Which one of the following could be true after exactly two rounds of matches have been played?

Irina August 17, 2019

@Julie,

That's correct, you do have to consider both scenarios. Let's look at the setup for this question. The question asks us which of the following could be true after exactly two matches are played. Let's say scenario A is EO and scenario B is OE.

Scenario A

round (1) E
R J S M L
J & R and M &S play against each other.

round (2) O
teams in positions 3 & 5 play teams in positions 2 & 4
L definitely plays either S or M
S or M play against R or J

Scenario B

round (1) O
R J S M L
S & J and L & M play against each other

round (2) E
J or S plays against R
M or L play against S or J

Let's look at the answer choices:

(A) J has won two matches

Correct and could be true under scenario B. Under scenario A, if J wins against R, it becomes #1, and is not in play in round 2. Under scenario B, if J wins in round 1, it stays in position #2, and then could play and win against R in round 2.

Let's check the rest of the answer choices.

(B) L has lost two matches.

Impossible. L is not even in play in round 1 under scenario A, and L could only lose round 1 under Scenario B, if it loses in round 1, it stays #5 and is not in play in round 2.

(C) R has won two matches

Impossible. If R wins round 1 under scenario A, it stays #1 and is not in play in round 2. R is not even in play in round 1 under Scenario B, and thus cannot possibly win two matches.

(D) L's only match was played against J.

Impossible. Under Scenario A, J is out of play in round 1 and must play either S or M in round 2. Under Scenario B, L plays against M in round 1, thus it is impossible for its ONLY match to be against J even if it plays against J in round 2.

(E) M played against S in two matches.

Impossible. Due to the game being played alternatively in odd-even rounds, it is impossible for two teams to play against each other in consecutive rounds.

Of course, on a real test you would not check any of the other answer choices once you have determined that (A) could be true given a fairly time-consuming nature of the question. For that reason, when the right answer is not obvious from the initial diagram and requires trying several scenarios, the correct answer answer choice is more likely to be (A) or (B) than (D) or (E).

Does this make sense?

Let me know if you have any further questions.

AlexanderX November 11, 2019

Hello, I just had a question that why we cannot have scenario that have both same round, like OO and EE? Please let me know, thanks so much.

shunhe January 8, 2020

Hi @AlexanderX,

Thanks for the question. Take a look at the first rule - Matches are played alternately in odd-position rounds and in even-position rounds. Make sure you read through all the rules carefully! Hope this helps.

izyat April 29, 2020

Why don't we consider scenarios where the lower letter does NOT better the upper letter and so stays in the same place? Wouldn't we have more scenarios to consider than just two?