Can you help me?

Question

A survey of a group of 112 tourists was taken in St. Louis. The survey showed

64 planned to visit the gateway arch
46 planned to visit the zoo
9 plan to visit the art museaum and the zoo, but not the gateway arch
14 plan to visit the art museaum and the gateway arch, but not the zoo
16 plan to vist the gateway arch and the zoo, but not the art museaum
9 plan to visit the gateway arch, the zoo and the art museaum
14 plan on visiting none of the three places
How many plan on visiting the Art Museaum only?

Answer 1

The answer is13 plan on visiting the Art Museum only.

112 total tourists. There are 8 visiting combinations:
#1>25 visiting gateway arch only
#2>12 visiting zoo only
#3> 9 visiting Art Museum & zoo but not gateway arch
#4>14 visiting Art Museum & gateway arch but not zoo
#5>16 visiting gateway arch & zoo but not Art Museum
#6> 9 visiting gateway arch & zoo & Art Museum
#7>14 visiting none of the three places
#8>13 visiting Art Museum only

Determined there were 25 visiting the gateway arch only:
64 visiting gateway arch - 39 visiting gateway arch & at
least one other location. (64-39)=25

Determined there were 12 visiting the zoo only:
46 visiting zoo - 34 visiting zoo & at least one other
location. (46-34)=12

We knew the tourist disposition of combinations
#3 through #7 when we began.

Combinations #1 through #7 total 99. Therefore the
8th and final combination (visiting Art Museum only)
is 13. (112-99)=13

Answer 2

Okay - draw up a venn diagram

GA is gateway arch (64)
Z is Zoo (46)
AM is art museum

Universe = 112
14 = (GA U Z U AM)' ie outside all of them (back home at the hotel playing hanky panky)

9 = GA ∩ Z ∩ AM

I guess x go see the AM without seeing GA and Z
(AM ∩ Z' ∩ GA')

So ... a total of 64 + 46 - 16 - 9 + x + 14 = 112

that's to say the GA people (64) plus the zoo people (46) subtract the ones counted twice (16 + 9)
add the ones going to the AM alone (ie. x)
add the ones back at the hotel (ie. 14)

and you should have the total number of people on the tour

So then solve for x

GUYS - read the question

32 people are going to the Art Museum AND (Gateway arch or Zoo)

How many people are going to Art Museum AND NOT (Gateway arch or Zoo)

c'mon

If you do 32 + 64 (going to GA) + 46 (going to Z) + 14 - 16 - 9 (counted twice) you get WAY more tourists than originally on the tour.

Maybe some of them got mugged!

Answer 3

9+14+9=32
32 people plan on visiting the Art Museum.

Answer 4

32 people are going to the art museum

Answer 5

this is simple. none, add me to msn for mi reasoning [e-mail] trust me i am right

Answer 6

!'m s0rry, ! |)0 n0t |
I'm sorry, I do not know