Set Language and Notation

[abcde]

AOA!
I require help in two questions.
1. Some people were interviewed to find out whether they spoke French, Spanish, French and Spanish, or neither French nor Spanish. E is the set of people who were interviewed, F is the set of people who spoke French, and S is the set of people who spoke Spanish. Given that n(E)= 250, n(F) = 80 and n(S) = 220, find
(c) the maximum possible number of people who spoke both Spanish and French.
I'm constantly getting 80 as the answer to this part. The answer at the back of the book is 30. Which is correct and why?

2. E = {1,2,3,4,5,6,7,8,9,10,11}
A = {x:x is an even number}
B = {x:x is a multiple of 3}
(b)(ii) A number n is chosen at random from E. A second number m is chosen at random from the complete set E. Find the probability that the sum of n and m is 18.
Here I'm getting an answer of 2/55 and the one at the back is 5/121.
Help me out please! Any assistance would be very much appreciated.

 

[Sehrish]

For the second question:
9, 10, 11 and 8. These are the four numbers which if added together wud give 18 as a result and the fifth result is 7+11.
Therefore, there are five numbers from the universal set which when added gives 18. There were two draws (one for getting m the next for getting n)
So 5/121.

For the first question:
I remember solving this question but I cant find the question. If only u cud help me wid the year. Btw I think 30 was the answer to the first part and not this one. Recheck ur answer at the back too.

 

[abcde]

I got the second question! Thank you!
For the first question, the answer for this part is 50 at the back (I just checked now and yeah it's not 30). The year is June 1992/2/4a. I'm doing it from the latest edition of classified, in which it is question 40 of unit 12: Sets.

 

[OakMoon!]

I got the answer 80 too. 50 is the minimum number of people who speak both spanish and french so how can 30 be the maximum. I believe the answer at the back of the book is wrong.

 

[OakMoon!]

I just read your last post. See if the question requires for minimum or maximum. Since, there are people who speak neither of the languages it is totally possible that every guy who speaks french also speaks spanish and the rest remaining out of 250 speak neither of the languages. Hope this helped.

 

[Firebender]

i agree. :/ 80 is the logical answer. The answer at the back could be wrong.

CIE has admitted that sometimes released answers in even marking schemes are revised or new possible answers are added when there's a genuine problem but they dont release the new answers. My tuition teacher used a few examples in chemistry to teach us to never take solved past papers as everything.

 

[abcde]

I get your point @hamidali391. Yeah, so the answer at the back is probably wrong and 80 would then be correct. 80 is the maximum number of people who speak both Spanish and French whereas 50 is the minimum number for it.

 

[OakMoon!]

Yes.

 

[Sehrish]

So that's a good news for me. I invested a lot of unproductive time in trying to get 50. Good thing the answer at the back is wrong. Hey btw abcde have u caught any other instance when answer at the back of this Classified book is wrong?

 

[abcde]

Yes, the answer is wrong some times! I appreciate your effort though!