12 Days of Christmas GMAT Competition - Day 8: Alex and Jordan play

Question

12 Days of Christmas 2024 - 2025 Competition with $40,000 of Prizes

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 · Accepted Answer

GMAT Club's Official Explanation:

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.

hr1212 · Answer

If Jordan lost $8, that means that Alex won 4 more rounds than Jordan, which means rest of the games were split 50-50.

So if total y rounds were played then (y - 4)/2 = x - 4, ie. Rounds won by either players equally = Total rounds won by Alex - 4 extra rounds won by Alex

y = 2x - 4

Checking out all options -

y 
 x

3 
 7/2

6 
 5

7 
 11/2

8 
 6 
 Only possible combination 
 
  9 
 13/2

Hence, (x, y) = (6, 8)

Krunaal · Answer

Let's test the answer choices,

If x = 3 then the maximum Jordan can lose to Alex is 6 dollars, which is incorrect.

If x = 6, the Jordan lost 12 dollars to Alex in these 6 rounds, now Jordan needs to win y-x rounds and recover $4 to make a total loss of $8. To win back $4, Jordan needs to win 2 rounds, therefore the total rounds they play can be 6 + 2 = 8 rounds.

We have x = 6 and y = 8 which is consistent with the given info.

Answer 6 and 8

missionmba2025 · Answer

If Alex won x rounds, this implies Jacob lost x rounds, and he won (y - x) rounds

2x - 2y + 2x = 8

4x - 2y = 8

2x - y = 4

y = 2(x - 2)

Therefore we can conclude that y = even

y = 6 ; x - 2 = 3
x = 5
No such combination exists

y = 8 ; x - 2 = 4
x = 6

Hence x = 6; y = 8

Karanjotsingh · Answer

Solve this step by step:  
 
  We know: 
 
 Each person bets $2 per round 
 Jordan lost $8 in total 
 Alex won x rounds  
 
  Jordan's perspective: 
 
 Jordan loses $2 each time he loses (when Alex wins) 
 Jordan wins $2 each time he wins 
 Total loss = $8 = (Losses × $2) - (Wins × $2)  
 
  If Alex won x rounds: 
 
 Jordan lost x rounds (same number) 
 Jordan won (y-x) rounds (where y is the total rounds)  
 
  Putting it in the equation: 
 
 $8 = (x × $2) - ((y-x) × $2) 
 4 = x - (y-x) 
 4 = 2x - y  
 
  Using values: 
 
 For y = 6: 2x - 6 = 4 → x = 5 
 For y = 7: 2x - 7 = 4 → x = 5.5 (impossible) 
 For y = 8: 2x - 8 = 4 → x = 6 
 For y = 9: 2x - 9 = 4 → x = 6.5 (impossible)  
  
  Therefore, x = 6 and y = 8 is the only valid solution.

Lizaza · Answer

If Jordan lost only 8 dollars, it means that his losses were only 4 higher then wins.
For Alex, it's the opposite - he won 4 times more than he lost.

Then, judging from Alex's perspective, total is going to be his wins X plus his losses X-4:
  y=x+(x-4) = 2x-4

Therefore, we need the values to fit into the above equation, and the only suitable values are  2*6-4=8 
So, the answer is   x=6 and y=8

Navya442001 · Answer

Alex and Jordan play a game where:
 
 Each bets $2 per round. 
 In each round, one of them wins, and the other loses $2. 
 At the end:
 
 Alex won x rounds. 
 Jordan lost $8 in total.  
  
We need to determine x (the number of rounds Alex won) and y (the total number of rounds played) based on the given conditions.

Let us analyze the options
If x=3, Alex won $6, however since the money Jordon lost overall is $8, this cannot be correct

If x=6 , Alex won $12, therefore Jordon must have lost $12. But we're given that Jordon lost $8 in total
To arrive at $8 loss from $12 loss, Jordan must have won two games since (-12 + 4 = -8), And Alex must have lost 2 games, therefore total games should be (6+2=8).  Therefore y=8.

If x=7 ,  Alex won $14, therefore Jordon must have lost $14. But we're given that Jordon lost $8 in total
To arrive at $8 loss from $14 loss, Jordan must have won three games since (-14 + 6 = -8), And Alex must have lost 3 games, therefore total games should be (7+3=10). However this is not an option choice.

Similary we can check for other options but since the total will keep on increasing, therefore only (x=6, y=8) will satisfy.

pintukr · Answer

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.  
     x   
   y

3

6

7

8

9

say, Total rounds = Y

If Alex won x rounds, then Alex lost (Y-x) rounds
Gain for Alex = $ 2 * x 
Loss for Alex = $ 2 * (Y-x)

Overall , for Alex = (2 * x) - ( 2 * (Y-x))..............(1)

Similarly, Jordan won Y-x rounds, and lost x rounds
Gain for Alex = $ 2 * (Y-x) 
Loss for Alex = $ 2 * x

Overall , for Jordan = ( 2 * (Y-x)) - (2 * x) ..............(1)

Since, Jordan lost $8 in total

Putting Y = 8, and x = 6; we get 
 for Alex = $ 8 (gain)...--->i.e. Won = 6, Lost =2 
 for Jordan = $ 8 (loss)...----> i.e. Lost = 6, Won =2

x=6; y =8 is the CORRECT answer

Prakhar9802 · Answer

HIT AND TRIAL

Each round, each one of them bets $2 and one of them wins.

Jordan lost $8 in total, which means after winning and losing certain games, his total was a loss of $8.
This means Alex has a final profit of $8.

Alex won x rounds. Which means Jordan lost x rounds.

Y is the total number of rounds played.

If Alex has a total profit in the end, it means that out of the total games played, Alex has won more than half of them and Jordan has won less than half of them.

Therefore, putting in x=3 and y=9 cannot be the answer.
Infact, putting x=3 with y as anything above 5 cannot be the answer.

put x=6 and y = 8,
this means that alex won 6 games and lost 2 games.

Total earnings of alex = +12 - 4 = +8

This also means that Jordan lost 6 games and won 2 games.

Total earnings of Jordan = -12 + 4 = -8

Therefore, x = 6, y = 8.

maddscientistt · Answer

winning one round will get +2
losing one round will get -2

calculating only the wins and losses for alex and jordan

Rounds 
 1 
 2 
 3 
 4 
 5 
 6 
 7 
 8 
 
  Win 
 a 
 a 
 a 
 a 
 a 
 j 
 a 
 j 
 
  Alex 
 2 
 4 
 6 
 8 
 10 
 8 
 10 
 8 
 
  Jordan 
 -2 
 -4 
 -6 
 -8 
 -10 
 -8 
 -10 
 -8

The values that match with the given options are
x = 6, y=8

prashantthawrani · Answer

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,   which means he lost at least 4 rounds and Alex won at least 4 rounds.  
  x=4, y=4 (no option available)

Additionally, Alex may have won 1 round and lost 1 round 
 x=5, y=6 (no option available)

Additionally, Alex may have won 1 more round and lost 1 more round 
 x=6, y=8 option available

arunbhati · Answer

Hi Sir,

My approach is correct or not in order to solve this question

Here we know that Jordan lost 8 USD means Alex won 8 USD

X is number of won 
Y is number of lost matches

2 is for getting if match is won and -2 for lost match

2X-2Y=8

X-Y=4

We will get 6-2=4

Hence x is 6 and Y is 2 means total match played is 8 and 6 are won

I also want to know that I am getting 635 to 645 on GMAT club mock test. Should I go for actual exam . I realised that in DI eventhough I got 12 correct in Gmat club mock test still I got 83 in DI but in official mock test it is was only 78

Should I believe in Scire of gmat club mock test and is it possible that I can get wsame score in actual Gmat exam that I got in Gmat club mock test

Dereno · Answer

Alex and Jordon play a game and they bet $2 on each round. So, it’s only one wining the round and the other losing it. As, there is no draw in rounds.

Alex wins x rounds, which means Jordan has lost x rounds.

Alex gained $2x and Jordon has lost $2x.

Now, to the  next most interesting and most likely error prone part : Jordon  lost $8  in  total .

So, it means Jordon at the end of all rounds, have a loss of $8. This, also means the number of wins is LESSER than the number of loses.

Given that : Total of y rounds are being played between them.

Since, the total amount is given with Jordan. Let’s stick with him for now.

Number of rounds Jordan lost = x

Number of rounds Jordan wins = Total - lost = y-x

Amount from Losses - Amount from wins = $8

2x - 2*(y-x) = 8

2x - 2y +2x = 8

2y = 4x - 8

y = 2x - 4

Re framing it, 2x = y+4

So, we can surely say, y has to be an even number.

Among the options, y = 6 or 8 qualifies.

If y= 6, then x =5 ( not in option).

If y =8, then x = 6.

Thus the values of  x and y = 6,8  respectively.

12 Days of Christmas GMAT Competition - Day 8: Alex and Jordan play

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Rounds	1	2	3	4	5	6	7	8
Win	a	a	a	a	a	j	a	j
Alex	2	4	6	8	10	8	10	8
Jordan	-2	-4	-6	-8	-10	-8	-10	-8

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12 Days of Christmas GMAT Competition - Day 8: Alex and Jordan play

Prep Toolkit

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