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24 Jan 2025, 09:39
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x: 6
y: 8
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.
• 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 |
ShowHide Answer
Official Answer
x: 6
y: 8
24 Jan 2025, 09:39
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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"
Bunuel
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
Joined: 03 Mar 2022
Last visit: 16 May 2026
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Location: India
Schools: BU'26 (A$$) ESSEC (A$) NTU'26 (D)
07 Jul 2025, 05:32
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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
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
Bunuel
