perms and coms questions (1 Viewer)

[DnaRna]

hi struggling with these questions pls help


answers:
12) x=5
13) n=225
14) 13
15) 7

ty.

 

[Grey Council]

question 12:
when you divide by 7, you can only get 7 possible remainders, as follows:
7 ÷ 7 = 1 remainder 0
8 ÷ 7 = 1 remainder 1
9÷ 7 = 1 remainder 2
10÷ 7 = 1 remainder 3
11 ÷ 7 = 1 remainder 4
12÷ 7 = 1 remainder 5
13 ÷ 7 = 1 remainder 6
14 ÷ 7 = 2 remainder 0

the question is asking, when you divide the numbers from 1 to 30, find the minimum number of numbers which have the same remainder

1-7 --> each remainder has appeared once
8-14 --> each remainder has appeared twice
15-21 --> each remainder has appeared thrice
22-28 --> each remainder has appeared four times
29-30 --> two of the remainders have appeared five times

at least '5' of the numbers have the same remainder

 

[Grey Council]

13 and 14 are very confusingly worded, and imo bad questions.
But I'll reword them into what I belive the author intended:

13: You have 'n' number of people, placed in 8 levels of karate. How many people would you require to guarantee that at least 29 people would be in at least 1 level?

Solution: 8 levels x 28 people = 224. On the 225th students, at least one group would have minimum 29 people.

14: You survey 450 people as to what takeaway food they like in a multiple-choice type quiz. You are guaranteed that at least 35 people will choose the same category. How many categories must there have been?

Solution: Imagine you had 450 categories. You're not guaranteed that 35 people will choose 1 category, it's possible that all 450 people would choose their own unique category from those 450 categories. Similarly, if you had 225 categories, it's entirely possible that each category would have 2 people.

If there were 13 categories, and each category had 34 fans, this would only make up for 442 of the voters. The remaining 8 must have voted for one of the 13 categories, thereby guarantee'ing us that at least 1 category has at least 35 fans.

 

[Grey Council]

15:
There are 3 groups: A, B and C.
Let's take the worst case scenario, and say that 2 people chose each of A, B and C.
This is 6 people. The 7th friend MUST join one of the three groups, thereby guarantee'ing that at least one of the groups has at least 3 people.

 

[CM_Tutor]

I thought these looked like poorly worded pigeonhole principle questions... good job, Grey Council!

 

[Grey Council]

hehe, those questions are from maths in focus (i think).
Maths in Focus continues to be a poor choice of textbook (imho) :<
Cambridge is relatively better for pigeonhole principle.

IB textbooks (from england i believe) and exam papers are good for this topic. Fairly easy to find using google.

 

[DnaRna]

hehe, those questions are from maths in focus (i think).
Maths in Focus continues to be a poor choice of textbook (imho) :<
Cambridge is relatively better for pigeonhole principle.

IB textbooks (from england i believe) and exam papers are good for this topic. Fairly easy to find using google.

hey, thanks for the help !!!!!!
how are u so good at these types of questions? share your secrets plssssss im so bad at this!

 

[Grey Council]

it's more logic than maths, tbh

also, i teach this stuff, and i've seen a fair few examples. after a while, the questions tend to be quite similar.