have made my way through college algebra and he made it almost fun - okay well the combination of him, and some rum helped! Good luck!

citizen of the world said...

I worked it out before I checked the responses so I wouldn't cheat. I did it as a quick chart 1/1, 1/2 and so on to the first line, 6/1, 6/2 in the last. Then it was wasy to see that 1 first would yiled no correct answers, 2 first 1, and so on to 5 if 6 is first, for a total of 15 out the of the 36 possible spin combos.

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