I28-21

Question

Alex and Jordan play a game, each betting $2 on each round. In each round, one of them wins. At the end:
 
• Alex won  x  rounds.
 
• Jordan lost $8 in total.
 
Select for  x  the number of rounds Alex won, and select for  y  the total number of rounds they played that would be jointly consistent with the given information. Make only two selections, one in each column.

Bunuel · Answer

Official Solution:

Jordan losing $8 in total means that Jordan lost 4 more games than he won. This implies that Alex winning  x  rounds means Jordan won  x - 4  rounds, making the total number of rounds played  x + (x - 4) = 2x - 4 , which must be even.
 
• If  2x - 4 = 6 , then  x = 5 . However,  x = 5  is not an option.
 
• If  2x - 4 = 8 , then  x = 6 , which is an available option.
 
Thus, Alex won  x = 6  rounds, and the total number of rounds they played was  y = 2x - 4 = 8 .

Correct answer:

x  "6"

y  "8"

Dhruvek · Answer

x rounds alex won which means Jordan lost x rounds, lets say total rounds T then Jordan won (T-x) rounds,

x rounds lost therefore net money lost is -2x;
(T-x) rounds won therefore net money won is 2(t-x)

-2x +2(t-x) = -8
2t=4x-8
t=2x-4
only 6 and 8 satisfies equation

Goldenfuture · Answer

my logic was simpler. J lost 8 which means Alice won atleast 4 rounds. Look at options - 6 rounds
If Alex played 6 rounds, had she won all she would have got 12 points. 
Now she needs to get rid of 4 points for that she needs to play 2 more games, and lose them. Total games played 8
Option exists of 6,8

Try option 2. 7 games
let A win 7 games. She won 14 points. Needs to get rid of 6 points - so need to play extra 3 games.7+3 total games is not even an option - so Answer is 6 & 8

anushree01 · Answer

I still dont get it

Let the total games by T. Alex won x so Jorden won T-x games.
Jorden invested - jorden won = Money that jorden lost
2T - 2 (T-x) = 8

What`s wrong in this, if someone can please help!!

Bunuel · Answer

The issue is in this part:

2T - 2(T - x)

When Jordan wins a round, he does not just get back his own $2. He also wins Alex’s $2, so the total pot he receives is $4.

So Jordan’s loss should be:

2T - 4(T - x) = 8

This gives T = 2x - 4, which matches the official solution.

Vivek1707 · Answer

This is a great question that’s helpful for learning.

I28-21

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