# Thread: F! Contest - Master-Mind of the DAY: Day 7

1. ## F! Contest - Master-Mind of the DAY: Day 7

This is the Seventh thread for master mind of the day...

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Here's the First Question for DAY 7 of Master mind of the day--

Q1.) Rahul likes statistics and so he calculated the average height of his friends as X. He also calculated the average of the average heights of all the possible pair of his friends (two friends taken at a time) as Y.
Later, he calculates the average of the average heights of all possible triplets (three friends taken at a time) as Z.
Find the relationship among X,Y,Z ?

Correct Answer will win FREE Mobile Recharge worth Rs.100!!!

Entries will be accepted till 7PM, 5th Dec. 2011!

2. ## Re: F! Contest - Master-Mind of the DAY: Day 7

ans 1 == for X:Y:Z is 1:2:3

---------- Post added at 06:17 PM ---------- Previous post was at 06:16 PM ----------

or ans 1 == X:Y:Z is 1:2:3

---------- Post added at 06:18 PM ---------- Previous post was at 06:17 PM ----------

Originally Posted by Sagar Agarwal

or ans 1 == X:Y:Z is 1:2:3
i wanted to write

or ans 1 ==== X:Y:Z is 3:2:1

3. ## Re: F! Contest - Master-Mind of the DAY: Day 7

the answer for the first question of day7 isy>x>z

4. ## Re: F! Contest - Master-Mind of the DAY: Day 7

answer for question of day 7 is X=Y=Z

5. ## Re: F! Contest - Master-Mind of the DAY: Day 7

can nt say anything any relation do not holds true for all possible cases

6. ## Re: F! Contest - Master-Mind of the DAY: Day 7

X,Y,Z are equal.
X=Y=Z

7. ## Re: F! Contest - Master-Mind of the DAY: Day 7

ans fr the 1st question
x=y=z

8. ## Re: F! Contest - Master-Mind of the DAY: Day 7

Hi, my answer is Z (> or =) Y(> or =) X i.e. Z can be equal to as well as greater than Y and Y can be equal to as well as greater than X depending upon the values.

---------- Post added at 10:13 AM ---------- Previous post was at 10:10 AM ----------

Originally Posted by vikas1306
Hi, my answer is Z (> or =) Y(> or =) X i.e. Z can be equal to or greater than Y and Y can be equal to or greater than X depending upon the values.
I want rephrase my earlier post as shown in bold.

9. ## Re: F! Contest - Master-Mind of the DAY: Day 7

I think the relation will be
X>Y=Z
MEANS X is the greatest and Y and Z are equal

10. ## Re: F! Contest - Master-Mind of the DAY: Day 7

Ans.1)x=y=z.....

11. ## Re: F! Contest - Master-Mind of the DAY: Day 7

But it should be given that the number of students in the class should be a multiple of 6,only then the averages of pairs and triplets can be taken

12. ## Re: F! Contest - Master-Mind of the DAY: Day 7

Equal : X=Y=Z

solution:
let there be n students with heights a1, a2, a3.... an.
so average = 1/n{(sum of all heights)}

now for avg heights of pair:
there will be nC2 pairs like (a1+a2)/2 , (a1+a3)/2 and so on.. so every students height was added (n-1) times.
so avg of pair =(1/nC2)*(n-1)*{sum of all heights/2) = 1/n {sum of all heights}

for triplets:
there will be total nC3 triplets like... (a1+a2+a3)/3, (a1+a2+a4)/3 and so on.. by observation you can see that the sum of all triplet is equal to
(n-1)*(n-2)/3{sum of all heights)
hence avg: (1/nC3)*sum = 1/n {sum of all heights}

13. ## Re: F! Contest - Master-Mind of the DAY: Day 7

Question 1): X=Y=Z

14. ## Re: F! Contest - Master-Mind of the DAY: Day 7

ans is x=y=zex:three students 5 ,5.1, 5.2 average=5.1aver of pairs 1st 2 studs are 5.05 and 2nd 2 studs are 5.15 and total average is 5.1 aver of triplets3 students is 5.1(x=y=z)...........

15. ## Re: F! Contest - Master-Mind of the DAY: Day 7

According to me Z<Y<X

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