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# Logic word problem

Tue 14 Jul, 2015 04:12 pm

The results of a questionnaire sent to all the alumni of a certain university showed that 66 percent alumni expected to attend the forthcoming activities celebrating the 150th anniversary of the schools founding. On the day of the festivies, it was learned that 90% of those whow did attend had previously indicated that they would attend, while 30% of those who did not attend had previously indicated that they would attend. Determine (a) what percent of the total alumni attended and (b) what percent of the total alumni acted differently than they had first indicated

If you help, please explain it to me in great detail because I don't understand things very well. Thanks in advance.
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Type: Question • Score: 1 • Views: 1,802 • Replies: 13

markr

3
Tue 14 Jul, 2015 10:03 pm
@johnr,
Let N be the total number of alumni
Let A be the number of alumni that attended

The number that expected to attend are made up of those that did attend and those that did not attend. The former is .90*A (90% of the attendees). The latter is .30*(N-A) (30% of the non-attendees)

Therefore, .66*N = .90*A + .30*(N-A)
.66*N = .90*A + .30*N - .30*A
.36*N = .6*A
.6*N = A
So, 60% of the alumni attended.

90% of the attendees said they'd attend, and they did. So, .90*.60=54% of the alumni fall into that category.
70% (100-30) of those who did not attend said they wouldn't. So .70*.40=28% of the alumni fall into that category.
Therefore, 54%+28%=82% did what they said they would do. That means 18% acted differently.
johnr

1
Fri 17 Jul, 2015 08:36 am
Thanks so much! I finally understand it!
0 Replies

dalehileman

2
Fri 17 Jul, 2015 09:10 am
@markr,
Markr I'm really impressed that you'd go to so much effort for a complete stranger at a remote website

Without revealing anything revealing I wonder if you'd give us a few facts about yourself

With thanks from The Community
engineer

2
Fri 17 Jul, 2015 11:02 am
@dalehileman,
Mark is a regular on the math and science problems. Whenever a thorny problem arises, you will find Mark with a clever solution.
dalehileman

2
Fri 17 Jul, 2015 01:18 pm
@engineer,
Eng I'm glad indeed we have several such. A couple of the others unfortunately have nasty tempers. At least one would become your lifetime enemy if you were to omit one letter of his name
0 Replies

markr

1
Sat 18 Jul, 2015 02:58 am
@engineer,
Gee, thanks. The same goes for you.
0 Replies

markr

2
Sat 18 Jul, 2015 03:07 am
@dalehileman,
If the problem is interesting enough, I'll take the time. I scan riddles, math, mathematics, and probability somewhat regularly - I'm partial to probability and the combinatorics that are often involved. I write firmware, and I've got degrees in CS and math (1982). I'm into board games and recreational math. Besides this site, I frequent puzzleup(dot)com (tied for first last year), projecteuler(dot)net (fallen WAY behind), and boardgamegeek(dot)com (lots of info to consume).
dalehileman

1
Sat 18 Jul, 2015 11:18 am
@markr,
Thanks Mark. How about nat'l, age

How do you compare those 4 forums
markr

1
Sat 18 Jul, 2015 02:55 pm
@dalehileman,
USA, 54.

I used to love Riddles when TryAgain was posting regularly. The other ones don't get posted to enough - part of that may be the time of year (school's out).
dalehileman

1
Sat 18 Jul, 2015 05:56 pm
@markr,
Quote:
The other ones don't get posted to enough
I wonder Mark whether a2k might be one of these, judging by the volume of response from some of my postings
markr

1
Sat 18 Jul, 2015 07:59 pm
@dalehileman,
I think I misunderstood your question. I thought you were asking about riddles vs. math vs. probability, etc on this site.

Project Euler is a great site for tough mathematical programming problems. They post problems weekly except during most of the summer.

PuzzleUp is a 20-problem competition that runs from July to December with a new problem each week. Some of the problems are rather trivial. Others can be quite difficult.

Boardgamegeek is a massive database of games with reviews, rules, variants, strategy discussions, etc. If you're into board games, it's a treasure trove.

I used to be very active in Project Euler (kept pace until about 250), but they upped the difficulty, so I now answer problems very infrequently. I continue to be active in PuzzleUp - it's getting ready to start for 2015. I spend tons of time on Boardgamegeek - not posting, just reading/researching. I spend very little time at this site any more with TryAgain no longer posting in riddles and interesting problems showing up in math/probability only sporadically.

dalehileman

1
Sun 19 Jul, 2015 09:55 am
@markr,
Thanks Mark

Without revealing anything revealing I still wonder if you might reveal your age, nat'l, job, even family
markr

1
Mon 20 Jul, 2015 12:15 pm
@dalehileman,
0 Replies

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