9 runnersLea, May, Nora, Olga, Pat, Queta, Rhea, Sue, and Tiaare div

Team 2 but not team 3 - Olga.

Any team - Lea.


1. May runs faster than Queta -> M>Q

2. Queta runs faster than both Olga and Lea. Q > O & L

3. Lea runs faster than both Sue and Nora. L > S & N

4. Tia runs slower than Olga. O > T

5. Rhea runs slower than Tia. T > R

6. Rhea runs faster than Pat. R > P.

From above statements, M and Q are two fastest, so they will be in team 1.

From 4,5 and 6, definitely there are 3 persons who are slower than O, so O will not be in team 3.

From above statements it can also be seen that L can be in any team.

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Let the first letter of each of the runners' names be their respective speeds.

Then, from the problem statement we can write the following relations:

1) m>q>o>t>r>p
2) m>q>l>s
3) m>q>l>n

i) From relations 1, 2 and 3, we can clearly see of all runners Olga (with speed o) could be on Team 2 (but never team 3) since there are 3 runners slower than her.
ii) Also from relations 1,2 and 3 we can say that Lea (with speed l) could be on any team (i.e. Team 1, Team 2 or Team 3) depending on her speed relative to others. For example if l > o (Lea is on Team 1); if o > l > at least one among t, r, p (Lea is on Team 2); and if p>l (Lea is on Team 3)

M>Q
Q>O & L
L> S & N
O>T>R>P

Team 2 but not on Team 3: Olga.

Olga can be faster than Lea or slower than Lea. If Olga is faster than Lea, then Olga will be in the fastest team(Team 1), but if Olga is slower than Lea, then Olga will be in Team 2, but cannot go to Team 3.

If Olga is slower than Lea, then M Q L is the fastest team.
We know that S & N is less than L. So, S & N can be in Team 2 or in Team 3.
It is already established that O>T>R>P, O has to be paired with S & N, otherwise, the slowest 3 members condition will not be satisfied.

Any Team : Lea

If Lea is faster than Olga, then Olga will be in team 1.
If Lea is slower than Olga, then one possible combination is
Team 1 = M Q O
Team 2 = L S N ( Since L>S & N)
Team 3 = T R P ( Since O>T>R>P)

Or another combination is
Team 1 = M Q O
Team 2 = T R P ( Since O>T>R>P)
Team 3 = L S N ( Since L>S & N)

So, we can see that L can be a part of Team 1, Team 2, and Team 3
_________________

1.Olga(Team 2 but not Team 3)
2.Lea(Any Team)

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[quote="Sajjad1994"]9 runners—Lea, May, Nora, Olga, Pat, Queta, Rhea, Sue, and Tia—are divided into 3 relay teams. The 3 fastest runners are placed on team 1, the 3 slowest runners on team 3, and the remaining 3 runners on team 2.

No two runners run at the same speed. May runs faster than Queta. Queta runs faster than both Olga and Lea. Lea runs faster than both Sue and Nora. Tia runs slower than Olga. Rhea runs slower than Tia. Rhea runs faster than Pat.

Select the runner who could be on team 2 but not on team 3, and select the runner who could be on any team.

Team 2 but not team 3	Any team
	Yes	Lea
		Nora
Yes		Olga
		Rhea
		Sue
		Tia

Order of runners :

1. M>Q>O>T>R>P>L>S>N - O in Team 1, L in Team 3
2. M>Q>L>S>N>O>T>R>P - O in Team 2, L in Team 1
3. M>Q>O>T>L>S>N>R>P - L in Team 2
In any case O will be in Team 2 or Team but not in Team 3 and L could be in all 3 teams

N, R, S and T can be in both Team 2 and Team 3

Team 2 but not team 3 ： Olga
Any team： Lea

Better draw a chart to show their relative speed. But the basic shape is as follows:
M > Q > O > T > R > P
M > Q > L > S
M > Q > L > N

So, M and Q must be in the Team 1.
the third member in Team 1 can be either O or L
If O is in team 1, L can be in team 2, but L can also be in team 3.
If L is in team 1, O can only be in team 2 because TRP are slower than O.

Hello Everyone!

All of you have got this question correct, Great!

OA to the question is:

Team 2 but not team 3: Olga
Any team: Lea

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